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class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目錄</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">收埋</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">文頭</div> </a> </li> <li id="toc-背景" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#背景"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>背景</span> </div> </a> <button aria-controls="toc-背景-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去背景細章節</span> </button> <ul id="toc-背景-sublist" class="vector-toc-list"> <li id="toc-科學方法" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#科學方法"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>科學方法</span> </div> </a> <ul id="toc-科學方法-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-推論問題" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#推論問題"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>推論問題</span> </div> </a> <ul id="toc-推論問題-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-定位" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#定位"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>定位</span> </div> </a> <button aria-controls="toc-定位-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去定位細章節</span> </button> <ul id="toc-定位-sublist" class="vector-toc-list"> <li id="toc-兩大範疇" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#兩大範疇"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>兩大範疇</span> </div> </a> <ul id="toc-兩大範疇-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-收集數據" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#收集數據"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>收集數據</span> </div> </a> <button aria-controls="toc-收集數據-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去收集數據細章節</span> </button> <ul id="toc-收集數據-sublist" class="vector-toc-list"> <li id="toc-變數" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#變數"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>變數</span> </div> </a> <ul id="toc-變數-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-抽樣" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#抽樣"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>抽樣</span> </div> </a> <ul id="toc-抽樣-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-量度" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#量度"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>量度</span> </div> </a> <ul id="toc-量度-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-敘述數據" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#敘述數據"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>敘述數據</span> </div> </a> <button aria-controls="toc-敘述數據-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去敘述數據細章節</span> </button> <ul id="toc-敘述數據-sublist" class="vector-toc-list"> <li id="toc-概率分佈" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#概率分佈"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>概率分佈</span> </div> </a> <ul id="toc-概率分佈-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-相關定實驗性質" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#相關定實驗性質"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>相關定實驗性質</span> </div> </a> <button aria-controls="toc-相關定實驗性質-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去相關定實驗性質細章節</span> </button> <ul id="toc-相關定實驗性質-sublist" class="vector-toc-list"> <li id="toc-相關性質" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#相關性質"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>相關性質</span> </div> </a> <ul id="toc-相關性質-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-實驗性質" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#實驗性質"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>實驗性質</span> </div> </a> <ul id="toc-實驗性質-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-假說檢定" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#假說檢定"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>假說檢定</span> </div> </a> <button aria-controls="toc-假說檢定-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>切換去假說檢定細章節</span> </button> <ul id="toc-假說檢定-sublist" class="vector-toc-list"> <li id="toc-估計量" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#估計量"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>估計量</span> </div> </a> <ul id="toc-估計量-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-信心區間" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#信心區間"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>信心區間</span> </div> </a> <ul id="toc-信心區間-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-虛無同備擇假說" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#虛無同備擇假說"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>虛無同備擇假說</span> </div> </a> <ul id="toc-虛無同備擇假說-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-顯著性" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#顯著性"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>顯著性</span> </div> </a> <ul id="toc-顯著性-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-比較平均值" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#比較平均值"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>比較平均值</span> </div> </a> <ul id="toc-比較平均值-sublist" class="vector-toc-list"> <li id="toc-t_測試流程" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#t_測試流程"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.1</span> <span>t 測試流程</span> </div> </a> <ul id="toc-t_測試流程-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-t_測試變種" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#t_測試變種"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5.2</span> <span>t 測試變種</span> </div> </a> <ul id="toc-t_測試變種-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-誤用" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#誤用"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>誤用</span> </div> </a> <ul id="toc-誤用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-簡史" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#簡史"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>簡史</span> </div> </a> <ul id="toc-簡史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-睇埋" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#睇埋"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>睇埋</span> </div> </a> <ul id="toc-睇埋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-註釋" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#註釋"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>註釋</span> </div> </a> <ul id="toc-註釋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-文獻" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#文獻"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>文獻</span> </div> </a> <ul id="toc-文獻-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#參考"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>參考</span> </div> </a> <ul id="toc-參考-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-拎" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#拎"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>拎</span> </div> </a> <ul id="toc-拎-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目錄" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="開/收內容一覽" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">開/收內容一覽</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">統計學</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="去睇另一種語文嘅文章。有154種語言版本。" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-154" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">154種語言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Statistiek" title="Statistiek – 南非荷蘭文" lang="af" hreflang="af" data-title="Statistiek" data-language-autonym="Afrikaans" data-language-local-name="南非荷蘭文" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Statistik" title="Statistik – 德文（瑞士）" lang="gsw" hreflang="gsw" data-title="Statistik" data-language-autonym="Alemannisch" data-language-local-name="德文（瑞士）" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8B%9D%E1%88%AD%E1%8B%9D%E1%88%AD_%E1%88%82%E1%88%B3%E1%89%A5_(%E1%8A%A5%E1%88%B5%E1%89%B3%E1%89%B2%E1%88%B5%E1%89%B2%E1%8A%AD%E1%88%B5)" title="የዝርዝር ሂሳብ (እስታቲስቲክስ) – 阿姆哈拉文" lang="am" hreflang="am" data-title="የዝርዝር ሂሳብ (እስታቲስቲክስ)" data-language-autonym="አማርኛ" data-language-local-name="阿姆哈拉文" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Estatistica" title="Estatistica – 阿拉貢文" lang="an" hreflang="an" data-title="Estatistica" data-language-autonym="Aragonés" data-language-local-name="阿拉貢文" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%AD%D8%B5%D8%A7%D8%A1" title="إحصاء – 阿拉伯文" lang="ar" hreflang="ar" data-title="إحصاء" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A7%B0%E0%A6%BF%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="পৰিসংখ্যা – 阿薩姆文" lang="as" hreflang="as" data-title="পৰিসংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="阿薩姆文" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – 阿斯圖里亞文" lang="ast" hreflang="ast" data-title="Estadística" data-language-autonym="Asturianu" data-language-local-name="阿斯圖里亞文" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Statistika" title="Statistika – 亞塞拜然文" lang="az" hreflang="az" data-title="Statistika" data-language-autonym="Azərbaycanca" data-language-local-name="亞塞拜然文" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A2%D9%85%D8%A7%D8%B1" title="آمار – South Azerbaijani" lang="azb" hreflang="azb" data-title="آمار" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 巴什客爾文" lang="ba" hreflang="ba" data-title="Статистика" data-language-autonym="Башҡортса" data-language-local-name="巴什客爾文" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Stat%C4%97st%C4%97ka" title="Statėstėka – 薩莫吉希亞文" lang="sgs" hreflang="sgs" data-title="Statėstėka" data-language-autonym="Žemaitėška" data-language-local-name="薩莫吉希亞文" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Estadistika" title="Estadistika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Estadistika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0" title="Статыстыка – 白俄羅斯文" lang="be" hreflang="be" data-title="Статыстыка" data-language-autonym="Беларуская" data-language-local-name="白俄羅斯文" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0" title="Статыстыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Статыстыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Statistik" title="Statistik – 貝塔維文" lang="bew" hreflang="bew" data-title="Statistik" data-language-autonym="Betawi" data-language-local-name="貝塔維文" class="interlanguage-link-target"><span>Betawi</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 保加利亞文" lang="bg" hreflang="bg" data-title="Статистика" data-language-autonym="Български" data-language-local-name="保加利亞文" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Statistikis" title="Statistikis – 比斯拉馬文" lang="bi" hreflang="bi" data-title="Statistikis" data-language-autonym="Bislama" data-language-local-name="比斯拉馬文" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A8" title="পরিসংখ্যান – 孟加拉文" lang="bn" hreflang="bn" data-title="পরিসংখ্যান" data-language-autonym="বাংলা" data-language-local-name="孟加拉文" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Stadegouriezh" title="Stadegouriezh – 布列塔尼文" lang="br" hreflang="br" data-title="Stadegouriezh" data-language-autonym="Brezhoneg" data-language-local-name="布列塔尼文" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Statistika" title="Statistika – 波士尼亞文" lang="bs" hreflang="bs" data-title="Statistika" data-language-autonym="Bosanski" data-language-local-name="波士尼亞文" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – 加泰羅尼亞文" lang="ca" hreflang="ca" data-title="Estadística" data-language-autonym="Català" data-language-local-name="加泰羅尼亞文" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Estadistica" title="Estadistica – Chavacano" lang="cbk" hreflang="cbk" data-title="Estadistica" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%D8%A7%D9%85%D8%A7%D8%B1" title="ئامار – 索拉尼庫爾德文" lang="ckb" hreflang="ckb" data-title="ئامار" data-language-autonym="کوردی" data-language-local-name="索拉尼庫爾德文" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Statistica" title="Statistica – 科西嘉文" lang="co" hreflang="co" data-title="Statistica" data-language-autonym="Corsu" data-language-local-name="科西嘉文" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Statistika" title="Statistika – 捷克文" lang="cs" hreflang="cs" data-title="Statistika" data-language-autonym="Čeština" data-language-local-name="捷克文" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 楚瓦什文" lang="cv" hreflang="cv" data-title="Статистика" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ystadegaeth" title="Ystadegaeth – 威爾斯文" lang="cy" hreflang="cy" data-title="Ystadegaeth" data-language-autonym="Cymraeg" data-language-local-name="威爾斯文" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Statistik" title="Statistik – 丹麥文" lang="da" hreflang="da" data-title="Statistik" data-language-autonym="Dansk" data-language-local-name="丹麥文" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Statistik" title="Statistik – 德文" lang="de" hreflang="de" data-title="Statistik" data-language-autonym="Deutsch" data-language-local-name="德文" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/%C4%B0statistik" title="İstatistik – Zazaki" lang="diq" hreflang="diq" data-title="İstatistik" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%8C%DE%A6%DE%8A%DE%A7%DE%90%DE%B0_%DE%80%DE%A8%DE%90%DE%A7%DE%84%DE%AA" title="ތަފާސް ހިސާބު – 迪維西文" lang="dv" hreflang="dv" data-title="ތަފާސް ހިސާބު" data-language-autonym="ދިވެހިބަސް" data-language-local-name="迪維西文" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%84%CE%B1%CF%84%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE" title="Στατιστική – 希臘文" lang="el" hreflang="el" data-title="Στατιστική" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Statistics" title="Statistics – 英文" lang="en" hreflang="en" data-title="Statistics" data-language-autonym="English" data-language-local-name="英文" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Statistiko" title="Statistiko – 世界文" lang="eo" hreflang="eo" data-title="Statistiko" data-language-autonym="Esperanto" data-language-local-name="世界文" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – 西班牙文" lang="es" hreflang="es" data-title="Estadística" data-language-autonym="Español" data-language-local-name="西班牙文" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Statistika" title="Statistika – 愛沙尼亞文" lang="et" hreflang="et" data-title="Statistika" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu badge-Q17437796 badge-featuredarticle mw-list-item" title="正文"><a href="https://eu.wikipedia.org/wiki/Estatistika" title="Estatistika – 巴斯克文" lang="eu" hreflang="eu" data-title="Estatistika" data-language-autonym="Euskara" data-language-local-name="巴斯克文" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Esta%C3%ADstica" title="Estaística – 埃斯特雷馬杜拉文" lang="ext" hreflang="ext" data-title="Estaística" data-language-autonym="Estremeñu" data-language-local-name="埃斯特雷馬杜拉文" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%85%D8%A7%D8%B1" title="آمار – 波斯文" lang="fa" hreflang="fa" data-title="آمار" data-language-autonym="فارسی" data-language-local-name="波斯文" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tilastotiede" title="Tilastotiede – 芬蘭文" lang="fi" hreflang="fi" data-title="Tilastotiede" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Statistiga" title="Statistiga – 佛羅文" lang="vro" hreflang="vro" data-title="Statistiga" data-language-autonym="Võro" data-language-local-name="佛羅文" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Hagfr%C3%B8%C3%B0i" title="Hagfrøði – 法羅文" lang="fo" hreflang="fo" data-title="Hagfrøði" data-language-autonym="Føroyskt" data-language-local-name="法羅文" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Statistique" title="Statistique – 法文" lang="fr" hreflang="fr" data-title="Statistique" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Statistik" title="Statistik – 北弗里西亞文" lang="frr" hreflang="frr" data-title="Statistik" data-language-autonym="Nordfriisk" data-language-local-name="北弗里西亞文" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Statistiche" title="Statistiche – 弗留利文" lang="fur" hreflang="fur" data-title="Statistiche" data-language-autonym="Furlan" data-language-local-name="弗留利文" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Statistyk" title="Statistyk – 西弗里西亞文" lang="fy" hreflang="fy" data-title="Statistyk" data-language-autonym="Frysk" data-language-local-name="西弗里西亞文" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Staitistic" title="Staitistic – 愛爾蘭文" lang="ga" hreflang="ga" data-title="Staitistic" data-language-autonym="Gaeilge" data-language-local-name="愛爾蘭文" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學 – 贛語" lang="gan" hreflang="gan" data-title="統計學" data-language-autonym="贛語" data-language-local-name="贛語" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Statistik" title="Statistik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Statistik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Staitistearachd" title="Staitistearachd – 蘇格蘭蓋爾文" lang="gd" hreflang="gd" data-title="Staitistearachd" data-language-autonym="Gàidhlig" data-language-local-name="蘇格蘭蓋爾文" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Estat%C3%ADstica" title="Estatística – 加里西亞文" lang="gl" hreflang="gl" data-title="Estatística" data-language-autonym="Galego" data-language-local-name="加里西亞文" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Papyrekokuaa" title="Papyrekokuaa – 瓜拉尼文" lang="gn" hreflang="gn" data-title="Papyrekokuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="瓜拉尼文" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Staydraa" title="Staydraa – 曼島文" lang="gv" hreflang="gv" data-title="Staydraa" data-language-autonym="Gaelg" data-language-local-name="曼島文" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Kumuhana" title="Kumuhana – 夏威夷文" lang="haw" hreflang="haw" data-title="Kumuhana" data-language-autonym="Hawaiʻi" data-language-local-name="夏威夷文" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94" title="סטטיסטיקה – 希伯來文" lang="he" hreflang="he" data-title="סטטיסטיקה" data-language-autonym="עברית" data-language-local-name="希伯來文" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BE%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BF%E0%A4%95%E0%A5%80" title="सांख्यिकी – 北印度文" lang="hi" hreflang="hi" data-title="सांख्यिकी" data-language-autonym="हिन्दी" data-language-local-name="北印度文" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Aankrraa" title="Aankrraa – 斐濟印地文" lang="hif" hreflang="hif" data-title="Aankrraa" data-language-autonym="Fiji Hindi" data-language-local-name="斐濟印地文" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Statistika" title="Statistika – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Statistika" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estatistik" title="Estatistik – 海地文" lang="ht" hreflang="ht" data-title="Estatistik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地文" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Statisztika" title="Statisztika – 匈牙利文" lang="hu" hreflang="hu" data-title="Statisztika" data-language-autonym="Magyar" data-language-local-name="匈牙利文" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8E%D5%AB%D5%B3%D5%A1%D5%AF%D5%A1%D5%A3%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Վիճակագրություն – 亞美尼亞文" lang="hy" hreflang="hy" data-title="Վիճակագրություն" data-language-autonym="Հայերեն" data-language-local-name="亞美尼亞文" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Statistica" title="Statistica – 國際文" lang="ia" hreflang="ia" data-title="Statistica" data-language-autonym="Interlingua" data-language-local-name="國際文" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Statistik" title="Statistik – 伊班文" lang="iba" hreflang="iba" data-title="Statistik" data-language-autonym="Jaku Iban" data-language-local-name="伊班文" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Statistika" title="Statistika – 印尼文" lang="id" hreflang="id" data-title="Statistika" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Statistiko" title="Statistiko – 伊多文" lang="io" hreflang="io" data-title="Statistiko" data-language-autonym="Ido" data-language-local-name="伊多文" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/T%C3%B6lfr%C3%A6%C3%B0i" title="Tölfræði – 冰島文" lang="is" hreflang="is" data-title="Tölfræði" data-language-autonym="Íslenska" data-language-local-name="冰島文" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Statistica" title="Statistica – 義大利文" lang="it" hreflang="it" data-title="Statistica" data-language-autonym="Italiano" data-language-local-name="義大利文" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-iu mw-list-item"><a href="https://iu.wikipedia.org/wiki/%E1%91%AD%E1%93%AF%E1%91%A6%E1%93%AF%E1%93%AF%E1%96%95%E1%96%91%E1%95%90%E1%93%97%E1%92%8B%E1%91%A6_%E1%90%B9%E1%93%AF%E1%94%85%E1%93%B1%E1%91%8E%E1%94%85%E1%93%B4%E1%91%A6" title="ᑭᓯᑦᓯᓯᖕᖑᕐᓗᒋᑦ ᐹᓯᔅᓱᑎᔅᓴᑦ – 因紐特文" lang="iu" hreflang="iu" data-title="ᑭᓯᑦᓯᓯᖕᖑᕐᓗᒋᑦ ᐹᓯᔅᓱᑎᔅᓴᑦ" data-language-autonym="ᐃᓄᒃᑎᑐᑦ / inuktitut" data-language-local-name="因紐特文" class="interlanguage-link-target"><span>ᐃᓄᒃᑎᑐᑦ / inuktitut</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E5%AD%A6" title="統計学 – 日文" lang="ja" hreflang="ja" data-title="統計学" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Statistix" title="Statistix – 牙買加克裏奧爾英文" lang="jam" hreflang="jam" data-title="Statistix" data-language-autonym="Patois" data-language-local-name="牙買加克裏奧爾英文" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Statistika" title="Statistika – 爪哇文" lang="jv" hreflang="jv" data-title="Statistika" data-language-autonym="Jawa" data-language-local-name="爪哇文" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%90%E1%83%A2%E1%83%98%E1%83%A1%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="სტატისტიკა – 喬治亞文" lang="ka" hreflang="ka" data-title="სტატისტიკა" data-language-autonym="ქართული" data-language-local-name="喬治亞文" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Addadan_(tussna)" title="Addadan (tussna) – 卡比爾文" lang="kab" hreflang="kab" data-title="Addadan (tussna)" data-language-autonym="Taqbaylit" data-language-local-name="卡比爾文" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Sama%C9%A3_%C3%B1%CA%8A%CA%8A_t%C9%A9l%CA%8A%CA%8A" title="Samaɣ ñʊʊ tɩlʊʊ – Kabiye" lang="kbp" hreflang="kbp" data-title="Samaɣ ñʊʊ tɩlʊʊ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 哈薩克文" lang="kk" hreflang="kk" data-title="Статистика" data-language-autonym="Қазақша" data-language-local-name="哈薩克文" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ – 坎那達文" lang="kn" hreflang="kn" data-title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="坎那達文" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%86%B5%EA%B3%84%ED%95%99" title="통계학 – 韓文" lang="ko" hreflang="ko" data-title="통계학" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Amar" title="Amar – 庫爾德文" lang="ku" hreflang="ku" data-title="Amar" data-language-autonym="Kurdî" data-language-local-name="庫爾德文" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Statystek" title="Statystek – 康瓦耳文" lang="kw" hreflang="kw" data-title="Statystek" data-language-autonym="Kernowek" data-language-local-name="康瓦耳文" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Statistica" title="Statistica – 拉丁文" lang="la" hreflang="la" data-title="Statistica" data-language-autonym="Latina" data-language-local-name="拉丁文" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lad mw-list-item"><a href="https://lad.wikipedia.org/wiki/Estadistika" title="Estadistika – 拉迪諾文" lang="lad" hreflang="lad" data-title="Estadistika" data-language-autonym="Ladino" data-language-local-name="拉迪諾文" class="interlanguage-link-target"><span>Ladino</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Statistik" title="Statistik – 盧森堡文" lang="lb" hreflang="lb" data-title="Statistik" data-language-autonym="Lëtzebuergesch" data-language-local-name="盧森堡文" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Statistica" title="Statistica – 新共同語言" lang="lfn" hreflang="lfn" data-title="Statistica" data-language-autonym="Lingua Franca Nova" data-language-local-name="新共同語言" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Sjtatistiek" title="Sjtatistiek – 林堡文" lang="li" hreflang="li" data-title="Sjtatistiek" data-language-autonym="Limburgs" data-language-local-name="林堡文" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Statistega" title="Statistega – 利古里亞文" lang="lij" hreflang="lij" data-title="Statistega" data-language-autonym="Ligure" data-language-local-name="利古里亞文" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Statistega" title="Statistega – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Statistega" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%AA%E0%BA%B0%E0%BA%96%E0%BA%B4%E0%BA%95%E0%BA%B4%E0%BA%AA%E0%BA%B2%E0%BA%94" title="ສະຖິຕິສາດ – 寮文" lang="lo" hreflang="lo" data-title="ສະຖິຕິສາດ" data-language-autonym="ລາວ" data-language-local-name="寮文" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Statistika_(mokslas)" title="Statistika (mokslas) – 立陶宛文" lang="lt" hreflang="lt" data-title="Statistika (mokslas)" data-language-autonym="Lietuvių" data-language-local-name="立陶宛文" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Statistika" title="Statistika – 拉脫維亞文" lang="lv" hreflang="lv" data-title="Statistika" data-language-autonym="Latviešu" data-language-local-name="拉脫維亞文" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Statistika" title="Statistika – 馬都拉文" lang="mad" hreflang="mad" data-title="Statistika" data-language-autonym="Madhurâ" data-language-local-name="馬都拉文" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Statistika" title="Statistika – 馬拉加什文" lang="mg" hreflang="mg" data-title="Statistika" data-language-autonym="Malagasy" data-language-local-name="馬拉加什文" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 馬其頓文" lang="mk" hreflang="mk" data-title="Статистика" data-language-autonym="Македонски" data-language-local-name="馬其頓文" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BF%E0%B4%A4%E0%B4%BF%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="സ്ഥിതിഗണിതം – 馬來亞拉姆文" lang="ml" hreflang="ml" data-title="സ്ഥിതിഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="馬來亞拉姆文" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="संख्याशास्त्र – 馬拉地文" lang="mr" hreflang="mr" data-title="संख्याशास्त्र" data-language-autonym="मराठी" data-language-local-name="馬拉地文" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Perangkaan" title="Perangkaan – 馬來文" lang="ms" hreflang="ms" data-title="Perangkaan" data-language-autonym="Bahasa Melayu" data-language-local-name="馬來文" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Stat%C3%ADstica" title="Statística – 米蘭德斯文" lang="mwl" hreflang="mwl" data-title="Statística" data-language-autonym="Mirandés" data-language-local-name="米蘭德斯文" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%AC%E1%80%9B%E1%80%84%E1%80%BA%E1%80%B8%E1%80%A1%E1%80%84%E1%80%BA%E1%80%B8_%E1%80%95%E1%80%8A%E1%80%AC" title="စာရင်းအင်း ပညာ – 緬甸文" lang="my" hreflang="my" data-title="စာရင်းအင်း ပညာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="緬甸文" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A4%A5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%99%E0%A5%8D%E0%A4%95" title="तथ्याङ्क – 尼泊爾文" lang="ne" hreflang="ne" data-title="तथ्याङ्क" data-language-autonym="नेपाली" data-language-local-name="尼泊爾文" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A4%E0%A4%A5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%99%E0%A5%8D%E0%A4%95" title="तथ्याङ्क – 尼瓦爾文" lang="new" hreflang="new" data-title="तथ्याङ्क" data-language-autonym="नेपाल भाषा" data-language-local-name="尼瓦爾文" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Statistiek" title="Statistiek – 荷蘭文" lang="nl" hreflang="nl" data-title="Statistiek" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Statistikk" title="Statistikk – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Statistikk" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Statistikk" title="Statistikk – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Statistikk" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Estatistica" title="Estatistica – 奧克西坦文" lang="oc" hreflang="oc" data-title="Estatistica" data-language-autonym="Occitan" data-language-local-name="奧克西坦文" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Xiinannoo" title="Xiinannoo – 奧羅莫文" lang="om" hreflang="om" data-title="Xiinannoo" data-language-autonym="Oromoo" data-language-local-name="奧羅莫文" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AA%E0%AC%B0%E0%AC%BF%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE%E0%AC%A8" title="ପରିସଂଖ୍ୟାନ – 歐利亞文" lang="or" hreflang="or" data-title="ପରିସଂଖ୍ୟାନ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="歐利亞文" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A9%B0%E0%A8%95%E0%A9%9C%E0%A8%BE_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਅੰਕੜਾ ਵਿਗਿਆਨ – 旁遮普文" lang="pa" hreflang="pa" data-title="ਅੰਕੜਾ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普文" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Stetistiks" title="Stetistiks – Norfuk / Pitkern" lang="pih" hreflang="pih" data-title="Stetistiks" data-language-autonym="Norfuk / Pitkern" data-language-local-name="Norfuk / Pitkern" class="interlanguage-link-target"><span>Norfuk / Pitkern</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Statystyka" title="Statystyka – 波蘭文" lang="pl" hreflang="pl" data-title="Statystyka" data-language-autonym="Polski" data-language-local-name="波蘭文" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Stat%C3%ACstica" title="Statìstica – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Statìstica" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%DB%8C%D8%A7%D8%AA" title="شماریات – Western Punjabi" lang="pnb" hreflang="pnb" data-title="شماریات" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B4%D9%85%DB%8C%D8%B1%D9%86%D9%87" title="سرشمیرنه – 普什圖文" lang="ps" hreflang="ps" data-title="سرشمیرنه" data-language-autonym="پښتو" data-language-local-name="普什圖文" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Estat%C3%ADstica" title="Estatística – 葡萄牙文" lang="pt" hreflang="pt" data-title="Estatística" data-language-autonym="Português" data-language-local-name="葡萄牙文" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Khipukamay" title="Khipukamay – 蓋楚瓦文" lang="qu" hreflang="qu" data-title="Khipukamay" data-language-autonym="Runa Simi" data-language-local-name="蓋楚瓦文" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Statistic%C4%83" title="Statistică – 羅馬尼亞文" lang="ro" hreflang="ro" data-title="Statistică" data-language-autonym="Română" data-language-local-name="羅馬尼亞文" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 俄文" lang="ru" hreflang="ru" data-title="Статистика" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A8%D1%82%D0%B0%D1%82%D1%96%D1%81%D1%82%D1%96%D0%BA%D0%B0" title="Штатістіка – 盧森尼亞文" lang="rue" hreflang="rue" data-title="Штатістіка" data-language-autonym="Русиньскый" data-language-local-name="盧森尼亞文" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Stat%C3%ACstica" title="Statìstica – 西西里文" lang="scn" hreflang="scn" data-title="Statìstica" data-language-autonym="Sicilianu" data-language-local-name="西西里文" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Stateestics" title="Stateestics – 蘇格蘭文" lang="sco" hreflang="sco" data-title="Stateestics" data-language-autonym="Scots" data-language-local-name="蘇格蘭文" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%8A%D8%A7%D8%AA" title="شماريات – 信德文" lang="sd" hreflang="sd" data-title="شماريات" data-language-autonym="سنڌي" data-language-local-name="信德文" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Statistika" title="Statistika – 塞爾維亞克羅埃西亞文" lang="sh" hreflang="sh" data-title="Statistika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞爾維亞克羅埃西亞文" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%B1%E0%B6%BA" title="සංඛ්‍යානය – 僧伽羅文" lang="si" hreflang="si" data-title="සංඛ්‍යානය" data-language-autonym="සිංහල" data-language-local-name="僧伽羅文" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Statistics" title="Statistics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Statistics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C5%A0tatistika" title="Štatistika – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Štatistika" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Statistika" title="Statistika – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Statistika" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Statistika" title="Statistika – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Statistika" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Статистика" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Statistik" title="Statistik – 沙特菲士蘭文" lang="stq" hreflang="stq" data-title="Statistik" data-language-autonym="Seeltersk" data-language-local-name="沙特菲士蘭文" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Statistika" title="Statistika – 巽他文" lang="su" hreflang="su" data-title="Statistika" data-language-autonym="Sunda" data-language-local-name="巽他文" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Statistik" title="Statistik – 瑞典文" lang="sv" hreflang="sv" data-title="Statistik" data-language-autonym="Svenska" data-language-local-name="瑞典文" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Takwimu" title="Takwimu – 史瓦希里文" lang="sw" hreflang="sw" data-title="Takwimu" data-language-autonym="Kiswahili" data-language-local-name="史瓦希里文" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%81%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="புள்ளியியல் – 坦米爾文" lang="ta" hreflang="ta" data-title="புள்ளியியல்" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ – 圖盧文" lang="tcy" hreflang="tcy" data-title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ" data-language-autonym="ತುಳು" data-language-local-name="圖盧文" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-tet mw-list-item"><a href="https://tet.wikipedia.org/wiki/Estat%C3%ADstika" title="Estatístika – 泰頓文" lang="tet" hreflang="tet" data-title="Estatístika" data-language-autonym="Tetun" data-language-local-name="泰頓文" class="interlanguage-link-target"><span>Tetun</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9E%D0%BC%D0%BE%D1%80" title="Омор – 塔吉克文" lang="tg" hreflang="tg" data-title="Омор" data-language-autonym="Тоҷикӣ" data-language-local-name="塔吉克文" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%96%E0%B8%B4%E0%B8%95%E0%B8%B4%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="สถิติศาสตร์ – 泰文" lang="th" hreflang="th" data-title="สถิติศาสตร์" data-language-autonym="ไทย" data-language-local-name="泰文" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Statistika" title="Statistika – 土庫曼文" lang="tk" hreflang="tk" data-title="Statistika" data-language-autonym="Türkmençe" data-language-local-name="土庫曼文" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Estadistika" title="Estadistika – 塔加路族文" lang="tl" hreflang="tl" data-title="Estadistika" data-language-autonym="Tagalog" data-language-local-name="塔加路族文" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0statistik" title="İstatistik – 土耳其文" lang="tr" hreflang="tr" data-title="İstatistik" data-language-autonym="Türkçe" data-language-local-name="土耳其文" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 韃靼文" lang="tt" hreflang="tt" data-title="Статистика" data-language-autonym="Татарча / tatarça" data-language-local-name="韃靼文" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – 烏克蘭文" lang="uk" hreflang="uk" data-title="Статистика" data-language-autonym="Українська" data-language-local-name="烏克蘭文" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%DB%8C%D8%A7%D8%AA" title="شماریات – 烏都文" lang="ur" hreflang="ur" data-title="شماریات" data-language-autonym="اردو" data-language-local-name="烏都文" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Statistika" title="Statistika – 烏茲別克文" lang="uz" hreflang="uz" data-title="Statistika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="烏茲別克文" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Stat%C3%ACstega" title="Statìstega – 威尼斯文" lang="vec" hreflang="vec" data-title="Statìstega" data-language-autonym="Vèneto" data-language-local-name="威尼斯文" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Statistik" title="Statistik – 維普森文" lang="vep" hreflang="vep" data-title="Statistik" data-language-autonym="Vepsän kel’" data-language-local-name="維普森文" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AA" title="Thống kê – 越南文" lang="vi" hreflang="vi" data-title="Thống kê" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Estadistik%C3%A1" title="Estadistiká – 瓦瑞文" lang="war" hreflang="war" data-title="Estadistiká" data-language-autonym="Winaray" data-language-local-name="瓦瑞文" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学 – 吳語" lang="wuu" hreflang="wuu" data-title="统计学" data-language-autonym="吴语" data-language-local-name="吳語" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%90%E1%83%A2%E1%83%98%E1%83%A1%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="სტატისტიკა – 明格列爾文" lang="xmf" hreflang="xmf" data-title="სტატისტიკა" data-language-autonym="მარგალური" data-language-local-name="明格列爾文" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A1%D7%98%D7%90%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7" title="סטאטיסטיק – 意第緒文" lang="yi" hreflang="yi" data-title="סטאטיסטיק" data-language-autonym="ייִדיש" data-language-local-name="意第緒文" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%8Csir%C3%B2_Statistiki" title="Ìsirò Statistiki – 約魯巴文" lang="yo" hreflang="yo" data-title="Ìsirò Statistiki" data-language-autonym="Yorùbá" data-language-local-name="約魯巴文" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%99%E2%B5%8F%E2%B5%8E%E2%B4%BD%E2%B5%9C%E2%B4%B0" title="ⵜⴰⵙⵏⵎⴽⵜⴰ – 標準摩洛哥塔馬塞特文" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵙⵏⵎⴽⵜⴰ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="標準摩洛哥塔馬塞特文" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学 – 中文" lang="zh" hreflang="zh" data-title="统计学" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Th%C3%B3ng-k%C3%A8-ha%CC%8Dk" title="Thóng-kè-ha̍k – 閩南語" lang="nan" hreflang="nan" data-title="Thóng-kè-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="閩南語" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Izibalomininingo" title="Izibalomininingo – 祖魯文" lang="zu" hreflang="zu" data-title="Izibalomininingo" data-language-autonym="IsiZulu" data-language-local-name="祖魯文" class="interlanguage-link-target"><span>IsiZulu</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12483#sitelinks-wikipedia" title="改跨語言拎" class="wbc-editpage">改拎</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="空間名"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="睇吓內容頁[c]" accesskey="c"><span>文章</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E7%B5%B1%E8%A8%88%E5%AD%B8" rel="discussion" title="關於內容頁嘅討論[t]" accesskey="t"><span>討論</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="改語言變體" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">粵語</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="外觀"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8"><span>閱</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit" title="改呢版嘅代碼[e]" accesskey="e"><span>改</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=history" title="呢一頁之前嘅修訂[h]" accesskey="h"><span>睇返紀錄</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="頁面工具"> <div id="vector-page-tools-dropdown" 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data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">架撐</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">收埋</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="多啲選項" > <div class="vector-menu-heading"> 動作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8"><span>閱</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit" title="改呢版嘅代碼[e]" accesskey="e"><span>改</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=history"><span>睇返紀錄</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 基本 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%82%8A%E5%BA%A6%E9%8F%88%E5%8E%BB%E5%91%A2%E7%89%88/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="列出所有連接過嚟呢度嘅頁面[j]" accesskey="j"><span>有乜連過嚟</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E5%A4%96%E9%8F%88%E4%BF%AE%E6%94%B9/%E7%B5%B1%E8%A8%88%E5%AD%B8" rel="nofollow" title="由呢版連出去嘅版嘅最近修改[k]" accesskey="k"><span>連結頁嘅更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E8%BC%89" title="上載檔案[u]" accesskey="u"><span>上載檔案</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E5%B0%88%E9%96%80%E7%89%88" title="所有專門版一覽[q]" accesskey="q"><span>專門版</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&oldid=2067890" title="呢版呢個修訂嘅永久網址"><span>固定連結</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=info" title="多啲同呢版有拏褦嘅資料"><span>此版明細</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8&page=%E7%B5%B1%E8%A8%88%E5%AD%B8&id=2067890&wpFormIdentifier=titleform" title="點樣引用呢頁嘅資訊"><span>引用呢篇文</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fzh-yue.wikipedia.org%2Fwiki%2F%25E7%25B5%25B1%25E8%25A8%2588%25E5%25AD%25B8"><span>攞短網址</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh-yue.wikipedia.org%2Fwiki%2F%25E7%25B5%25B1%25E8%25A8%2588%25E5%25AD%25B8"><span>下載QR code</span></a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/匯出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=show-download-screen"><span>下載PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="呢一版印得嘅版本[p]" accesskey="p"><span>印得嘅版本</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 第啲維基項目 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Statistics" hreflang="en"><span>維基同享</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12483" title="連到接住資料儲存庫嘅項目[g]" accesskey="g"><span>維基數據項</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="頁面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="閱讀設定"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">閱讀設定</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">收埋</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-featured-star" class="mw-indicator"><div class="mw-parser-output"><span typeof="mw:File"><a href="/wiki/Wikipedia:%E6%AD%A3%E6%96%87" title="呢篇係一篇正文。撳呢度睇吓更多嘅資料。"><img alt="呢篇係一篇正文。撳呢度睇吓更多嘅資料。" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/20px-Cscr-featured.svg.png" decoding="async" width="20" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/30px-Cscr-featured.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Cscr-featured.svg/40px-Cscr-featured.svg.png 2x" data-file-width="466" data-file-height="443" /></a></span></div></div> </div> <div id="siteSub" class="noprint">出自維基百科，自由嘅百科全書</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="yue" dir="ltr"><p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1488945/mw-parser-output/.tmulti">.mw-parser-output .tmulti .thumbinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}</style><div class="thumb tmulti tright"><div class="thumbinner" style="width:334px;max-width:334px"><div class="trow"><div class="tsingle" style="width:332px;max-width:332px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Standard_Normal_Distribution.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/330px-Standard_Normal_Distribution.png" decoding="async" width="330" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/495px-Standard_Normal_Distribution.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/660px-Standard_Normal_Distribution.png 2x" data-file-width="5986" data-file-height="3700" /></a></span></div><div class="thumbcaption">統計學成日會用嘅<a href="/wiki/%E5%B8%B8%E6%85%8B%E5%88%86%E4%BD%88" title="常態分佈">常態分佈</a>；幅圖 <a href="/wiki/X_%E8%BB%B8" class="mw-redirect" title="X 軸">X 軸</a>表示<a href="/wiki/%E8%AE%8A%E6%95%B8_(%E7%A7%91%E7%A0%94)" title="變數 (科研)">變數</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 嘅數值，而 <a href="/wiki/Y_%E8%BB%B8" class="mw-redirect" title="Y 軸">Y 軸</a>表示嗰個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 值喺<a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>入面出現嘅<a href="/wiki/%E6%A9%9F%E7%8E%87" class="mw-redirect" title="機率">機率</a>。</div></div></div><div class="trow"><div class="tsingle" style="width:332px;max-width:332px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Linear_regression.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Linear_regression.svg/330px-Linear_regression.svg.png" decoding="async" width="330" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Linear_regression.svg/495px-Linear_regression.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Linear_regression.svg/660px-Linear_regression.svg.png 2x" data-file-width="438" data-file-height="289" /></a></span></div><div class="thumbcaption">藍色點代表<a href="/wiki/%E6%95%B8%E6%93%9A%E5%BA%AB" title="數據庫">數據庫</a>當中嘅個體，每個個體都喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> 上有個值，條紅色線係一個<a href="/wiki/%E8%BF%B4%E6%AD%B8%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="迴歸模型">迴歸模型</a>，用條線同已知嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 值嚟預測 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> 嘅值會俾到大致上啱，但唔完全準嘅預測。</div></div></div></div></div> <p><b>統計學</b>（<a href="/wiki/Wikipedia:%E7%B2%B5%E6%96%87%E6%8B%BC%E9%9F%B3" title="Wikipedia:粵文拼音">粵拼</a>：<span class="plainlinks" style="display:inline-block"><a rel="nofollow" class="external text" href="http://yue.forvo.com/word/yue/統計學/#yue"><span>tung<span class="Jpingtone">2</span> gai<span class="Jpingtone">3</span> hok<span class="Jpingtone">6</span></span></a></span>；<a href="/wiki/%E8%8B%B1%E6%96%87" title="英文">英文</a>：<span lang="en"><b>statistics</b></span>）係<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>嘅一個子領域<sup id="cite_ref-hays_1-0" class="reference"><a href="#cite_note-hays-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>，專門研究點樣喺各個<a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>領域當中搜集、分析、演繹同埋呈現<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a>。喺用統計方法嚟研究啲乜嗰陣，個科學家會跟<a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%B9%E6%B3%95" title="科學方法">以下噉嘅步驟</a>：首先講明佢研究緊乜嘢<a href="/wiki/%E8%AE%8A%E6%95%B8_(%E7%A7%91%E7%A0%94)" title="變數 (科研)">變數</a>；跟手就搵個特定嘅<a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a>（指一柞有某啲共通點所以俾人擺埋一齊研究嘅個體）嚟研究；由呢個總體嗰度<a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽個</a><a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>出嚟<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>；喺個樣本度<a href="/wiki/%E6%94%B6%E9%9B%86%E6%95%B8%E6%93%9A" title="收集數據">收集數據</a>，睇吓個樣本入面每個個體喺啲變數度嘅數值係幾多<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>；用某啲<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%88%86%E6%9E%90" class="mw-redirect" title="統計分析">統計分析</a>方法嚟去搵出柞變數之間有乜嘢關係<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。 </p><p>例如有個<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8%E5%AE%B6" title="生物學家">生物學家</a>想研究吓<a href="/wiki/%E7%8B%BC" title="狼">狼</a>嘅<a href="/wiki/%E7%8D%B5%E9%A3%9F" class="mw-redirect" title="獵食">獵食</a><a href="/wiki/%E8%A1%8C%E7%82%BA" title="行為">行為</a>同地方嘅<a href="/wiki/%E6%B0%A3%E5%80%99" title="氣候">氣候</a>之間有冇拏褦。喺呢份研究入面，佢研究緊嘅變數包含咗喺「啲狼嘅獵食行為」（<a href="/wiki/%E6%87%89%E8%AE%8A%E6%95%B8" class="mw-redirect" title="應變數">應變數</a>）同「啲狼身處嘅地方嘅氣候」（<a href="/wiki/%E8%87%AA%E8%AE%8A%E6%95%B8" class="mw-redirect" title="自變數">自變數</a>）；佢會將成個世界嘅狼擺埋一齊研究（<b>全世界嘅狼</b>就係研究嘅總體）；但世上咁多隻狼，要攞嗮佢哋嚟<a href="/wiki/%E8%A7%80%E5%AF%9F" title="觀察">觀察</a>嘥時間得滯，所以佢就用<a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%8A%BD%E6%A8%A3" title="隨機抽樣">隨機抽樣</a>－<a href="/wiki/%E9%9A%A8%E6%A9%9F" title="隨機">隨機</a>噉由全世界嘅狼嗰度抽（例如）100 隻出嚟研究；跟住佢就要向個樣本收集數據，用各種嘅方法去<a href="/wiki/%E9%87%8F%E5%BA%A6" title="量度">量度</a>樣本入面每一隻狼（一隻狼為止一個個體）嘅獵食行為－好似係隻狼每日用幾多個<a href="/wiki/%E9%90%98%E9%A0%AD" title="鐘頭">鐘頭</a>獵食、食咗幾多<a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">公斤</a>嘅肉呀噉－同埋佢身處地方嘅氣候－好似係嗰個地區<a href="/wiki/%E8%90%BD%E9%9B%A8" class="mw-redirect" title="落雨">落雨</a><a href="/wiki/%E9%99%8D%E6%B0%B4" title="降水">落得有幾密</a>同平均<a href="/wiki/%E6%B0%A3%E6%BA%AB" class="mw-redirect" title="氣溫">氣溫</a>等等；攞完數據之後，研究者就要用各種統計分析嚟計吓柞變數之間有乜拏褦。 </p><p>同樣嘅做法喺<a href="/wiki/%E7%89%A9%E7%90%86%E7%A7%91%E5%AD%B8" title="物理科學">物理科學</a>同<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>嗰度都會用到<sup id="cite_ref-hays_1-1" class="reference"><a href="#cite_note-hays-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。因為統計學廣泛嘅應用價值，統計學知識經已成為咗現代科學研究上走唔甩嘅一個部份，<a href="/wiki/%E5%A4%A7%E5%AD%B8" title="大學">大學</a>科學學科嘅<a href="/wiki/%E6%9C%AC%E7%A7%91" class="mw-redirect" title="本科">本科</a>課程基本上冚唪唥都會教統計學嘅嘢<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="背景"><span id=".E8.83.8C.E6.99.AF"></span>背景</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=1" title="編輯小節: 背景"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Black_Swan_at_Martin_Mere.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Black_Swan_at_Martin_Mere.JPG/270px-Black_Swan_at_Martin_Mere.JPG" decoding="async" width="270" height="360" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Black_Swan_at_Martin_Mere.JPG/405px-Black_Swan_at_Martin_Mere.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Black_Swan_at_Martin_Mere.JPG/540px-Black_Swan_at_Martin_Mere.JPG 2x" data-file-width="2193" data-file-height="2924" /></a><figcaption><a href="/wiki/%E9%BB%91%E5%A4%A9%E9%B5%9D" title="黑天鵝">黑天鵝</a>成日俾人攞嚟做科學方法思路嘅例子－「就算之前見過嘅天鵝都係白色，都唔表示跟住見到嘅天鵝都 100% 會係白色」。</figcaption></figure> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>同<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a></div> <div class="mw-heading mw-heading3"><h3 id="科學方法"><span id=".E7.A7.91.E5.AD.B8.E6.96.B9.E6.B3.95"></span>科學方法</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=2" title="編輯小節: 科學方法"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%B9%E6%B3%95" title="科學方法">科學方法</a></div> <p><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%93%B2%E5%AD%B8" title="科學哲學">科學哲學</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>e 1<span class="cite-bracket">]</span></a></sup>係<a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>嘅基礎，簡單講就係指<a href="/wiki/%E7%A7%91%E5%AD%B8%E5%AE%B6" title="科學家">科學家</a>對於「科學係乜同埋應該點搞」嘅睇法。科學哲學嘅基礎係<a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%B9%E6%B3%95" title="科學方法">科學方法</a>，意思係話科學研究係用以下嘅步驟嚟理解<a href="/wiki/%E5%AE%87%E5%AE%99" title="宇宙">宇宙</a>當中<a href="/wiki/%E5%AF%A6%E8%AD%89" title="實證">可觀察</a>嘅事物，嘗試預測未來嘅現象<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>： </p> <ol><li>根據手上已知係真嘅<a href="/wiki/%E4%BA%8B%E5%AF%A6" title="事實">事實</a>，諗一啲<a href="/wiki/%E7%A7%91%E5%AD%B8%E7%90%86%E8%AB%96" title="科學理論">理論</a>出嚟－「基於我哋經已觀察到嘅呢啲現象，我推測啲現象背後嘅<a href="/wiki/%E7%89%A9%E7%90%86%E6%B3%95%E5%89%87" class="mw-redirect" title="物理法則">物理法則</a>係噉噉噉，令<a href="/wiki/%E7%89%A9%E8%B3%AA" title="物質">物質</a><a href="/wiki/%E8%83%BD%E9%87%8F" title="能量">能量</a>有呢啲行為」，呢啲理論最理想係用<a href="/wiki/%E6%95%B8%E5%AD%B8%E6%A8%A1%E5%9E%8B" title="數學模型">數學模型</a>嘅方式表達嘅；</li> <li>跟手就靠<a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a>嘅思考，去諗吓呢柞理論會做點樣嘅<b>預測</b>－「如果我提倡嘅呢個理論係真確嘅，理應會...」；</li> <li>然後就做<a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗</a>同<a href="/wiki/%E8%A7%80%E5%AF%9F" title="觀察">觀察</a>嚟攞<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a>，驗證吓個理論嘅預測係咪真確－「如果我呢個理論係真確，呢個實驗理應會得出某個某個結果，而個實際嘅實驗結果係...」；</li> <li>如果數據顯示，個理論係做唔到準確嘅預測嘅話，就要一係根據攞到嘅數據睇吓個理論要點改先可以令佢做到準確啲嘅預測，一係就要諗新理論取代舊理論<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>。</li></ol> <p>上述嘅過程會係噉重複，直至手上嘅理論做到完全準確嘅預測為止－於是科學就有持續嘅發展，做到愈嚟愈準嘅預測。到咗現代，科學上經已有龐大嘅理論體系，按所研究嘅現象分做<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8" title="物理學">物理學</a>（用科學方法研究<a href="/wiki/%E7%89%A9%E7%90%86%E5%AE%9A%E5%BE%8B" title="物理定律">宇宙基本定律</a>）、<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8" title="生物學">生物學</a>（用科學方法研究<a href="/wiki/%E7%94%9F%E5%91%BD" title="生命">生命</a>）、<a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%B8" title="心理學">心理學</a>（用科學方法研究人嘅<a href="/wiki/%E8%A1%8C%E7%82%BA" title="行為">行為</a>）同<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>（用科學方法研究<a href="/wiki/%E7%A4%BE%E6%9C%83" title="社會">社會</a>）等嘅多個領域，每個領域都有諗出用嚟描述同預測自己所研究嘅現象嘅理論，而一啲重要嘅理論（例如係<a href="/wiki/%E9%80%B2%E5%8C%96%E8%AB%96" class="mw-redirect" title="進化論">進化論</a>）往往俾科學家用實驗同觀察驗證過上百次－非常經得起考驗，所以學界一般認為呢啲理論係<b>有返咁上下正確嘅模型</b><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>e 2<span class="cite-bracket">]</span></a></sup>－能夠充分噉描述現實。除此之外，科學家仲會不斷搵新嘅現象研究，睇吓呢啲理論能唔能夠解釋新現象，又或者使唔使諗新嘅理論，令科學知識得以持續噉發展<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="推論問題"><span id=".E6.8E.A8.E8.AB.96.E5.95.8F.E9.A1.8C"></span>推論問題</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=3" title="編輯小節: 推論問題"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E6%AD%B8%E7%B4%8D" title="歸納">歸納</a>、<a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A" title="不確定">不確定</a>同<a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></div> <p><a href="/wiki/%E6%AD%B8%E7%B4%8D" title="歸納">歸納</a><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>e 3<span class="cite-bracket">]</span></a></sup>係科學家嘅基本諗嘢方法，指由啲個別嘅事例嗰度去推斷出一啲普遍原理。响歸納性質嘅<a href="/wiki/%E8%AB%96%E8%AD%89" title="論證">論證</a>入面，前提真確冇辦法保證到結論真確，只係可以靠住大量嘅事例嚟提升個論證嘅強度，好似係以下呢個論證噉<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>： </p> <dl><dd><b>前提</b>：我之前見過嘅<a href="/wiki/%E5%A4%A9%E9%B5%9D" title="天鵝">天鵝</a>都係白色嘅：</dd> <dd><b>結論</b>：呢個世界上所有天鵝都係白色嘅。</dd></dl> <p>呢個係一個典型嘅歸納論證：就算個<a href="/wiki/%E5%89%8D%E6%8F%90" class="mw-redirect" title="前提">前提</a>係真，都保證唔到個<a href="/wiki/%E7%B5%90%E8%AB%96" title="結論">結論</a>係真－前提入面嗰個「我」並冇見過嗮世界上所有嘅天鵝，而事實係世界上有<a href="/wiki/%E9%BB%91%E5%A4%A9%E9%B5%9D" title="黑天鵝">黑天鵝</a>，個觀察者會噉諗只不過係因為佢咁啱未見過黑天鵝；如果個觀察者想佢個論證強啲嘅話，佢就一啲要去見多啲天鵝：如果佢睇勻嗮全<a href="/wiki/%E6%AD%90%E6%B4%B2" title="歐洲">歐洲</a>嘅天鵝，呢個論證嘅說服力會比較強；相反，如果佢淨係見過<a href="/wiki/%E8%8B%B1%E5%9C%8B" title="英國">英國</a>嘅天鵝，噉呢個論證嘅說服力會渣好多。科學家都係跟住呢種諗嘢方式搞科學：喺驗證「<a href="/wiki/%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B" title="萬有引力">萬有引力</a>係真嘅」呢句說話嗰陣，<a href="/wiki/%E7%89%9B%E9%A0%93" class="mw-redirect" title="牛頓">牛頓</a>觀察到一個<a href="/wiki/%E8%98%8B%E6%9E%9C" title="蘋果">蘋果</a>由樹上面跌落嚟，佢亦都觀察到好多嘢都係跟呢條規則，但佢始終冇辦法去真係「<a href="/wiki/%E8%AD%89%E6%98%8E" class="mw-redirect" title="證明">證明</a>」呢個<a href="/wiki/%E5%AE%87%E5%AE%99" title="宇宙">宇宙</a>入面真係所有嘢都有萬有引力－因為可能喺宇宙嘅某啲黑暗角落度會有啲冇引力嘅嘢，只係人類仲未搵到。科學家靠嘅係實驗同觀察，佢哋冇辦法好似<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%AE%B6" title="數學家">數學家</a>噉真係證明佢哋講嘅嘢，只可以靠住重複做實驗同觀察嚟加強自己嘅論證，但始終係冇方法排除一個可能性：呢個宇宙入面可能真係有啲嘢係唔跟佢哋諗出嚟嗰啲定律嘅，只係佢哋未搵到呢啲嘢<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>。 </p><p>就係因為噉，喺正式嘅<a href="/wiki/%E5%AD%B8%E8%A1%93%E6%96%87" class="mw-redirect" title="學術文">科學論文</a>入面，科學家好少可會話自己「證明」咗乜嘢乜嘢理論，只係會話「觀察同實驗嘅<a href="/wiki/%E8%AD%89%E6%93%9A" title="證據">證據</a>結果撐嗰個理論」，而且佢哋仲會好積極噉去搵新數據，睇吓呢啲佢哋之前未見過嘅數據會唔會推翻舊嘅理論。如果會嘅話，佢哋就會開始諗新理論，或者睇吓點樣將舊嗰個理論改吓等個理論可以同新數據夾得埋<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Univerza1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Univerza1.jpg/500px-Univerza1.jpg" decoding="async" width="500" height="307" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Univerza1.jpg/750px-Univerza1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Univerza1.jpg/1000px-Univerza1.jpg 2x" data-file-width="1140" data-file-height="699" /></a><figcaption>想像 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> 表示宇宙入面一切嘅現象，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 表示人類觀察得到嘅現象，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7815638370f616885fa8162b06697d078459f5ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:2.343ex;" alt="{\displaystyle A^{c}}"></span> 表示宇宙當中人類觀察唔到嘅現象。原則上，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 永遠會細過 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> 一大截，所以難保 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7815638370f616885fa8162b06697d078459f5ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.687ex; height:2.343ex;" alt="{\displaystyle A^{c}}"></span> 裏面唔會有啲「唔跟從人類嘅科學定律，但人類唔知佢哋存在」嘅事物。</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="定位"><span id=".E5.AE.9A.E4.BD.8D"></span>定位</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=4" title="編輯小節: 定位"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Mean_median_mode_SPSS_Syntax.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Mean_median_mode_SPSS_Syntax.JPG/300px-Mean_median_mode_SPSS_Syntax.JPG" decoding="async" width="300" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Mean_median_mode_SPSS_Syntax.JPG/450px-Mean_median_mode_SPSS_Syntax.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Mean_median_mode_SPSS_Syntax.JPG/600px-Mean_median_mode_SPSS_Syntax.JPG 2x" data-file-width="761" data-file-height="531" /></a><figcaption>喺統計<a href="/wiki/%E8%BB%9F%E4%BB%B6" class="mw-redirect" title="軟件">軟件</a> <a href="/wiki/SPSS" title="SPSS">SPSS</a> 入面嘅數據；喺呢度佢哋只係俾咗柞變數嘅平均值等嘅資料－即係用咗敘述統計學。如果佢哋做埋分析嚟睇吓啲變數之間嘅關係，噉就係推斷統計學。</figcaption></figure> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a></div> <p>喺<a href="/wiki/%E5%AE%9A%E7%BE%A9" title="定義">定義</a>上，統計學就係為咗思考「點樣由手上<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a>推導出普遍知識」而生嘅<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>子領域<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>，尤其關注帶有<a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A" title="不確定">不確定</a>嘅數據<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>：無論係邊個科學領域，科學家做嘅都係「由手上睇到嘅現象（<a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>嘅數據）嗰度嘗試推導出能夠廣泛噉描述同類現嘅理論」，呢種做法本質上就有<a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A" title="不確定">不確定</a>－難以保證個樣本實係代表到個總體，例如研究者想研究<a href="/wiki/%E7%8B%BC" title="狼">狼</a>嘅<a href="/wiki/%E9%87%8D%E9%87%8F" title="重量">體重</a>，因為人力物力嘅限制，佢冇可能研究嗮古往今來所有嘅狼，所以佢就去搵 100 隻狼（樣本）返嚟做研究，佢量度到呢個樣本嘅狼<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均</a>體重係 40 <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">kg</a>（數據），就最嚴格嘅<a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a>基準嚟講，呢個數可能 </p> <ul><li>真係代表到全世界嘅狼；但又有可能</li> <li>全世界嘅狼嘅平均體重查實係 60 kg，個研究者之所以搵到 40 kg 呢個數只係佢咁啱得咁橋唔好彩，抽到個代表唔到個總體嘅樣本；</li></ul> <p>喺呢個思考過程當中，就經已必然涉及「手上嘅樣本有幾大機會代表到全世界嘅狼」嘅問題，會用到<a href="/wiki/%E6%A9%9F%E6%9C%83%E7%8E%87" class="mw-redirect" title="機會率">機會率</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>e 4<span class="cite-bracket">]</span></a></sup>同埋相關嘅數學概念（可以睇埋<a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a>）。好似機會率等科研工作上用嚟分析數據嘅數學概念就形成咗統計學呢門學問<sup id="cite_ref-feller1968_24-0" class="reference"><a href="#cite_note-feller1968-24"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>。 </p><p>統計學用途好廣泛。喺<a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>上，<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a>係好重要嘅一環，噉係因為科學嘅基礎係<b>實證</b>。科學家嘅職責係諗啲理論出嚟解釋自然現象，而佢哋發表親啲乜嘢理論都一定要搵<a href="/wiki/%E8%AD%89%E6%93%9A" title="證據">證據</a>嚟驗證吓個理論。要驗證一個理論就要去現實世界嗰度收集數據－所以搞科研實會有一大柞數據要處理<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>。除此之外，統計學喺<a href="/wiki/%E5%95%86%E6%A5%AD" title="商業">商業</a>範疇上都有用：統計師會喺一啲<a href="/wiki/%E5%85%AC%E5%8F%B8" title="公司">公司</a>嗰度幫手解答一啲研發上遇到嘅問題<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="兩大範疇"><span id=".E5.85.A9.E5.A4.A7.E7.AF.84.E7.96.87"></span>兩大範疇</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=5" title="編輯小節: 兩大範疇"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%95%98%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="敘述統計學">敘述統計學</a>同<a href="/wiki/%E6%8E%A8%E6%96%B7%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="推斷統計學">推斷統計學</a></div> <p>統計學大致上分做兩範，負責總括同埋形容啲數據嘅叫<a href="/wiki/%E6%95%98%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="敘述統計學">敘述統計學</a><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>e 5<span class="cite-bracket">]</span></a></sup>，而用一啲分析方法嚟去估計同研究<a href="/wiki/%E8%AE%8A%E6%95%B8_(%E7%A7%91%E7%A0%94)" title="變數 (科研)">變數</a>與變數之間嘅關係嘅就叫做<a href="/wiki/%E6%8E%A8%E6%96%B7%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="推斷統計學">推斷統計學</a><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>e 6<span class="cite-bracket">]</span></a></sup>。前者會俾出一啲好似啲變數嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>等嘅<a href="/wiki/%E8%B3%87%E8%A8%8A" title="資訊">資訊</a>，而後者會將數據入面嘅資訊變做<a href="/wiki/%E6%95%B8%E5%AD%B8%E6%A8%A1%E5%9E%8B" title="數學模型">數學模型</a>，而呢啲數學模型打後可以用嚟做出預測，例如分析幾個變數之間嘅關係有幾勁<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>。 </p><p>攞返上面個狼研究嘅例子做說明，假設做完推斷統計分析之後，發覺一隻狼每日食嘅嘢嘅總量（以 <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">kg</a> 嚟計）同佢身處嘅地區嘅平均<a href="/wiki/%E6%B0%A3%E6%BA%AB" class="mw-redirect" title="氣溫">氣溫</a>（以<a href="/wiki/%E6%94%9D%E6%B0%8F" title="攝氏">攝氏</a>計）成<a href="/wiki/%E5%8F%8D%E6%AF%94" class="mw-redirect" title="反比">反比</a>（即係一隻狼身處嘅地方愈凍，佢就愈食得多嘢），而佢哋之間嘅關係可以大致上用一條式表達（可以睇吓<a href="/wiki/%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="迴歸分析">迴歸分析</a>）： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y=bX+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> <mo>=</mo> <mi>b</mi> <mi>X</mi> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y=bX+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98960065dcc50ce21a7e51a4781b174670b59c8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.92ex; height:2.343ex;" alt="{\displaystyle Y=bX+a}"></span>，設 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> 做「隻狼食幾多 kg 嘢食」而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 做「佢身處嗰度嘅平均攝氏氣溫」，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> 係某啲<a href="/wiki/%E5%AF%A6%E6%95%B8" title="實數">實數</a>。</dd></dl> <p>收集咗一輪數據之後，就有得用啲數據嚟估計 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> 嘅數值，打後下次再搵到隻狼嗰陣就可以用呢個模型嚟按佢身處嗰度嘅平均氣溫嚟估計佢每日會食幾多嘢。一般嚟講，收集到嘅數據愈多（喺呢個例子入面即係研究過愈多嘅狼），可以做到嘅預測就會愈準<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="收集數據"><span id=".E6.94.B6.E9.9B.86.E6.95.B8.E6.93.9A"></span>收集數據</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=6" title="編輯小節: 收集數據"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Simple_random_sampling_canto_%26_mando.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Simple_random_sampling_canto_%26_mando.png/300px-Simple_random_sampling_canto_%26_mando.png" decoding="async" width="300" height="231" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Simple_random_sampling_canto_%26_mando.png/450px-Simple_random_sampling_canto_%26_mando.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Simple_random_sampling_canto_%26_mando.png/600px-Simple_random_sampling_canto_%26_mando.png 2x" data-file-width="618" data-file-height="476" /></a><figcaption>一個<a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a>嘅過程係由一大柞研究對象嗰度抽一部份出嚟研究－因為要睇嗮所有嘅研究對象通常都會太嘥時間或者太嘥錢所以唔可行。</figcaption></figure> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%94%B6%E9%9B%86%E6%95%B8%E6%93%9A" title="收集數據">收集數據</a></div> <p><a href="/wiki/%E6%94%B6%E9%9B%86%E6%95%B8%E6%93%9A" title="收集數據">收集數據</a><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>e 7<span class="cite-bracket">]</span></a></sup>係做統計分析必要嘅一個工序：用<a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%B9%E6%B3%95" title="科學方法">科學方法</a>做研究係要由對現實嘅<a href="/wiki/%E8%A7%80%E5%AF%9F" title="觀察">觀察</a>當中<a href="/wiki/%E6%AD%B8%E7%B4%8D" title="歸納">歸納</a>出一啲能夠描述現實嘅法則或者理論；而要對現實作出系統化嘅觀察，就一定要攞<a href="/wiki/%E6%95%B8%E6%93%9A" title="數據">數據</a>－用某啲<a href="/wiki/%E7%AC%A6%E8%99%9F" title="符號">符號</a>（喺統計學上通常係數目字）記低現實世界嘅狀態<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="變數"><span id=".E8.AE.8A.E6.95.B8"></span>變數</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=7" title="編輯小節: 變數"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E8%AE%8A%E6%95%B8_(%E7%A7%91%E7%A0%94)" title="變數 (科研)">變數 (科研)</a></div> <p><a href="/wiki/%E8%AE%8A%E6%95%B8_(%E7%A7%91%E7%A0%94)" title="變數 (科研)">變數</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>e 8<span class="cite-bracket">]</span></a></sup>，又叫做「未知數」，係做統計學一定會處理嘅嘢。變數指喺<a href="/wiki/%E5%AE%87%E5%AE%99" title="宇宙">宇宙</a>入面一啲有可能變、兼且係形容緊某啲事物嘅特性。例如<a href="/wiki/%E8%BA%AB%E9%AB%98" title="身高">身高</a>、<a href="/wiki/%E9%AB%94%E9%87%8D" class="mw-redirect" title="體重">體重</a>同<a href="/wiki/%E5%AE%97%E6%95%99" title="宗教">宗教</a>呢啲特性都可以用嚟形容人，而且呢幾樣嘢個個人唔同，所以呢三個都係屬於「用嚟形容人」嘅變數。大細同<a href="/wiki/%E8%B3%AA%E9%87%8F" title="質量">質量</a>呢啲可以攞嚟形容人或者物件都得，而且呢兩樣嘢個個人或者件件物件都可以唔同，所以係屬於「形容人同物件」嘅變數<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>。 </p><p>變數大致上有得分做兩種： </p> <ul><li><a href="/wiki/%E9%80%A3%E7%BA%8C%E8%AE%8A%E6%95%B8" class="mw-redirect" title="連續變數">連續變數</a><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>e 9<span class="cite-bracket">]</span></a></sup>指啲有得用數字嚟量度、兼且去到<a href="/wiki/%E5%B0%8F%E6%95%B8%E9%BB%9E" class="mw-redirect" title="小數點">小數點</a>後幾多位都得嘅變數，呢啲數值攞得嚟比較大細同埋做數學嘅運算，例如人有幾高有幾重都可以講係連續變數－<b>身高</b>同<b>體重</b>有得用數字嚟度，兼且可以用有小數點嘅數字，而人有得用呢柞數值嚟比較唔同人嘅身高同體重，仲可以用佢哋嚟計數；</li> <li>相反，好似<b>屬邊個宗教</b>呢個<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>上成日研究嘅變數就係一個<a href="/wiki/%E5%94%94%E9%80%A3%E7%BA%8C%E8%AE%8A%E6%95%B8" class="mw-redirect" title="唔連續變數">唔連續變數</a><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>e 10<span class="cite-bracket">]</span></a></sup>－<b>宗教</b>唔可以用數字嚟度，而佢嘅值一般都唔可以攞嚟計數－好似係 <b>183 <a href="/wiki/%E5%8E%98%E7%B1%B3" title="厘米">厘米</a></b>同 <b>80 <a href="/wiki/%E5%85%AC%E6%96%A4" class="mw-redirect" title="公斤">公斤</a></b>呢啲數值有得加減乘除，而<b>信<a href="/wiki/%E4%BD%9B" title="佛">佛</a></b>同<b>信<a href="/wiki/%E8%80%B6%E7%A9%8C" title="耶穌">耶穌</a></b>呢啲值雖然都係形容緊啲嘢，但唔可攞<a href="/wiki/%E8%A8%88%E6%95%B8%E6%A9%9F" title="計數機">計數機</a>去撳加減乘除。連續變數喺統計學入面比較常見－因為前者先至可以攞嚟計數，而後者唔得<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup>。</li></ul> <p>變數可以話係科學嘅關鍵，因為無論係邊個學科，科學嘅重點基本上就係想搵出變數同變數之間有啲乜嘢關係，而「知道嗮成個宇宙入面所有嘅變數同埋佢哋之間嘅相互關係」基本上就係科學嘅終極目標。 </p> <div class="mw-heading mw-heading3"><h3 id="抽樣"><span id=".E6.8A.BD.E6.A8.A3"></span>抽樣</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=8" title="編輯小節: 抽樣"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a></div> <p><a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>e 11<span class="cite-bracket">]</span></a></sup>係做科研嘅一個程序，指由個<a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a>嗰度攞一部份嘅個體嚟研究。所有研究都係研究緊某啲<a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>e 12<span class="cite-bracket">]</span></a></sup>，例如喺上面個狼例子個總體就係「世界上嘅狼」，而（例如）<a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%B8" title="心理學">心理學</a>所研究嘅總體就係「世界上所有嘅<a href="/wiki/%E6%99%BA%E4%BA%BA" title="智人">智人</a><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>e 13<span class="cite-bracket">]</span></a></sup>」。但研究嘅總體通常都太大，搞到研究佢哋嘅科學家好難由個總體入面嘅所有個體收集數據，例如世界上有數以億計嘅人，要逐個逐個噉嚟研究太嘥時間，根本冇可能行得通，於是乎科學家喺做研究嗰陣往往要做抽樣－由研究緊個總體嗰度抽一小部份出嚟，而呢個部份就係所謂嘅<a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>e 14<span class="cite-bracket">]</span></a></sup>，希望透過研究呢一小部份嚟去了解嗮總體入面所有嘅個體。例如係想研究<a href="/wiki/%E9%BB%91%E6%B4%9E" title="黑洞">黑洞</a>嘅話，<a href="/wiki/%E5%A4%A9%E9%AB%94%E7%89%A9%E7%90%86%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="天體物理學家">天體物理學家</a>可以去搵 10 個特定嘅黑洞嚟研究，希望透過研究呢 10 個黑洞（呢 10 個黑洞只係全宇宙成千上萬個黑洞之中嘅一小部份）嚟了解埋其餘嘅黑洞<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup>。 </p><p>抽樣呢個程序係做科研好關鍵嘅一環，因為做抽樣嗰個科學家一定要確保到佢抽出嚟個樣本真係代表得到成個總體，噉先至可以說服到啲人話佢個研究得出嘅結果可以<a href="/wiki/%E5%BB%A3%E7%BE%A9%E5%8C%96" title="廣義化">普遍化</a><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>e 15<span class="cite-bracket">]</span></a></sup>到去成個總體嗰度。例如係頭先嗰個狼研究噉，一個<a href="/wiki/%E5%8B%95%E7%89%A9%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="動物學家">動物學家</a>有至少兩個抽樣方法可以揀： </p> <ol><li>喺<a href="/wiki/%E8%8F%AF%E5%8D%97" title="華南">華南</a>嗰度<a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%8A%BD%E6%A8%A3" title="隨機抽樣">隨機噉</a>攞 200 隻狼嚟研究；</li> <li>喺全世界各個洲嗰度隨機噉抽 200 隻狼嚟研究。</li></ol> <p>一般認為，後者更加代表得到嗮個總體－「全世界嘅狼」－而前者就比較有<a href="/wiki/%E4%BB%A5%E5%81%8F%E6%A6%82%E5%85%A8" title="以偏概全">以偏概全</a>之嫌。好多時啲科學家詏話一份研究冇辦法將得出嘅結果普遍化，都係指控緊佢個樣本唔夠代表性，好似係好多廿世紀嘅<a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="心理學家">心理學家</a>喺做心理學研究嗰陣都貪方便，喺<a href="/wiki/%E5%A4%A7%E5%AD%B8" title="大學">大學</a>度攞啲大學生嚟做研究嘅樣本，搞到科學界成日都話佢哋嗰啲所謂嘅心理學只不過係「大學生嘅心理學」，根本代表唔到大學生以外嘅群體嘅心理<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="量度"><span id=".E9.87.8F.E5.BA.A6"></span>量度</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=9" title="編輯小節: 量度"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E9%87%8F%E5%BA%A6%E5%B1%A4%E6%AC%A1" title="量度層次">量度層次</a>、<a href="/wiki/%E4%BF%A1%E5%BA%A6" title="信度">信度</a>同<a href="/wiki/%E6%95%88%E5%BA%A6" title="效度">效度</a></div> <p>要做統計，就實要首先將啲現實世界入面嘅變數轉化做數據入面嘅數字，呢個過程就係所謂嘅<a href="/wiki/%E9%87%8F%E5%BA%A6" title="量度">量度</a>，攞個<a href="/wiki/%E7%A3%85%E9%87%8D%E7%A3%85" title="磅重磅">磅重磅</a>磅一隻動物嘅過程係量度緊隻動物嘅<a href="/wiki/%E9%87%8D%E9%87%8F" title="重量">重量</a>（將「隻動物嘅重量」呢個變數轉化做一個數字），而做<a href="/wiki/%E6%99%BA%E5%95%86%E6%B8%AC%E9%A9%97" class="mw-redirect" title="智商測驗">智商測驗</a><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>e 16<span class="cite-bracket">]</span></a></sup>嘅過程就係量度緊一個人嘅<a href="/wiki/%E6%99%BA%E8%83%BD" title="智能">智能</a>（將「個人嘅智能」呢個變數轉化做一個數字）... 呀噉。而<a href="/wiki/%E9%87%8F%E5%BA%A6%E5%B1%A4%E6%AC%A1" title="量度層次">量度層次</a><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>e 17<span class="cite-bracket">]</span></a></sup>係統計學上嘅一個概念，係指基於一個量度方法提供到幾多<a href="/wiki/%E8%B3%87%E8%A8%8A" title="資訊">資訊</a>嚟到劃分嘅分類法，可以話係反映一個量度方法有幾「好使」，一共有四層<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup>： </p> <table class="wikitable"> <tbody><tr> <th>層次</th> <th>名</th> <th>用得嘅<a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a>同<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>運算</th> <th>例子</th> <th>點計中間趨勢</th> <th>點計離散趨勢</th> <th>定性抑或<br />定量 </th></tr> <tr> <td><center>1</center></td> <td><b>名目</b><br /><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>e 18<span class="cite-bracket">]</span></a></sup></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a4ceef454c69dffd23792c84b90f488543743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle =}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }"></span></td> <td>二元名目：<a href="/wiki/%E6%80%A7%E5%88%A5" class="mw-redirect" title="性別">性別</a>（男、女）、<a href="/wiki/%E7%9C%9F%E7%9B%B8" title="真相">真實性</a>（真、假）、出席狀況（出席、缺席）<br />多元名目：<a href="/wiki/%E8%AA%9E%E8%A8%80" title="語言">語言</a>（<a href="/wiki/%E5%BB%A3%E6%9D%B1%E8%A9%B1" class="mw-redirect" title="廣東話">廣東話</a>、<a href="/wiki/%E6%99%AE%E9%80%9A%E8%A9%B1" class="mw-redirect" title="普通話">普通話</a>同<a href="/wiki/%E8%8B%B1%E6%96%87" title="英文">英文</a>等）...</td> <td><a href="/wiki/%E7%9C%BE%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="眾數 (統計學)">眾數</a></td> <td>冇</td> <td><center>定性</center> </td></tr> <tr> <td><center>2</center></td> <td><b>次序</b><br /><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>e 19<span class="cite-bracket">]</span></a></sup></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a4ceef454c69dffd23792c84b90f488543743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle =}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }"></span>；<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle >}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle >}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b27b77ab4e3293ea9ce65cef60fea655c398423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle >}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle <}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33737c89a17785dacc8638b4d66db3d5c8670de1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle <}"></span></td> <td>多元次序：服務評等（傑出、好、欠佳）、教育程度（小學、初中、高中、學士、碩士同博士等）</td> <td><a href="/wiki/%E7%9C%BE%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="眾數 (統計學)">眾數</a>、<a href="/wiki/%E4%B8%AD%E4%BD%8D%E6%95%B8" title="中位數">中位數</a></td> <td><a href="/w/index.php?title=%E5%88%86%E4%BD%8D%E6%95%B8&action=edit&redlink=1" class="new" title="分位數 (無呢版)">分位數</a></td> <td><center>定性</center> </td></tr> <tr> <td><center>3</center></td> <td><b>等距</b><br /><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>e 20<span class="cite-bracket">]</span></a></sup></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a4ceef454c69dffd23792c84b90f488543743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle =}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }"></span>；<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle >}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle >}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b27b77ab4e3293ea9ce65cef60fea655c398423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle >}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle <}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33737c89a17785dacc8638b4d66db3d5c8670de1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle <}"></span><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle -}"></span></td> <td><a href="/wiki/%E6%BA%AB%E5%BA%A6" title="溫度">溫度</a>、<a href="/wiki/%E5%B9%B4%E4%BB%BD" class="mw-redirect" title="年份">年份</a>、<a href="/wiki/%E7%B7%AF%E5%BA%A6" class="mw-redirect" title="緯度">緯度</a>等</td> <td><a href="/wiki/%E7%9C%BE%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="眾數 (統計學)">眾數</a>、<a href="/wiki/%E4%B8%AD%E4%BD%8D%E6%95%B8" title="中位數">中位數</a>、<a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B8" class="mw-redirect" title="平均數">平均數</a></td> <td><a href="/w/index.php?title=%E5%88%86%E4%BD%8D%E6%95%B8&action=edit&redlink=1" class="new" title="分位數 (無呢版)">分位數</a>、<a href="/wiki/%E5%85%A8%E8%B7%9D" title="全距">全距</a></td> <td><center>定量</center> </td></tr> <tr> <td><center>4</center></td> <td><b>等比</b><br /><sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>e 21<span class="cite-bracket">]</span></a></sup></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/505a4ceef454c69dffd23792c84b90f488543743" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.307ex; margin-bottom: -0.478ex; width:1.808ex; height:1.343ex;" alt="{\displaystyle =}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≠</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38cc3d8d8c60120bc2f905bae4d5e10d8ad6a3f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle \neq }"></span>；<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle >}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>></mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle >}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b27b77ab4e3293ea9ce65cef60fea655c398423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle >}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle <}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33737c89a17785dacc8638b4d66db3d5c8670de1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle <}"></span><br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04bd52ce670743d3b61bec928a7ec9f47309eb36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle -}"></span>；<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span>、<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \div }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>÷</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \div }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/837b35ee5d25b5ce7b07f292c27cc90533dd9fd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \div }"></span></td> <td><a href="/wiki/%E5%83%B9%E9%8C%A2" class="mw-redirect" title="價錢">價錢</a>、<a href="/wiki/%E5%B9%B4%E9%BD%A1" title="年齡">年齡</a>、<a href="/wiki/%E8%BA%AB%E9%AB%98" title="身高">身高</a>、<a href="/wiki/%E7%B5%95%E5%B0%8D%E6%BA%AB%E5%BA%A6" title="絕對溫度">絕對溫度</a>、絕大多數嘅<a href="/wiki/%E7%89%A9%E7%90%86%E9%87%8F" title="物理量">物理量</a></td> <td><a href="/wiki/%E7%9C%BE%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="眾數 (統計學)">眾數</a>、<a href="/wiki/%E4%B8%AD%E4%BD%8D%E6%95%B8" title="中位數">中位數</a>、<a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B8" class="mw-redirect" title="平均數">平均數</a>等</td> <td><a href="/w/index.php?title=%E5%88%86%E4%BD%8D%E6%95%B8&action=edit&redlink=1" class="new" title="分位數 (無呢版)">分位數</a>、<a href="/wiki/%E5%85%A8%E8%B7%9D" title="全距">全距</a>、<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a>等</td> <td><center>定量</center> </td></tr></tbody></table> <p>一般嚟講，科學家都想自己嘅研究嘅量度層次盡可能有咁高得咁高（即係盡可能接近等比），不過現實世界嘅技術等嘅限制唔一定俾到佢哋噉樣做。 </p><p>順帶一提，除咗層次之外，科學家亦都好關注量度方法嘅<a href="/wiki/%E4%BF%A1%E5%BA%A6" title="信度">信度</a><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>e 22<span class="cite-bracket">]</span></a></sup>同<a href="/wiki/%E6%95%88%E5%BA%A6" title="效度">效度</a><sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>e 23<span class="cite-bracket">]</span></a></sup>：信度同效度係兩種用嚟衡量一種量度方法掂唔掂嘅基準；信度指用嗰個方法對一樣嘅現象進行重複觀察之後係咪可以得到相同嘅結果，而效度係指個方法有幾量度到佢理應要量度嗰樣嘢，喺<a href="/wiki/%E5%BF%83%E7%90%86%E6%B8%AC%E9%87%8F%E5%AD%B8" title="心理測量學">心理測量學</a>（研究用統計方法量度<a href="/wiki/%E5%BF%83%E7%90%86" class="mw-redirect" title="心理">心理</a>特性嘅領域）等嘅領域上，研究者仲會有多種方法評估一種量度方法嘅信度同效度<sup id="cite_ref-furr2017_56-0" class="reference"><a href="#cite_note-furr2017-56"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="敘述數據"><span id=".E6.95.98.E8.BF.B0.E6.95.B8.E6.93.9A"></span>敘述數據</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=10" title="編輯小節: 敘述數據"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:DVD_Rental_Query.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/DVD_Rental_Query.png/300px-DVD_Rental_Query.png" decoding="async" width="300" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/DVD_Rental_Query.png/450px-DVD_Rental_Query.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/DVD_Rental_Query.png/600px-DVD_Rental_Query.png 2x" data-file-width="968" data-file-height="839" /></a><figcaption>一個典型嘅<a href="/wiki/%E6%95%B8%E6%93%9A%E9%9B%86" title="數據集">數據集</a>；當中每一個直行代表一個變數，每一個橫行代表一個個案，個數據集會有每個個案喺各變數上嘅數值。</figcaption></figure> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%95%98%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="敘述統計學">敘述統計學</a></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E4%BA%8B%E5%89%8D%E6%95%B8%E6%93%9A%E8%99%95%E7%90%86" title="事前數據處理">事前數據處理</a></div> <p>喺搵咗數據返嚟之後，研究者手上會有個<a href="/wiki/%E6%95%B8%E6%93%9A%E9%9B%86" title="數據集">數據集</a><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>e 24<span class="cite-bracket">]</span></a></sup>，每個個案都會喺每個變數上有個數值，而一般嚟講，研究者首先會做嘅係搵一啲指標描述吓柞數據大致係點樣嘅（<a href="/wiki/%E6%95%98%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" class="mw-redirect" title="敘述統計學">敘述統計學</a>），常用嘅敘述統計指標包括咗<sup id="cite_ref-data1988_59-0" class="reference"><a href="#cite_note-data1988-59"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>： </p> <ul><li><a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B8" class="mw-redirect" title="平均數">平均數</a><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>e 25<span class="cite-bracket">]</span></a></sup>：平均數（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>）最常係指將啲個案嘅數值（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\displaystyle a_{i}}"></span>）加埋一齊，再除以個案數量（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>）： <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90330653b40adf032ea8e144f84d7eec1a88054d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:35.426ex; height:6.843ex;" alt="{\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}}"></span></dd></dl></li> <li><a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8" class="mw-redirect" title="變異數">變異數</a><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>e 26<span class="cite-bracket">]</span></a></sup>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f2c4cf561a4f5d5b10607c350760f34a29f0b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.814ex; height:3.176ex;" alt="{\displaystyle \sigma _{Y}^{2}}"></span>）：以下嘅數值： <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}^{2}={\frac {1}{n}}\sum _{i=1}^{n}\left(Y_{i}-{\overline {Y}}\right)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Y</mi> <mo accent="false">¯</mo> </mover> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}^{2}={\frac {1}{n}}\sum _{i=1}^{n}\left(Y_{i}-{\overline {Y}}\right)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac4fa5e860e50e24486daa41f68837eedec8ee27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.255ex; height:6.843ex;" alt="{\displaystyle \sigma _{Y}^{2}={\frac {1}{n}}\sum _{i=1}^{n}\left(Y_{i}-{\overline {Y}}\right)^{2}}"></span>，</dd></dl> <ul><li>當中 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> 係個案數量，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d57be496fff95ee2a97ee43c7f7fe244b4dbf8ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.15ex; height:2.509ex;" alt="{\displaystyle Y_{i}}"></span> 係第 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> 個個案喺個變數上嘅值，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {Y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Y</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {Y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e430df50efa67ea2e08d9c37afd5fe1434803b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:2.163ex; height:2.843ex;" alt="{\displaystyle {\overline {Y}}}"></span> 係個樣本嘅平均值－<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f2c4cf561a4f5d5b10607c350760f34a29f0b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.814ex; height:3.176ex;" alt="{\displaystyle \sigma _{Y}^{2}}"></span> 反映咗啲個案平均距離平均值幾遠。</li></ul></li> <li><a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>e 27<span class="cite-bracket">]</span></a></sup>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a9fb889441f514e155f65e77dc5b7c7a5a84f35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.814ex; height:2.009ex;" alt="{\displaystyle \sigma _{Y}}"></span>）：變異數嘅<a href="/wiki/%E9%96%8B%E6%96%B9" class="mw-redirect" title="開方">開方</a>。 <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}={\sqrt {\sigma _{Y}^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}={\sqrt {\sigma _{Y}^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8f81811acf3461e87dbbeed7838e5868385793a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.049ex; height:4.843ex;" alt="{\displaystyle \sigma _{Y}={\sqrt {\sigma _{Y}^{2}}}}"></span></dd></dl></li></ul> <p>... 等等。 </p> <div class="mw-heading mw-heading3"><h3 id="概率分佈"><span id=".E6.A6.82.E7.8E.87.E5.88.86.E4.BD.88"></span>概率分佈</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=11" title="編輯小節: 概率分佈"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a></div> <p><a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>e 28<span class="cite-bracket">]</span></a></sup>係成日用嚟描述「柞數據乜嘢樣」嘅架生。一個概率分佈係一個<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%87%BD%E6%95%B8" class="mw-redirect" title="數學函數">數學函數</a><sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>e 29<span class="cite-bracket">]</span></a></sup>，而呢個函數表達咗每個數值喺某個<a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a>或者<a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>入面出現嘅<a href="/wiki/%E6%A6%82%E7%8E%87" title="概率">概率</a>（<a href="/wiki/%E6%A9%9F%E6%9C%83%E7%8E%87" class="mw-redirect" title="機會率">機會率</a>），<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Pr(X=x)=f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Pr(X=x)=f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de77f093e966fdeeb7fc3afbe68522eea9235c6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.228ex; height:2.843ex;" alt="{\displaystyle \Pr(X=x)=f(x)}"></span>，當中 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> 就係個概率分佈。例如假設而家<a href="/wiki/%E6%8E%9F%E9%8A%80%E4%BB%94" title="掟銀仔">掟一個銀仔</a>，用 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 代表掟個銀仔嘅結果，掟 10 次（個總體係「全世界嘅掟銀仔結果」，而呢 10 次就係一個樣本）。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 係公嘅機會率係 0.5（即係 50%），而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 係字嘅機會率都係 0.5（假設個銀仔冇做過手腳），相應嘅概率分佈如下<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>註 1<span class="cite-bracket">]</span></a></sup>： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(X=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(X=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/096d468585ba6b98548ec1f395a1fe8a9e403419" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.083ex; height:2.843ex;" alt="{\displaystyle P(X=}"></span> <b>公</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle )=0.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle )=0.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70d155d00bb65fc1d280a7dfedc035c9543cec29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.33ex; height:2.843ex;" alt="{\displaystyle )=0.5}"></span>，「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 係公嘅機會率係 50%」。</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(X=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(X=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/096d468585ba6b98548ec1f395a1fe8a9e403419" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.083ex; height:2.843ex;" alt="{\displaystyle P(X=}"></span> <b>字</b> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle )=0.5}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.5</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle )=0.5}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70d155d00bb65fc1d280a7dfedc035c9543cec29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.33ex; height:2.843ex;" alt="{\displaystyle )=0.5}"></span>，「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 係字嘅機會率係 50%」。</dd></dl> <p>响現實世界嘅科研入面，啲變數好少可會「一係公一係字」咁二元，但個原理一樣：<a href="/wiki/%E5%B8%B8%E6%85%8B%E5%88%86%E4%BD%88" title="常態分佈">常態分佈</a><sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>e 30<span class="cite-bracket">]</span></a></sup>就係科學入面最常用嘅概率分佈之一，如果由一個常態分佈嘅總體嗰度抽樣，個變數嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>會係出現得最密嘅數值，低過平均嘅數值同高過平均嘅數值出現嘅機會率一樣，而離平均值愈遠嘅數值，抽到出嚟嘅機會率就愈低，如果按住個樣本畫一個概率分佈圖（打橫個條 <a href="/wiki/X_%E8%BB%B8" class="mw-redirect" title="X 軸">X 軸</a>係<b>個變數嘅可能數值</b>，而打戙嗰條 <a href="/wiki/Y_%E8%BB%B8" class="mw-redirect" title="Y 軸">Y 軸</a>係<b>每個數值出現嘅機會率</b>），一個常態分佈會俾出一條好似<a href="/wiki/%E9%90%98%E5%BD%A2%E6%9B%B2%E7%B7%9A" class="mw-redirect" title="鐘形曲線">鐘噉嘅形狀嘅線</a><sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>e 31<span class="cite-bracket">]</span></a></sup>。常態分佈嘅<a href="/wiki/%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B8" title="概率密度函數">概率密度函數</a>係（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span> 係個分佈嘅<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a>）<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup>： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>π</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>μ</mi> </mrow> <mi>σ</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00cb9b2c9b866378626bcfa45c86a6de2f2b2e40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:24.446ex; height:6.676ex;" alt="{\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}"></span></dd></dl> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Standard_deviation_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/510px-Standard_deviation_diagram.svg.png" decoding="async" width="510" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/765px-Standard_deviation_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/1020px-Standard_deviation_diagram.svg.png 2x" data-file-width="400" data-file-height="200" /></a><figcaption>一個概率分佈圖；幅圖打橫個條 X 軸係「個變數嘅可能數值」，而打直嗰條 Y 軸係「每個數值出現嘅機會率」。呢幅係一幅常態分佈。</figcaption></figure> <p>譬如話以下呢個情況噉：想像有<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8%E5%AE%B6" title="生物學家">生物學家</a>想研究成年<a href="/wiki/%E4%B8%AD%E8%8F%AF%E7%99%BD%E6%B5%B7%E8%B1%9A" title="中華白海豚">中華白海豚</a>嘅身長，但佢冇可能捉嗮世界上咁多隻白海豚遂隻遂隻嚟度佢哋幾長，於是乎佢就抽個樣本出嚟，用個樣本嚟估計全世界嘅白海豚嘅身長；呢個樣本入面有 20 隻白海豚，佢哋嘅平均身長係 2.2 米，唔係隻隻都啱啱好 2.2 米長－有隻係 1.8 米長，有隻係 2.6 米長呀噉－但一隻白海豚身長高過呢個值嘅機會率大致上等如佢身長低過呢個值嘅機會率，而且離 2.2 米愈遠嘅數值出現嘅機會率愈低。如果畫幅概率分佈圖，「隻白海豚嘅身長」做 X 軸，而「每個身長數值出現嘅機會率」做 Y 軸，幅圖會出一條近似鐘形嘅線。 </p><p>一般嚟講，做統計嗰陣都會假設抽樣個過程係<a href="/wiki/%E7%8D%A8%E7%AB%8B%E5%90%8C%E5%88%86%E4%BD%88" title="獨立同分佈">獨立同分佈</a><sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>e 32<span class="cite-bracket">]</span></a></sup>嘅－噉講嘅意思係指，樣本入面每個個體嘅數值喺由個總體嗰度抽出嚟嗰陣嘅概率分佈都係一樣，而且相互之間<a href="/wiki/%E7%8D%A8%E7%AB%8B_(%E6%A6%82%E7%8E%87%E8%AB%96)" title="獨立 (概率論)">獨立</a><sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>e 33<span class="cite-bracket">]</span></a></sup>（一個抽到嘅數值嘅概率分佈唔會影響到下一個抽到嘅數值嘅）。呢個假設慳咗好多時間同精神－如果吓吓做統計都要諗第二個抽出嚟嘅數值同第一個抽出嚟嘅數值嘅概率分佈會唔會唔同咗嘅話，計起統計上嚟就會撈絞得好交關<sup id="cite_ref-dinov2008_72-0" class="reference"><a href="#cite_note-dinov2008-72"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Comparing_normal_distributions_001.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Comparing_normal_distributions_001.png/450px-Comparing_normal_distributions_001.png" decoding="async" width="450" height="302" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Comparing_normal_distributions_001.png/675px-Comparing_normal_distributions_001.png 1.5x, //upload.wikimedia.org/wikipedia/commons/7/72/Comparing_normal_distributions_001.png 2x" data-file-width="745" data-file-height="500" /></a><figcaption><a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>（Mu）同<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a>（Sigma）嘅數值對常態分佈嘅影響；數值大嘅標準差表示啲個體普遍同個樣本嘅平均值差好遠。</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="相關定實驗性質"><span id=".E7.9B.B8.E9.97.9C.E5.AE.9A.E5.AF.A6.E9.A9.97.E6.80.A7.E8.B3.AA"></span>相關定實驗性質</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=12" title="編輯小節: 相關定實驗性質"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>得到咗呢啲數值之後，研究者就可以做進一步嘅分析，理解變數之間嘅關係，而研究有得大致上分做兩種：<a href="/wiki/%E7%9B%B8%E9%97%9C" class="mw-redirect" title="相關">相關性質</a><sup id="cite_ref-73" class="reference"><a href="#cite_note-73"><span class="cite-bracket">[</span>e 34<span class="cite-bracket">]</span></a></sup>同<a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗性質</a><sup id="cite_ref-74" class="reference"><a href="#cite_note-74"><span class="cite-bracket">[</span>e 35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-75" class="reference"><a href="#cite_note-75"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup>： </p> <div class="mw-heading mw-heading3"><h3 id="相關性質"><span id=".E7.9B.B8.E9.97.9C.E6.80.A7.E8.B3.AA"></span>相關性質</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=13" title="編輯小節: 相關性質"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E8%A7%80%E5%AF%9F" title="觀察">觀察</a>同<a href="/wiki/%E7%B5%B1%E8%A8%88%E7%9B%B8%E9%97%9C" title="統計相關">統計相關</a></div> <p>相關研究嘅目的係要搵出變數之間嘅<a href="/wiki/%E7%B5%B1%E8%A8%88%E7%9B%B8%E9%97%9C" title="統計相關">統計相關</a><sup id="cite_ref-76" class="reference"><a href="#cite_note-76"><span class="cite-bracket">[</span>e 36<span class="cite-bracket">]</span></a></sup>有幾勁。<a href="/wiki/%E7%9A%AE%E4%BA%9E%E9%81%9C%E7%A9%8D%E5%B7%AE%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8" title="皮亞遜積差相關係數">皮亞遜積差相關係數</a><sup id="cite_ref-77" class="reference"><a href="#cite_note-77"><span class="cite-bracket">[</span>e 37<span class="cite-bracket">]</span></a></sup>係統計學成日用嘅一個指標，「兩個變數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 之間嘅皮亞遜積差相關係數」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{X,Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{X,Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/722f0de20522fdccaab8cd208d982c45fc5ce39a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.546ex; height:2.343ex;" alt="{\displaystyle \rho _{X,Y}}"></span>）係噉樣<a href="/wiki/%E5%AE%9A%E7%BE%A9" title="定義">定義</a>嘅： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{X,Y}=\mathrm {corr} (X,Y)={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E[(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">v</mi> </mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mo stretchy="false">[</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>Y</mi> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{X,Y}=\mathrm {corr} (X,Y)={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E[(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/703c6c57ff55837364925723de4071e5c3e19167" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:58.191ex; height:6.009ex;" alt="{\displaystyle \rho _{X,Y}=\mathrm {corr} (X,Y)={\mathrm {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={E[(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}}}"></span></dd></dl> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 係第 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> 個個案嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 數值；</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> 係第 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> 個個案嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 數值；</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bfe6d3f115b8d6cb595119ea9bc7962a11db65a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.034ex; height:2.176ex;" alt="{\displaystyle \mu _{X}}"></span> 係啲個案喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 上嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>；</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d61d6c2c7513bb6589518e6c034e7988aadf91c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.888ex; height:2.176ex;" alt="{\displaystyle \mu _{Y}}"></span> 係啲個案喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 上嘅平均值；</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/380c53c60c8301a5c80924b66363d831dfa80b9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.96ex; height:2.009ex;" alt="{\displaystyle \sigma _{X}}"></span> 係啲個案喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 上嘅<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a>；</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a9fb889441f514e155f65e77dc5b7c7a5a84f35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.814ex; height:2.009ex;" alt="{\displaystyle \sigma _{Y}}"></span> 係啲個案喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 上嘅標準差。</li></ul> <p>呢條式會得出一個<b>相關值</b>，個數值會喺 -1 同 1 之間，<a href="/wiki/%E8%B2%A0%E6%95%B8" title="負數">負數</a>表示兩個變數成反比（一個數值高嗰陣另一個傾向數值低），而<a href="/wiki/%E6%AD%A3%E6%95%B8" title="正數">正數</a>就表示兩個變數成正比（兩個數值傾向一齊高或者一齊低），個相關值愈接近零表示兩個變數之間嘅關係愈弱，而如果個相關值等於零就表示兩個變數根本唔啦更。喺做相關性研究嗰陣科學家會先收集一啲數據，再用好似上面呢條式等嘅方法計出變數之間嘅相關值，搵出研究緊嘅變數之間有乜嘢啦掕，而呢個過程俾出嚟嘅資訊喺將來有得攞嚟預測某啲現象<sup id="cite_ref-rodgers1988_78-0" class="reference"><a href="#cite_note-rodgers1988-78"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Correlation_coefficient.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Correlation_coefficient.png/510px-Correlation_coefficient.png" decoding="async" width="510" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Correlation_coefficient.png/765px-Correlation_coefficient.png 1.5x, //upload.wikimedia.org/wikipedia/commons/3/34/Correlation_coefficient.png 2x" data-file-width="960" data-file-height="530" /></a><figcaption>圖嘅 <a href="/wiki/X_%E8%BB%B8" class="mw-redirect" title="X 軸">X 軸</a>同 <a href="/wiki/Y_%E8%BB%B8" class="mw-redirect" title="Y 軸">Y 軸</a>代表變數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span>，每個有色圓點代表一個個案，每個個案都喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span> 上各有數值，而每幅圖表示唔同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{X,Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>,</mo> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{X,Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/722f0de20522fdccaab8cd208d982c45fc5ce39a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.546ex; height:2.343ex;" alt="{\displaystyle \rho _{X,Y}}"></span> 值下啲數據會係點嘅樣。</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="實驗性質"><span id=".E5.AF.A6.E9.A9.97.E6.80.A7.E8.B3.AA"></span>實驗性質</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=14" title="編輯小節: 實驗性質"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗</a></div> <p>實驗性研究可以話係做得再犀利啲，仲可以幫手搵出變數之間嘅<a href="/wiki/%E5%9B%A0%E6%9E%9C" class="mw-redirect" title="因果">因果</a><sup id="cite_ref-79" class="reference"><a href="#cite_note-79"><span class="cite-bracket">[</span>e 38<span class="cite-bracket">]</span></a></sup>關係。齋靠<a href="/wiki/%E8%A7%80%E5%AF%9F" title="觀察">觀察</a>變數之間嘅統計相關做唔到搵出事物之間嘅因果關係，噉係就算一個研究者觀察到 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 之間有<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著</a>嘅正統計相關，噉依然有三個可能性： </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> <a href="/wiki/%E5%9B%A0%E6%9E%9C" class="mw-redirect" title="因果">引致</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>、</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 引致 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>、</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 有同一個成因<sup id="cite_ref-80" class="reference"><a href="#cite_note-80"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup>。</li></ol> <p>上述嘅就係所謂嘅<a href="/wiki/%E7%9B%B8%E9%97%9C%E5%94%94%E8%98%8A%E5%90%AB%E5%9B%A0%E6%9E%9C" title="相關唔蘊含因果">相關唔蘊含因果</a><sup id="cite_ref-81" class="reference"><a href="#cite_note-81"><span class="cite-bracket">[</span>e 39<span class="cite-bracket">]</span></a></sup>問題－就算一個研究者搵到兩樣嘢之間有統計相關，都唔能夠即刻判斷兩樣嘢之間嘅因果關係。一般認為喺科學上，要搵出事物之間嘅因果關係，就實要靠<a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗</a>嘅方法：實驗係指研究者特登<b>操作</b><sup id="cite_ref-82" class="reference"><a href="#cite_note-82"><span class="cite-bracket">[</span>e 40<span class="cite-bracket">]</span></a></sup>某啲變數，再睇吓個操作會造成乜嘢效果，例如「如果佢特登操作 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>，就會見到 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 跟住出現，而如果佢唔特登操作 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 就唔會跟住出現」，佢就有理由相信 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 真係能夠引致 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span>。順帶一提，因為廿世紀嘅<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>好多時都係齋靠觀察嘅相關研究，所以成日俾人插佢哋，話佢哋唔能夠確立唔同社會現象之間嘅因果關係<sup id="cite_ref-Roth2002_83-0" class="reference"><a href="#cite_note-Roth2002-83"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-84" class="reference"><a href="#cite_note-84"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Alignment_of_nanospray.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Alignment_of_nanospray.jpg/450px-Alignment_of_nanospray.jpg" decoding="async" width="450" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Alignment_of_nanospray.jpg/675px-Alignment_of_nanospray.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Alignment_of_nanospray.jpg/900px-Alignment_of_nanospray.jpg 2x" data-file-width="4608" data-file-height="3072" /></a><figcaption>一個科學家喺實驗室入面做研究；實驗室嘅環境好乾淨而且高度受控，令研究過程冇咁易受到干擾。</figcaption></figure> <p>一個實驗嘅基本步驟係噉嘅<sup id="cite_ref-Roth2002_83-1" class="reference"><a href="#cite_note-Roth2002-83"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup>： </p> <ul><li>响做實驗之前，要用過往嘅<a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%87%E7%8D%BB" title="科學文獻">文獻</a>同理論嚟諗吓研究緊嘅變數之間會有啲乜嘢因果關係；</li> <li>將研究嘅對象擺喺一個<b>受控制嘅環境</b><sup id="cite_ref-85" class="reference"><a href="#cite_note-85"><span class="cite-bracket">[</span>e 41<span class="cite-bracket">]</span></a></sup>裏面－「受控制嘅環境」指一個受人工控制，唔會俾啲外來因素干擾嘅環境，例如係一間<a href="/wiki/%E5%AF%A6%E9%A9%97%E5%AE%A4" title="實驗室">實驗室</a>；</li> <li>將研究嘅對象分做至少兩組－<a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84" class="mw-redirect" title="實驗組">實驗組</a><sup id="cite_ref-86" class="reference"><a href="#cite_note-86"><span class="cite-bracket">[</span>e 42<span class="cite-bracket">]</span></a></sup>同<a href="/wiki/%E5%B0%8D%E7%85%A7%E7%B5%84" class="mw-redirect" title="對照組">對照組</a><sup id="cite_ref-87" class="reference"><a href="#cite_note-87"><span class="cite-bracket">[</span>e 43<span class="cite-bracket">]</span></a></sup>；</li> <li>喺實驗組嗰度人工噉操控「因」（呢個係<a href="/wiki/%E8%87%AA%E8%AE%8A%E6%95%B8" class="mw-redirect" title="自變數">自變數</a>；IV）嘅變數嘅數值，而對照組就唔郁；</li> <li>比較吓兩個組別喺「果」（呢個係<a href="/wiki/%E6%87%89%E8%AE%8A%E6%95%B8" class="mw-redirect" title="應變數">應變數</a>；DV）個數值係點；</li> <li>如果實驗組喺應變數嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>上同對照組顯著噉有差異（可以睇埋<a href="/wiki/%E5%AD%B8%E7%94%9F_t_%E6%B8%AC%E8%A9%A6" title="學生 t 測試">學生 t 測試</a>），噉就可以話發現咗一個因果關係－自變數嘅變化會令到應變數跟住起變化。</li></ul> <p>有<a href="/wiki/%E7%B6%93%E6%BF%9F%E5%AD%B8" title="經濟學">經濟學</a>同<a href="/wiki/%E7%AE%A1%E7%90%86%E5%AD%B8" title="管理學">管理學</a>方面嘅學者試過喺<a href="/wiki/%E7%BE%8E%E5%9C%8B" title="美國">美國</a><a href="/wiki/%E4%BC%8A%E5%88%A9%E8%AB%BE%E4%BC%8A%E5%B7%9E" class="mw-redirect" title="伊利諾伊州">伊利諾伊州</a>嘅一間<a href="/wiki/%E5%B7%A5%E5%BB%A0" title="工廠">工廠</a>嗰度過所謂嘅<a href="/wiki/%E9%9C%8D%E6%A1%91%E6%95%88%E6%87%89" title="霍桑效應">霍桑效應</a><sup id="cite_ref-88" class="reference"><a href="#cite_note-88"><span class="cite-bracket">[</span>e 44<span class="cite-bracket">]</span></a></sup>實驗。喺呢個實驗當中，啲研究者想研究<b>俾人睇住</b>會點樣影響<a href="/wiki/%E5%B7%A5%E4%BA%BA" class="mw-disambig" title="工人">工人</a>嘅生產<a href="/wiki/%E6%95%88%E7%8E%87" title="效率">效率</a>－佢哋研究嘅總體係<b>世界上所有嘅工人</b>，但佢哋冇可能一次研究嗮咁多工人，所以只係攞咗一小部份嚟研究－嗰間工廠嘅工人（抽樣）。佢哋跟住做以下嘅嘢： </p> <ul><li>佢哋嘗試增強間廠入面嘅<a href="/wiki/%E7%87%88%E5%85%89" class="mw-redirect" title="燈光">燈光</a>（<b>燈光</b>係 IV），而燈光影響啲工人會唔會俾人睇到（IV 理應會引致嘅嘢），睇吓佢點樣影響流水線工人嘅生產率（<b>生產率</b>係應變數）；</li> <li>研究人員首先檢測咗間廠既有嘅生產率，打後再改變車間嘅燈光強度（人工噉操控 IV 嘅數值），再睇吓有乜嘢結果；</li> <li>結果係生產率喺實驗環境之下提升咗－表示「燈光」同「生產率」兩個變數之間有關係，而且前者係因，後者係果。</li></ul> <p>呢個實驗好出名，不過有唔少科學家都嫌呢個實驗嘅設計有少少唔掂，例如係缺少咗<a href="/wiki/%E5%B0%8D%E7%85%A7%E7%B5%84" class="mw-redirect" title="對照組">對照組</a>同埋「實驗環境唔係咁受控」呀噉<sup id="cite_ref-89" class="reference"><a href="#cite_note-89"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="假說檢定"><span id=".E5.81.87.E8.AA.AA.E6.AA.A2.E5.AE.9A"></span>假說檢定</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=15" title="編輯小節: 假說檢定"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E5%81%87%E8%AA%AA%E6%AA%A2%E5%AE%9A" title="假說檢定">假說檢定</a></div> <p><a href="/wiki/%E5%81%87%E8%AA%AA%E6%AA%A2%E5%AE%9A" title="假說檢定">假說檢定</a><sup id="cite_ref-90" class="reference"><a href="#cite_note-90"><span class="cite-bracket">[</span>e 45<span class="cite-bracket">]</span></a></sup>可以話係<a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">推論統計學</a>當中最重要嘅一個工序，指驗證一個<a href="/wiki/%E5%81%87%E8%AA%AA" title="假說">假說</a>（指一個仲未搵到<a href="/wiki/%E8%AD%89%E6%93%9A" title="證據">證據</a>支撐，但研究者有理由認為好可能係真確嘅論述）嘅過程。一個做假說檢定嘅研究者所做嘅工序如下： </p> <ol><li>睇過有關佢所研究嗰樣嘢嘅文獻，</li> <li>建基於已有嘅知識，作出一啲有關嗰樣嘢嘅新假說—「我睇過打前嘅研究，我認為有咗已知嘅嘢，我可以作出以下嘅判斷，而驗證呢個判斷係咪正確能夠帶嚟新知識」，</li> <li>諗出一個驗證呢假說嘅程序，</li> <li>用呢個程序攞數據，</li> <li>對數據作出分析，</li> <li>用分析結果判斷個假說係咪真確<sup id="cite_ref-myers2010_91-0" class="reference"><a href="#cite_note-myers2010-91"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup>。</li></ol> <p>假說檢定嘅過程會用到以下嘅概念： </p> <div class="mw-heading mw-heading3"><h3 id="估計量"><span id=".E4.BC.B0.E8.A8.88.E9.87.8F"></span>估計量</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=16" title="編輯小節: 估計量"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E4%BC%B0%E8%A8%88%E9%87%8F" title="估計量">估計量</a></div> <p>嚴格嚟講，個總體嘅<a href="/wiki/%E5%8F%83%E6%95%B8" title="參數">參數</a><sup id="cite_ref-92" class="reference"><a href="#cite_note-92"><span class="cite-bracket">[</span>e 46<span class="cite-bracket">]</span></a></sup>（指形容緊某個<a href="/wiki/%E7%B3%BB%E7%B5%B1" title="系統">系統</a>嘅特性）係不可知嘅－淨係有得透過個樣本嘅數值嚟<b>估</b>吓呢啲參數嘅數值。例如喺上面個中華白海豚研究嘅例子噉，要知道嗮古往今來所有中華白海豚嘅身長原則上係冇可能嘅，所以研究者亦都冇方法知道「全世界嘅白海豚嘅平均身長」嘅真正數值－唔單只啲科學家唔夠人力物力度嗮世上咁多隻白海豚，而且過去嘅白海豚同埋仲未出世嘅白海豚嘅身長都係冇辦法量度嘅，所以成個研究啲科學家都係喺度假設緊個樣本能夠代表到全世界嘅白海豚，並且用個樣本入面嘅白海豚嘅平均身長嚟估計全世界嘅白海豚嘅平均身長。除咗平均值，個樣本嘅<a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8" class="mw-redirect" title="變異數">變異數</a>等嘅敘述統計資料都會俾科學家攞嚟估計個總體嘅參數，呢啲俾人用嚟估計總體參數嘅就係所謂嘅<a href="/wiki/%E4%BC%B0%E8%A8%88%E9%87%8F" title="估計量">估計量</a><sup id="cite_ref-93" class="reference"><a href="#cite_note-93"><span class="cite-bracket">[</span>e 47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-94" class="reference"><a href="#cite_note-94"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="信心區間"><span id=".E4.BF.A1.E5.BF.83.E5.8D.80.E9.96.93"></span>信心區間</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=17" title="編輯小節: 信心區間"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E4%BF%A1%E5%BF%83%E5%8D%80%E9%96%93" title="信心區間">信心區間</a></div> <p>做科研嗰陣啲研究人員可以睇到嘅就淨係得個樣本嗰啲數值，而個總體嗰柞真實嘅數值係不可知嘅，所以任何由個樣本嗰度估計出嚟嘅數值頂嗮櫳都淨係有得話係個總體嘅<a href="/wiki/%E8%BF%91%E4%BC%BC%E5%80%BC" title="近似值">近似值</a>。<a href="/wiki/%E4%BF%A1%E5%BF%83%E5%8D%80%E9%96%93" title="信心區間">信心區間</a><sup id="cite_ref-95" class="reference"><a href="#cite_note-95"><span class="cite-bracket">[</span>e 48<span class="cite-bracket">]</span></a></sup>係指「有信心總體個真實數值係喺入面嘅區間」，喺做統計嗰時會俾人攞嚟表述個樣本嘅數值同個總體嘅真實數值之間估計差幾遠， </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(L_{n}<\theta <U_{n})=\gamma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo><</mo> <mi>θ</mi> <mo><</mo> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>γ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(L_{n}<\theta <U_{n})=\gamma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6246d6f24638c7cd2f1d95646e387fea5c926801" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.81ex; height:2.843ex;" alt="{\displaystyle P(L_{n}<\theta <U_{n})=\gamma }"></span></dd></dl> <p>舉個例說明，最常用嘅係「95% 信心區間」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma =0.95}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo>=</mo> <mn>0.95</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma =0.95}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da2269657267c9cbd5a29b9c114cc666dd2271b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.495ex; height:2.676ex;" alt="{\displaystyle \gamma =0.95}"></span>），用返上面白海豚嘅例子，啲科研人員會用個樣本入面嘅海豚嘅身長平均值嚟估計嗰個不可知嘅「世上所有白海豚嘅身長嘅平均值」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span>），而佢哋可以用一啲統計方法計個「白海豚身長平均值嘅 95% 信心區間」出嚟－呢個值係指「有信心 95% 機會世上所有白海豚嘅身長嘅平均值嘅真實數值係喺 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebec334cb04f246db1139e2ca6be0b957d2ef520" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.801ex; height:2.509ex;" alt="{\displaystyle L_{n}}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67b641ce10cb5e865397c4efe647cbffed98a024" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.806ex; height:2.509ex;" alt="{\displaystyle U_{n}}"></span> 之間」<sup id="cite_ref-96" class="reference"><a href="#cite_note-96"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup>。 </p> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:NormalDist1.96.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/NormalDist1.96.png/450px-NormalDist1.96.png" decoding="async" width="450" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/bf/NormalDist1.96.png 1.5x" data-file-width="499" data-file-height="333" /></a><figcaption><center>「有信心變數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 嘅真實平均值 95% 機會係喺 -1.96 同 1.96 之間。」</center></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="虛無同備擇假說"><span id=".E8.99.9B.E7.84.A1.E5.90.8C.E5.82.99.E6.93.87.E5.81.87.E8.AA.AA"></span>虛無同備擇假說</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=18" title="編輯小節: 虛無同備擇假說"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說">虛無假說</a>、<a href="/wiki/%E5%82%99%E6%93%87%E5%81%87%E8%AA%AA" title="備擇假說">備擇假說</a>同<a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E5%90%8C%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" title="第一型同第二型錯誤">第一型同第二型錯誤</a></div> <p><a href="/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說">虛無假說</a><sup id="cite_ref-97" class="reference"><a href="#cite_note-97"><span class="cite-bracket">[</span>e 49<span class="cite-bracket">]</span></a></sup>（<a href="/wiki/%E6%95%B8%E5%AD%B8%E7%AC%A6%E8%99%9F" title="數學符號">符號</a>：<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>）同<a href="/wiki/%E5%82%99%E6%93%87%E5%81%87%E8%AA%AA" title="備擇假說">備擇假說</a><sup id="cite_ref-98" class="reference"><a href="#cite_note-98"><span class="cite-bracket">[</span>e 50<span class="cite-bracket">]</span></a></sup>（<a href="/wiki/%E6%95%B8%E5%AD%B8%E7%AC%A6%E8%99%9F" title="數學符號">符號</a>：<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span>）係做科研上成日會用到嘅行話： </p> <ul><li>虛無假說係指做一份研究嗰陣嘅預設立場，指「兩個量度嘅變數之間冇關係」呢句嘢，而</li> <li>備擇假說係做一份研究嗰陣嘗試驗證嘅立場，指「兩個量度嘅變數之間有關係」呢句嘢。</li></ul> <p>舉個例說明，假想有個<a href="/wiki/%E8%AA%8D%E7%9F%A5%E5%BF%83%E7%90%86%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="認知心理學家">認知心理學家</a>想驗證「年紀」同「<a href="/wiki/%E8%A8%98%E6%86%B6%E5%8A%9B" class="mw-redirect" title="記憶力">記憶力</a>」呢兩個變數之間嘅關係，於是佢就搵咗兩批人返嚟做佢嘅<a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>，第一批人年紀喺 20 至 30 歲之間，第二批人年紀喺 50 至 60 歲之間，再用一啲測試量度呢兩批人嘅記憶力，設第一批人喺記憶力測試上嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均</a>得分係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6899621035d3359b9c1c064739b54c7004e220d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{1}}"></span>，而第二批人喺同一柞測試上嘅平均得分係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f841461ae8f2eafec3fe879f7c061a73c2f7170" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{2}}"></span>，噉呢份研究嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> 係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}=\mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}=\mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf91a4341c22a09d364352a9caa9b116084357ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.01ex; height:2.176ex;" alt="{\displaystyle \mu _{1}=\mu _{2}}"></span>，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span> 係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}\neq \mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≠</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}\neq \mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc1b01ed0016345ce726b489eb643eae68db2de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.01ex; height:2.676ex;" alt="{\displaystyle \mu _{1}\neq \mu _{2}}"></span>，當中後者係個認知科學家想證實嘅嘢<sup id="cite_ref-Adetal2007_99-0" class="reference"><a href="#cite_note-Adetal2007-99"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup>。虛無假說同備擇假說呢兩個詞語查實好簡單，但呢兩個詞語令到寫科研報告嗰陣慳好多位－啲科學家唔使吓吓都講嗮成句假說出嚟<sup id="cite_ref-100" class="reference"><a href="#cite_note-100"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup>。 </p><p>喺做假說檢定嗰陣，一般會將可能會出現嘅錯誤分兩種<sup id="cite_ref-101" class="reference"><a href="#cite_note-101"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup>： </p> <ul><li><a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E9%8C%AF%E8%AA%A4" class="mw-redirect" title="第一型錯誤">第一型錯誤</a><sup id="cite_ref-102" class="reference"><a href="#cite_note-102"><span class="cite-bracket">[</span>e 51<span class="cite-bracket">]</span></a></sup>指錯誤噉否定咗 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>，得出咗個<b>假陽性</b><sup id="cite_ref-103" class="reference"><a href="#cite_note-103"><span class="cite-bracket">[</span>e 52<span class="cite-bracket">]</span></a></sup>結果－兩個變數查實有啦掕，研究者但搵到咗一個陽性結果出嚟。</li> <li><a href="/wiki/%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" class="mw-redirect" title="第二型錯誤">第二型錯誤</a><sup id="cite_ref-104" class="reference"><a href="#cite_note-104"><span class="cite-bracket">[</span>e 53<span class="cite-bracket">]</span></a></sup>指 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> 其實係錯，但就冇俾人成功噉否定到，得出咗個<b>假陰性</b><sup id="cite_ref-105" class="reference"><a href="#cite_note-105"><span class="cite-bracket">[</span>e 54<span class="cite-bracket">]</span></a></sup>－兩個變數實際上有關但就搵到個陰性結果。</li></ul> <p>呢啲錯誤會發生有好多原因，包括係科研入面嘅某啲<a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%80%A7" class="mw-redirect" title="隨機性">隨機性</a>－例如有份研究想睇吓兩個地區嘅狼嘅平均身長係咪有分別，佢哋隨機噉喺兩個地區度抽樣，再度吓啲狼嘅身長，可能兩個地區啲狼嘅平均身長係冇分別嘅（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> 係真），但喺隨機抽樣嘅過程當中，咁啱得咁橋喺地區 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 抽咗啲嗰頭最大隻嘅狼出嚟，而喺地區 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 又咁橋淨係抽嗮啲嗰頭最細隻嘅狼出嚟，搞到最後搵到出嚟個結果話兩個地區啲狼嘅身長有<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著</a>分別，即係錯誤噉排除咗 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>－第一型錯誤。喺呢個個案入面，啲科研人員之所以搵到兩個變數（<b>地區</b>同埋<b>啲狼嘅身長</b>）之間有關唔係因為兩者之間真係有關，而係抽樣嗰陣唔好彩。呢啲事喺科學界間唔鐘會發生<sup id="cite_ref-106" class="reference"><a href="#cite_note-106"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="顯著性"><span id=".E9.A1.AF.E8.91.97.E6.80.A7"></span>顯著性</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=19" title="編輯小節: 顯著性"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">統計顯著性</a></div> <p><a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">統計顯著性</a><sup id="cite_ref-107" class="reference"><a href="#cite_note-107"><span class="cite-bracket">[</span>e 55<span class="cite-bracket">]</span></a></sup>（符號係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span>）<sup id="cite_ref-108" class="reference"><a href="#cite_note-108"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup>，簡稱<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著性</a>，反映一個俾統計者接受咗嘅假說 </p> <dl><dd>「有幾大機會係真確。」</dd></dl> <p>事實上，統計學喺答問題嗰陣好少可會話俾到<b>真</b>同<b>假</b>咁二元嘅答案。統計方法本質上係帶咗些少隨機性喺度，好似係頭先提咗嘅第一型錯誤嘅例子就顯示到，無論一份研究點精密，都梗會有少少機會會出錯，而呢啲錯誤好多時係人為冇可能控制得到嘅：啲科學家一方面冇可能度得嗮古往今來所有嘅狼嘅身長，但另一方面，佢哋一做抽樣，就梗會有機會攞到個代表唔到個總體嘅樣本－即係話無論點，用統計方法硬係會或多或少帶有啲<a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A" title="不確定">不確定</a>。於是乎統計學家就決定咗：用統計學做親啲乜嘢研究嗰陣，都唔會俾二元性嘅答案，而係會俾出好似信心區間呢類「某句嘢有幾大機會係啱」呢類帶咗啲機會率喺度嘅答案，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 就係用嚟做呢樣嘢嘅概念<sup id="cite_ref-109" class="reference"><a href="#cite_note-109"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup>。 </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 嘅定義係「如果<a href="/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說">虛無假說</a>係真，呢個結果出現嘅<a href="/wiki/%E6%A9%9F%E6%9C%83%E7%8E%87" class="mw-redirect" title="機會率">機會率</a>」， </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=P{\big (}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=P{\big (}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1af094c2846cbb23c6dfe30eb2e39c2f19d4f5e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:7.168ex; height:3.176ex;" alt="{\displaystyle p=P{\big (}}"></span>睇到個噉嘅結果<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mid H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">∣</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mid H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1bfac5e203e7ad6bb759e6f9dc0857f520e098b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.632ex; height:2.843ex;" alt="{\displaystyle \mid H_{0}}"></span> 係真 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce761ae2e3b447058cb0fbb2ac4bdaa3b709b2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:1.065ex; height:3.176ex;" alt="{\displaystyle {\big )}}"></span><sup id="cite_ref-110" class="reference"><a href="#cite_note-110"><span class="cite-bracket">[</span>註 2<span class="cite-bracket">]</span></a></sup></dd></dl> <p>一般嚟講，如果柞統計分析顯示 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 嘅數值係細過某個特定嘅數值（通常係 5%）嘅話（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p<.05}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo><</mo> <mn>.05</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p<.05}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd86e97490185df4a6ddb76d77a61217f63471c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:7.329ex; height:2.509ex;" alt="{\displaystyle p<.05}"></span>）<sup id="cite_ref-111" class="reference"><a href="#cite_note-111"><span class="cite-bracket">[</span>註 3<span class="cite-bracket">]</span></a></sup>－「如果 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> 係真，會得出呢個結果嘅機會好微」，噉研究者就有夠強嘅理由相信 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> 好有可能唔係真，噉做分析嗰個人就會當句 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span> 係真確嘅，並且<b>拒絕個虛無假說</b><sup id="cite_ref-112" class="reference"><a href="#cite_note-112"><span class="cite-bracket">[</span>e 56<span class="cite-bracket">]</span></a></sup>。喺實際嘅科研論文當中做統計嘅話，研究者幾乎實會報告自己做咗統計分析得出嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 值，並且用「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 值好細」呢一點嚟說服人，話自己嗰句 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span> 係真嘅<sup id="cite_ref-myers2010_91-1" class="reference"><a href="#cite_note-myers2010-91"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="比較平均值"><span id=".E6.AF.94.E8.BC.83.E5.B9.B3.E5.9D.87.E5.80.BC"></span>比較平均值</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=20" title="編輯小節: 比較平均值"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%AF%94%E8%BC%83%E5%B9%B3%E5%9D%87%E5%80%BC" class="mw-redirect" title="比較平均值">比較平均值</a>同<a href="/wiki/T_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="T 測試">T 測試</a></div> <p>要測試一個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span>，其中一種最常見嘅做法就係<a href="/wiki/%E6%AF%94%E8%BC%83%E5%B9%B3%E5%9D%87%E5%80%BC" class="mw-redirect" title="比較平均值">比較平均值</a><sup id="cite_ref-113" class="reference"><a href="#cite_note-113"><span class="cite-bracket">[</span>e 57<span class="cite-bracket">]</span></a></sup>，即係比較個樣本入面唔同組之間喺個變數嘅平均值上有冇差異。喺最簡單嗰種情況－得兩組要比較－之下，研究者可以用<a href="/wiki/%E5%AD%B8%E7%94%9F_t_%E6%B8%AC%E8%A9%A6" title="學生 t 測試">學生 t 測試</a><sup id="cite_ref-114" class="reference"><a href="#cite_note-114"><span class="cite-bracket">[</span>e 58<span class="cite-bracket">]</span></a></sup>（以下簡稱 <a href="/wiki/T_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="T 測試">t 測試</a>）。學生 t 測試呢種方法可以攞嚟分析兩個組（通常係<a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84%E5%90%8C%E5%B0%8D%E7%85%A7%E7%B5%84" title="實驗組同對照組">實驗組同對照組</a>）之間喺個指定變數嘅數值上係咪有<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著</a>嘅差異，當中最原始嗰種<a href="/wiki/%E7%8D%A8%E7%AB%8B%E6%A8%A3%E6%9C%AC_t_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="獨立樣本 t 測試">獨立樣本 t 測試</a><sup id="cite_ref-115" class="reference"><a href="#cite_note-115"><span class="cite-bracket">[</span>e 59<span class="cite-bracket">]</span></a></sup>係 t 測試嘅一種，獨立樣本 t 測試假設咗三點<sup id="cite_ref-ttestthingies_116-0" class="reference"><a href="#cite_note-ttestthingies-116"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup>： </p> <ol><li>個<a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a>喺個變數上嘅<a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a>係一個<a href="/wiki/%E5%B8%B8%E6%85%8B%E5%88%86%E4%BD%88" title="常態分佈">常態分佈</a>；</li> <li>要比較嗰兩個組係<a href="/wiki/%E7%8D%A8%E7%AB%8B_(%E6%A6%82%E7%8E%87%E8%AB%96)" title="獨立 (概率論)">獨立</a>（指兩個組入面啲個體係分別噉<a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a>入組嘅）嘅；</li> <li>要比較嗰兩個組喺個變數上嘅<a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8" class="mw-redirect" title="變異數">變異數</a>相等。</li></ol> <p>用返同上面類似嘅例子，班研究人員可能想做個實驗，睇吓提高氣溫會唔會改變狼嘅食量，佢哋可以 </p> <ul><li>隨機噉由全世界嘅狼嗰度抽一柞（例如係 200 隻）出嚟，將佢哋分做兩組－<a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84%E5%90%8C%E5%B0%8D%E7%85%A7%E7%B5%84" title="實驗組同對照組">實驗組同對照組</a>，兩組各有 100 隻狼，將前者擺喺一個有暖氣嘅環境度養，而後者就擺喺一棟模仿自然環境（氣溫正常）嘅地方度養（<b>氣溫</b>係<a href="/wiki/%E8%87%AA%E8%AE%8A%E6%95%B8" class="mw-redirect" title="自變數">自變數</a>）；</li> <li>跟手啲研究人員就要<a href="/wiki/%E9%87%8F%E5%BA%A6" title="量度">量度</a>個<a href="/wiki/%E6%87%89%E8%AE%8A%E6%95%B8" class="mw-redirect" title="應變數">應變數</a>（食量）－一個可能嘅方法係用<a href="/wiki/%E6%94%9D%E5%BD%B1%E6%A9%9F" title="攝影機">攝影機</a>監察住啲狼嘅一舉一動，佢哋一食嘢就記錄低，並且用影片影到嘅影像估計樣本入面嘅每隻狼大約每日食咗幾多公斤嘅嘢食。呢個步驟會得出一大柞數據，表述每一個個體喺個應變數上嘅數值（即係每隻狼嘅日常食量），而</li> <li>由呢啲數據嗰度，研究者亦會順理成章噉計到兩個組分別喺個應變數上嘅<a href="/wiki/%E5%B9%B3%E5%9D%87%E5%80%BC" title="平均值">平均值</a>－「實驗組啲狼嘅平均日常食量」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6899621035d3359b9c1c064739b54c7004e220d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{1}}"></span>）同「對照組啲狼嘅平均日常食量」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f841461ae8f2eafec3fe879f7c061a73c2f7170" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{2}}"></span>）；</li> <li>下一步就要睇吓 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6899621035d3359b9c1c064739b54c7004e220d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{1}}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f841461ae8f2eafec3fe879f7c061a73c2f7170" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{2}}"></span> 之間係咪有<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著</a>嘅分別－如果有，研究人員就有得否定個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span>，並且話今次攞到嘅實驗數據撐佢哋個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d4d9a872a55b209f2eb7cc23a71e5e1541bd1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{1}}"></span> 係「提高氣溫會影響狼嘅食量」呢句嘢）。</li> <li>因為佢哋嗰兩個組入面個體係分別噉抽樣嘅，而且得一個應變數（狼嘅食量），所以佢哋可以用獨立樣本 t 測試。</li></ul> <p>用好似 t 測試噉嘅統計分析可以提高一份研究嘅說服力：一方面，啲研究者可以淨係靠直接比較兩個組喺個變數上各自嘅平均值（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6899621035d3359b9c1c064739b54c7004e220d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{1}}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f841461ae8f2eafec3fe879f7c061a73c2f7170" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.456ex; height:2.176ex;" alt="{\displaystyle \mu _{2}}"></span>），但噉做唔會有乜嘢說服力；個變數係大致上呈常態分佈嘅－一隻狼嘅日常食量通常會接近所有狼嘅日常食量嘅平均值，離平均值愈遠嘅數值就會出現得愈少；如果齋靠比較兩個組嘅平均值，就等於冇考慮到抽樣等過程入面嘅隨機性－可能只係抽樣嗰陣唔好彩，大食嘅狼咁橋分嗮去實驗組嗰度，而食嘢少嘅狼就咁啱分嗮去對照組。於是啲研究人員為咗要提高佢哋份研究嘅說服力，就要攞啲數據嚟計吓<sup id="cite_ref-derrick2017_117-0" class="reference"><a href="#cite_note-derrick2017-117"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup>。 </p> <div style="clear: both;"></div> <figure class="mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Gaussian_differences.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Gaussian_differences.svg/570px-Gaussian_differences.svg.png" decoding="async" width="570" height="717" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Gaussian_differences.svg/855px-Gaussian_differences.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Gaussian_differences.svg/1140px-Gaussian_differences.svg.png 2x" data-file-width="543" data-file-height="683" /></a><figcaption><a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84%E5%90%8C%E5%B0%8D%E7%85%A7%E7%B5%84" title="實驗組同對照組">實驗組同對照組</a>喺個變數上各有個<a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a>（紅色線同藍色線）；上圖顯示兩組差異細－組之間嘅差異（由 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{1}-\mu _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{1}-\mu _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f923f77cc9f1769b60b5736084fbf4fc6ca565e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.752ex; height:2.509ex;" alt="{\displaystyle \mu _{1}-\mu _{2}}"></span> 反映）同組內部差異（由 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 反映）比起嚟好細，而下圖顯示兩組差異大。組嘅數量係三或者以上（<a href="/wiki/ANOVA" class="mw-redirect" title="ANOVA">ANOVA</a>）嗰陣可以用同樣方法想像。</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="t_測試流程"><span id="t_.E6.B8.AC.E8.A9.A6.E6.B5.81.E7.A8.8B"></span>t 測試流程</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=21" title="編輯小節: t 測試流程"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E7%AD%89%E5%88%86%E6%95%A3%E6%80%A7" title="等分散性">等分散性</a></div> <p>要評估兩組之間嘅差異嘅顯著性，首先要計兩組嘅<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a>（符號係「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>」或者「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle \sigma }"></span>」）出嚟： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00eb0cde84f0a838a2de6db9f382866427aeb3bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:22.628ex; height:7.676ex;" alt="{\displaystyle s={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}.}"></span>，當中</dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> 係<a href="/wiki/%E6%A8%A3%E6%9C%AC%E5%A4%A7%E7%B4%B0" title="樣本大細">樣本大細</a>（個樣本入面嘅個體數量，樣本嘅嘥<ruby><rb>士</rb><rt><span>si<span class="Jpingtone">2</span></span></rt></ruby>），<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"></span> 係個體 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> 喺個變數上嘅數值，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>x</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fa4039bbc2a0048c3a3c02e5fd24390cab0dc97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.445ex; height:2.343ex;" alt="{\displaystyle {\overline {x}}}"></span> 就係成個樣本喺個變數上嘅平均值。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 呢個數值反映咗個樣本入面每一個個體喺個變數上面嘅數值平均嚟講同成個樣本嘅平均值差幾遠，亦即係反映咗一個組嘅內部差異，而呢啲內部差異係隨機性嘅個體差異。<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 大嘅話就表示個體同個體之間嘅差異好大，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 細嘅話就表示啲個體普遍同成個樣本嘅平均唔係差好遠。得到兩個組嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 嘅數值，仲可以用另外一啲統計方法顯示到兩個組嘅標準差冇明顯差異。假設兩組嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> 冇差異（<a href="/wiki/%E7%AD%89%E5%88%86%E6%95%A3%E6%80%A7" title="等分散性">等分散性</a><sup id="cite_ref-118" class="reference"><a href="#cite_note-118"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup>）嘅話，就可以做下一步，計以下嘅數值： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}{\sqrt {2/n}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </msqrt> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}{\sqrt {2/n}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cad0574bf2031d40d0194bfbe427567367aab4a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.683ex; height:7.009ex;" alt="{\displaystyle t={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{s_{p}{\sqrt {2/n}}}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> 係成個樣本嘅大細，而 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {X}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {X}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6b461daee412274d0ee77810b2f9dc8d1d5501" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.034ex; height:2.843ex;" alt="{\displaystyle {\bar {X}}_{1}}"></span> 同 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {X}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {X}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05d52e00897984ea7c3e557bb8029bfee8e06939" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.034ex; height:2.843ex;" alt="{\displaystyle {\bar {X}}_{2}}"></span> 就係兩個組分別喺個變數上嘅平均值，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/577e6806693dcbbd731632cb9e9ead8d66947cb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.15ex; height:2.343ex;" alt="{\displaystyle s_{p}}"></span> 係兩個組嘅標準差（假設咗兩個組嘅標準差相等），最後計到一個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> 值出嚟，呢個數值同「兩個組嘅平均值嘅差距」成正比，同「兩個組嘅標準差」成反比。如果 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> 值好大，噉就表示咗「兩個組之間嘅差異」大過「組嘅內部差異」好多，噉就表示「個實驗嘅操作造成嘅差異」大過「隨機性嘅個體差異」－<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> 值愈大愈表示個實驗嘅操作嘅效果明顯過個體差異，愈係表示兩個組之間嘅差異係因為實驗嘅操作造成嘅。所以 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> 值愈大，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 值（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=P{\big (}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">(</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=P{\big (}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1af094c2846cbb23c6dfe30eb2e39c2f19d4f5e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:7.168ex; height:3.176ex;" alt="{\displaystyle p=P{\big (}}"></span>睇到個噉嘅結果<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mid H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">∣</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mid H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1bfac5e203e7ad6bb759e6f9dc0857f520e098b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.632ex; height:2.843ex;" alt="{\displaystyle \mid H_{0}}"></span> 係真 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\big )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.2em" minsize="1.2em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\big )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce761ae2e3b447058cb0fbb2ac4bdaa3b709b2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:1.065ex; height:3.176ex;" alt="{\displaystyle {\big )}}"></span>）理應會愈細<sup id="cite_ref-119" class="reference"><a href="#cite_note-119"><span class="cite-bracket">[</span>註 4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-derrick2017_117-1" class="reference"><a href="#cite_note-derrick2017-117"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading4"><h4 id="t_測試變種"><span id="t_.E6.B8.AC.E8.A9.A6.E8.AE.8A.E7.A8.AE"></span>t 測試變種</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=22" title="編輯小節: t 測試變種"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8%E5%88%86%E6%9E%90" class="mw-redirect" title="變異數分析">變異數分析</a></div> <ul><li><a href="/wiki/%E9%85%8D%E5%B0%8D%E6%A8%A3%E6%9C%AC_t_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="配對樣本 t 測試">配對樣本 t 測試</a><sup id="cite_ref-120" class="reference"><a href="#cite_note-120"><span class="cite-bracket">[</span>e 60<span class="cite-bracket">]</span></a></sup>：指做 t 測試嗰兩個組<b>唔</b>係<a href="/wiki/%E7%8D%A8%E7%AB%8B%E5%90%8C%E5%88%86%E4%BD%88" title="獨立同分佈">獨立同分佈</a>嘅，研究者做咗某啲嘢，令一組數值當中每一個都喺另外嗰組當中有個對應，例如做個心理學實驗，研究者想知個實驗操作會引致變數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 有乜變化，於是就喺實驗前量度 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 一次，跟住對受試者做實驗操作，然後喺實驗後又量度 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 一次（睇返<a href="/wiki/%E9%87%8D%E8%A4%87%E9%87%8F%E6%95%B8%E8%A8%AD%E8%A8%88" class="mw-redirect" title="重複量數設計">重複量數設計</a>）。喺呢個情況下，每位受試者都有一個 <dl><dd>「實驗前嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 值」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{pre}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pre</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{pre}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69c1ad290f0ce8c83c27b75852c519f8bedd8eff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.445ex; height:2.843ex;" alt="{\displaystyle X_{\text{pre}}}"></span>）同</dd> <dd>「實驗後嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> 值」（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{post}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>post</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{post}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ed5746efaab99f0d98b89e735838d896ed9631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.18ex; height:2.843ex;" alt="{\displaystyle X_{\text{post}}}"></span>），</dd></dl> <ul><li>研究者想比較兩組數值（總共有 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> 個數值，而受試者數量係 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95c3931a3fa03cc98cfacd2c49a7ca35b96eaa9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.72ex; height:2.843ex;" alt="{\displaystyle n/2}"></span>），但兩組數值唔係獨立同分佈嘅－每個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{pre}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pre</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{pre}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69c1ad290f0ce8c83c27b75852c519f8bedd8eff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.445ex; height:2.843ex;" alt="{\displaystyle X_{\text{pre}}}"></span> 值都有一個相應嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{post}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>post</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{post}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ed5746efaab99f0d98b89e735838d896ed9631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.18ex; height:2.843ex;" alt="{\displaystyle X_{\text{post}}}"></span> 值（一位受試者嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{pre}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>pre</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{pre}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69c1ad290f0ce8c83c27b75852c519f8bedd8eff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.445ex; height:2.843ex;" alt="{\displaystyle X_{\text{pre}}}"></span> 值同佢嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X_{\text{post}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>post</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X_{\text{post}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7ed5746efaab99f0d98b89e735838d896ed9631" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.18ex; height:2.843ex;" alt="{\displaystyle X_{\text{post}}}"></span> 值）<sup id="cite_ref-derrick2017_117-2" class="reference"><a href="#cite_note-derrick2017-117"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup>。</li></ul></li> <li><a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8%E5%88%86%E6%9E%90" class="mw-redirect" title="變異數分析">變異數分析</a><sup id="cite_ref-121" class="reference"><a href="#cite_note-121"><span class="cite-bracket">[</span>e 61<span class="cite-bracket">]</span></a></sup>：一系列用嚟分析唔同組嘅平均值嘅方法；假想家陣個研究者想比較三組喺變數 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 嘅平均值上嘅差異，如果三組之間有<a href="/wiki/%E7%B5%B1%E8%A8%88%E9%A1%AF%E8%91%97%E6%80%A7" class="mw-redirect" title="統計顯著性">顯著</a>嘅差異，噉組之間嘅 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 嘅<a href="/wiki/%E8%AE%8A%E7%95%B0%E6%95%B8" class="mw-redirect" title="變異數">變異數</a>應該會大過組內部嘅好多。最簡單嘅<a href="/wiki/%E5%96%AE%E5%9B%A0%E5%AD%90%E8%AE%8A%E7%95%B0%E6%95%B8%E5%88%86%E6%9E%90" class="mw-redirect" title="單因子變異數分析">單因子變異數分析</a><sup id="cite_ref-122" class="reference"><a href="#cite_note-122"><span class="cite-bracket">[</span>e 62<span class="cite-bracket">]</span></a></sup>分析一個<a href="/wiki/%E6%87%89%E8%AE%8A%E6%95%B8" class="mw-redirect" title="應變數">應變數</a>喺三個或者以上嘅組之間嘅差異（<b>組</b>就係<a href="/wiki/%E8%87%AA%E8%AE%8A%E6%95%B8" class="mw-redirect" title="自變數">自變數</a>），考慮以下嘅數值<sup id="cite_ref-123" class="reference"><a href="#cite_note-123"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup>： <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\frac {\text{組 之 間 嘅 變 異}}{\text{組 內 部 嘅 變 異}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>組 之 間 嘅 變 異</mtext> <mtext>組 內 部 嘅 變 異</mtext> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {\text{組之間嘅變異}}{\text{組內部嘅變異}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a3e6d91c697035987f7b5d598beb89190a74d99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:19.982ex; height:7.843ex;" alt="{\displaystyle F={\frac {\text{組之間嘅變異}}{\text{組內部嘅變異}}}}"></span></dd></dl> <ul><li>原則上，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> 數值愈大，研究者就愈有理由相信組之間有顯著嘅差異。</li></ul></li></ul> <p>...等等。 </p> <div class="mw-heading mw-heading2"><h2 id="誤用"><span id=".E8.AA.A4.E7.94.A8"></span>誤用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=23" title="編輯小節: 誤用"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Misusestatistics_0001.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Misusestatistics_0001.png/300px-Misusestatistics_0001.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Misusestatistics_0001.png/450px-Misusestatistics_0001.png 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f9/Misusestatistics_0001.png 2x" data-file-width="480" data-file-height="480" /></a><figcaption>同一樣嘅數據有得用唔同嘅方法呈現。</figcaption></figure> <div role="note" class="hatnote">内文：<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8%E5%98%85%E8%AA%A4%E7%94%A8" title="統計學嘅誤用">統計學嘅誤用</a></div> <p>統計學上嘅數據同分析方法對科研有巨大嘅幫助，但又時不時會俾人誤用。有人就曾經噉講<sup id="cite_ref-124" class="reference"><a href="#cite_note-124"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup>： </p> <table align="center" style="border-collapse:collapse; border-style:none; background-color:transparent; margin: 5px auto;" class="cquote"> <tbody><tr> <td valign="top" style="width:20px; color:#B2B7F2; font-size:40px; font-family:Elephant,'Times New Roman',serif; font-weight:bold; text-align:left; padding:10px 10px;">「 </td> <td><div style="display: table-cell; text-align: left; padding: 1em; vertical-align: middle;"><a href="/wiki/%E7%B2%B5%E6%96%87" title="粵文">粵文</a>翻譯：世上有三種大話：<a href="/wiki/%E5%A4%A7%E8%A9%B1%E3%80%81%E6%8A%B5%E6%AD%BB%E5%98%85%E5%A4%A7%E8%A9%B1%E3%80%81%E5%90%8C%E5%9F%8B%E7%B5%B1%E8%A8%88%E6%95%B8%E5%AD%97" title="大話、抵死嘅大話、同埋統計數字">大話、抵死嘅大話、同埋統計數字</a>。 </div> </td> <td valign="bottom" style="width:20px; color:#B2B7F2; font-size:40px; font-family:Elephant,'Times New Roman',serif; font-weight:bold; text-align:right; padding:10px 10px;">」 </td></tr></tbody></table> <p>舉附圖嚟說明，同一樣嘅統計數據可以用唔同嘅方法呈現，而唔同嘅呈現方法可以攞嚟誤導人，好似係附圖嗰兩幅<a href="/wiki/%E6%A3%92%E5%BD%A2%E5%9C%96" title="棒形圖">棒形圖</a>噉，兩幅圖表達嘅數據一樣，都係表達緊一間公司喺 2010 同 2011 年嘅<a href="/wiki/%E9%8A%B7%E5%94%AE%E9%87%8F" title="銷售量">銷售量</a>（Y 軸係銷售量，X 軸係年份），但係兩幅圖嘅原點唔同－左圖嘅 Y 軸係以 36 做起點，右圖嘅以 0 做起點，令到前者望落好似賺多咗好多錢噉<sup id="cite_ref-hays_1-2" class="reference"><a href="#cite_note-hays-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。除此之外，對分析嘅結果又有得用唔同嘅方法解讀，搞到好多人會特登用對自己有利嘅呈現同解讀方法嚟誤導人，而<a href="/wiki/%E7%BE%8E%E5%9C%8B" title="美國">美國</a><a href="/wiki/%E4%BD%9C%E5%AE%B6" title="作家">作家</a><a href="https://en.wikipedia.org/wiki/Darrell_Huff" class="extiw" title="en:Darrell Huff">達利哈夫</a><sup id="cite_ref-125" class="reference"><a href="#cite_note-125"><span class="cite-bracket">[</span>e 63<span class="cite-bracket">]</span></a></sup>嘅書《How to lie with statistics》（<a href="/wiki/%E7%B2%B5%E6%96%87" title="粵文">粵文</a>：點樣用統計學講大話）就揭露咗好多<a href="/wiki/%E7%94%9F%E6%84%8F%E4%BA%BA" title="生意人">生意人</a>同<a href="/wiki/%E6%94%BF%E6%B2%BB%E5%AE%B6" title="政治家">政治家</a>等嘅人物用類似嘅詭計嚟呃人嘅例子<sup id="cite_ref-126" class="reference"><a href="#cite_note-126"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup>。 </p><p>要預防統計學嘅誤用有好多方法，包括要用啱嘅圖表等等<sup id="cite_ref-127" class="reference"><a href="#cite_note-127"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup>。而且喺將用統計得出嘅結論<a href="/wiki/%E5%BB%A3%E7%BE%A9%E5%8C%96" title="廣義化">普遍化</a>嗰陣，要留意佢會唔會超出咗個樣本代表到嘅範圍，只有個當樣本可以代表到個總體嗰陣，統計方法得出嘅結果先至算係可信、精確嘅，例如係一份用<a href="/wiki/%E7%99%BD%E4%BA%BA" class="mw-redirect" title="白人">白人</a>做樣本嘅<a href="/wiki/%E9%86%AB%E5%AD%B8" title="醫學">醫學</a>研究得出嘅結論未必啱<a href="/wiki/%E5%94%90%E4%BA%BA" title="唐人">唐人</a>用<sup id="cite_ref-128" class="reference"><a href="#cite_note-128"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="簡史"><span id=".E7.B0.A1.E5.8F.B2"></span>簡史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=24" title="編輯小節: 簡史"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8%E5%8F%B2" title="統計學史">統計學史</a></div> <p>統計學呢門學問最少有得追溯到去<a href="/wiki/%E5%85%AC%E5%85%83%E5%89%8D" class="mw-redirect" title="公元前">公元前</a> 5 世紀咁久遠。一般認為，最早可以算得上係統計嘅著作嚟自公元 9 世紀嘅《密碼破譯》<sup id="cite_ref-129" class="reference"><a href="#cite_note-129"><span class="cite-bracket">[</span>e 64<span class="cite-bracket">]</span></a></sup>呢本書，由一位<a href="/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E4%BA%BA" title="阿拉伯人">阿拉伯人</a>學者編寫嘅。喺呢本書入面，作者佢詳細噉記錄咗點樣用統計數據同頻率分析破解<a href="/wiki/%E5%AF%86%E7%A2%BC" title="密碼">密碼</a>，而學界嘅主流意見認同，統計學同<a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" title="密碼學">密碼學</a>（研究點樣喺敵人存在下安全<a href="/wiki/%E9%80%9A%E8%A8%8A" title="通訊">通訊</a>嘅學問）就係噉一齊誕生<sup id="cite_ref-130" class="reference"><a href="#cite_note-130"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-131" class="reference"><a href="#cite_note-131"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup>。 </p><p>世上第一本統計學入門書一般認為係源自 14 至 17 世紀。喺 14 世紀，<a href="/wiki/%E4%BD%9B%E7%BE%85%E5%80%AB%E6%96%AF" class="mw-redirect" title="佛羅倫斯">佛羅倫斯</a>嘅<a href="/wiki/%E9%8A%80%E8%A1%8C%E5%AE%B6" title="銀行家">銀行家</a>兼執政官<a href="https://en.wikipedia.org/wiki/Giovanni_Villani" class="extiw" title="en:Giovanni Villani">佐凡尼·維蘭尼</a><sup id="cite_ref-132" class="reference"><a href="#cite_note-132"><span class="cite-bracket">[</span>e 65<span class="cite-bracket">]</span></a></sup>編訂咗《Nuova Cronica》呢本歷史書，包括咗好似係<a href="/wiki/%E4%BA%BA%E5%8F%A3" title="人口">人口</a>、法令、商貿、<a href="/wiki/%E6%95%99%E8%82%B2" title="教育">教育</a>同埋宗教場所呢啲嘢在內嘅統計數據，俾人話係歷史上第一本教人做基本統計嘅書；另一方面，有啲學者就將 1663 年<a href="https://en.wikipedia.org/wiki/John_Graunt" class="extiw" title="en:John Graunt">莊·葛蘭特</a><sup id="cite_ref-133" class="reference"><a href="#cite_note-133"><span class="cite-bracket">[</span>e 66<span class="cite-bracket">]</span></a></sup>根據死亡率統計表編訂出版嘅《Natural and Political Observations》（粵文：自然與政治觀察）呢本書定格做統計學嘅始祖<sup id="cite_ref-134" class="reference"><a href="#cite_note-134"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup>。 </p><p><b>統計學</b>嘅名可以追溯至 18 世紀：統計學嘅英文名 <b>statistics</b> 係源自 </p> <dl><dd><a href="/wiki/%E6%8B%89%E4%B8%81%E6%96%87" title="拉丁文">拉丁文</a>嘅詞語 <b>statisticum collegium</b>（意思係<b>國會</b>噉解）同埋</dd> <dd><a href="/wiki/%E6%84%8F%E5%A4%A7%E5%88%A9%E6%96%87" title="意大利文">意大利文</a>入面嘅 <b>statista</b>（<b>國民</b>或者<b>政治家</b>噉解）；</dd></dl> <p><a href="/wiki/%E5%BE%B7%E6%96%87" title="德文">德文</a>入面 <b>statistik</b> 呢個字最早係喺 1749 年有人用嘅，代表對<a href="/wiki/%E5%9C%8B%E5%AE%B6" class="mw-redirect" title="國家">國家</a>嘅數據做分析嘅一門學問，亦即係「研究國家嘅科學」；<a href="/wiki/%E6%B8%85%E6%9C%9D" class="mw-redirect" title="清朝">清朝</a>末期（19 世紀尾到廿世紀初），唐人學者將西學引入<a href="/wiki/%E5%A4%A7%E4%B8%AD%E8%8F%AF%E5%9C%B0%E5%8D%80" class="mw-redirect" title="大中華地區">大中華地區</a>，作咗<b>統計</b>呢個詞語嚟代表呢門研究數據嘅學術，俾人一路沿用到而家<sup id="cite_ref-135" class="reference"><a href="#cite_note-135"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-136" class="reference"><a href="#cite_note-136"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="睇埋"><span id=".E7.9D.87.E5.9F.8B"></span>睇埋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=25" title="編輯小節: 睇埋"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E6%A6%82%E7%8E%87%E5%8F%8A%E7%B5%B1%E8%A8%88%E5%AD%B8%E8%A9%9E%E5%BD%99%E8%A1%A8" class="mw-redirect" title="概率及統計學詞彙表">概率及統計學詞彙表</a></li> <li><a href="/wiki/R_%E7%A8%8B%E5%BC%8F%E8%AA%9E%E8%A8%80" class="mw-redirect" title="R 程式語言">R 程式語言</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/SPSS" title="SPSS">SPSS</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E6%9C%80%E4%BD%B3%E5%8C%96" class="mw-redirect" title="數學最佳化">數學最佳化</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%B3%87%E8%A8%8A%E7%90%86%E8%AB%96" title="資訊理論">資訊理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></li> <li><a href="/wiki/%E6%A9%9F%E6%A2%B0%E5%AD%B8%E7%BF%92" title="機械學習">機械學習</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E6%93%9A%E7%A7%91%E5%AD%B8" title="數據科學">數據科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E6%93%9A%E6%8E%A2%E5%8B%98" title="數據探勘">數據探勘</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%B8" title="統計力學">統計力學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/N-gram" title="N-gram">N-gram</a></li> <li><a href="/wiki/%E5%BF%83%E7%90%86%E6%B8%AC%E9%87%8F" class="mw-redirect" title="心理測量">心理測量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B6%93%E6%BF%9F%E6%B8%AC%E9%87%8F" class="mw-redirect" title="經濟測量">經濟測量</a></li> <li><a href="/wiki/%E5%85%88%E9%A9%97%E5%90%8C%E5%BE%8C%E9%A9%97" title="先驗同後驗">先驗同後驗</a></li></ul> <div style="clear: both;"></div> <div class="mw-heading mw-heading2"><h2 id="註釋"><span id=".E8.A8.BB.E9.87.8B"></span>註釋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=26" title="編輯小節: 註釋"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2020813">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-3"> <ol class="references"> <li id="cite_note-66"><span class="mw-cite-backlink"><a href="#cite_ref-66">↑</a></span> <span class="reference-text">喺<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>上，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/871e50f93f66412cc7052e6c158fda0bef991033" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.71ex; height:2.843ex;" alt="{\displaystyle P(y)}"></span> 係指「事件 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 發生嘅機會率」。</span> </li> <li id="cite_note-110"><span class="mw-cite-backlink"><a href="#cite_ref-110">↑</a></span> <span class="reference-text">喺<a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a>上，「<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(A\mid B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo>∣</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(A\mid B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f8f30f4da85b53901e0871eb41ed8827f511bb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.999ex; height:2.843ex;" alt="{\displaystyle P(A\mid B)}"></span>」係指「假如 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> 係真確，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> 係真確嘅機會率」。</span> </li> <li id="cite_note-111"><span class="mw-cite-backlink"><a href="#cite_ref-111">↑</a></span> <span class="reference-text">唔同嘅統計分析方法計 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 值嘅方法都唔同。</span> </li> <li id="cite_note-119"><span class="mw-cite-backlink"><a href="#cite_ref-119">↑</a></span> <span class="reference-text">查實係有方法可以更加精確噉計個 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> 值出嚟嘅，但呢度省略咗。</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="文獻"><span id=".E6.96.87.E7.8D.BB"></span>文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=27" title="編輯小節: 文獻"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="div-col columns column-count column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2; font-size:90%; column-count:3"> <ul><li>Cohen, J. (1990). <a rel="nofollow" class="external text" href="http://moityca.com.br/pdfs/Cohen_1990.pdf">Things I have learned (so far)</a>. <i>American Psychologist</i>, <i>45</i>, 1304-1312.</li> <li>Barbara Illowsky; Susan Dean (2014). <i>Introductory Statistics</i>. OpenStax CNX. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9781938168208" class="internal mw-magiclink-isbn">ISBN 9781938168208</a>.</li> <li>Stephen Jones, (2010). <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=mywdBQAAQBAJ">Statistics in Psychology: Explanations without Equations</a></i>. Palgrave Macmillan. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9781137282392" title="Special:書本來源/9781137282392">9781137282392</a>.</li> <li>Stockburger, David W. "<i>Introductory Statistics: Concepts, Models, and Applications</i>". Missouri State University (3rd Web ed.). Archived from the original on 28 May 2020.</li> <li>OpenIntro Statistics, 3rd edition by Diez, Barr, and Cetinkaya-Rundel</li> <li>Gigerenzer, G (2004). "Mindless statistics". <i>Journal of Socio-Economics</i>. 33: 587–606. doi:10.1016/j.socec.2004.09.033.</li> <li>Ioannidis, J.P.A. (2005). "Why most published research findings are false". <i>PLoS Medicine</i>. 2: 696–701. doi:10.1371/journal.pmed.0040168. PMC 1855693. <a class="external mw-magiclink-pmid" rel="nofollow" href="//www.ncbi.nlm.nih.gov/pubmed/17456002?dopt=Abstract">PMID 17456002</a>.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="參考"><span id=".E5.8F.83.E8.80.83"></span>參考</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=28" title="編輯小節: 參考"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>篇文用咗嘅<a href="/wiki/%E8%A1%8C%E8%A9%B1" title="行話">行話</a>或者<a href="/wiki/%E5%B0%88%E6%9C%89%E5%90%8D%E8%A9%9E" title="專有名詞">專有名詞</a>，<a href="/wiki/%E8%8B%B1%E6%96%87" title="英文">英文</a>名如下： </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2020813"><div class="reflist reflist-columns references-column-width reflist-columns-3"> <ol class="references"> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text">philosophy of science</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text">approximately accurate models</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text">inductive reasoning</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><a href="#cite_ref-23">↑</a></span> <span class="reference-text">probability</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><a href="#cite_ref-28">↑</a></span> <span class="reference-text">descriptive</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><a href="#cite_ref-29">↑</a></span> <span class="reference-text">inferential</span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><a href="#cite_ref-32">↑</a></span> <span class="reference-text">data collection</span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><a href="#cite_ref-34">↑</a></span> <span class="reference-text">variable</span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><a href="#cite_ref-36">↑</a></span> <span class="reference-text">continuous variable</span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><a href="#cite_ref-37">↑</a></span> <span class="reference-text">discrete variable</span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><a href="#cite_ref-39">↑</a></span> <span class="reference-text">sampling</span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><a href="#cite_ref-40">↑</a></span> <span class="reference-text">statistical population</span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><a href="#cite_ref-41">↑</a></span> <span class="reference-text">Homo sapien</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><a href="#cite_ref-42">↑</a></span> <span class="reference-text">sample</span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><a href="#cite_ref-44">↑</a></span> <span class="reference-text">generalize</span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><a href="#cite_ref-46">↑</a></span> <span class="reference-text">IQ test</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><a href="#cite_ref-47">↑</a></span> <span class="reference-text">level of measurement</span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><a href="#cite_ref-50">↑</a></span> <span class="reference-text">nominal</span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><a href="#cite_ref-51">↑</a></span> <span class="reference-text">ordinal</span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><a href="#cite_ref-52">↑</a></span> <span class="reference-text">interval</span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><a href="#cite_ref-53">↑</a></span> <span class="reference-text">ratio</span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><a href="#cite_ref-54">↑</a></span> <span class="reference-text">reliability</span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><a href="#cite_ref-55">↑</a></span> <span class="reference-text">validity</span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><a href="#cite_ref-58">↑</a></span> <span class="reference-text">dataset</span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><a href="#cite_ref-60">↑</a></span> <span class="reference-text">mean</span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><a href="#cite_ref-61">↑</a></span> <span class="reference-text">variance</span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><a href="#cite_ref-62">↑</a></span> <span class="reference-text">standard deviation</span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><a href="#cite_ref-63">↑</a></span> <span class="reference-text">probability distribution</span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><a href="#cite_ref-64">↑</a></span> <span class="reference-text">mathematical function</span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><a href="#cite_ref-67">↑</a></span> <span class="reference-text">normal distribution</span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><a href="#cite_ref-68">↑</a></span> <span class="reference-text">bell curve</span> </li> <li id="cite_note-70"><span class="mw-cite-backlink"><a href="#cite_ref-70">↑</a></span> <span class="reference-text">independent and identically distributed，IID</span> </li> <li id="cite_note-71"><span class="mw-cite-backlink"><a href="#cite_ref-71">↑</a></span> <span class="reference-text">independent</span> </li> <li id="cite_note-73"><span class="mw-cite-backlink"><a href="#cite_ref-73">↑</a></span> <span class="reference-text">correlational</span> </li> <li id="cite_note-74"><span class="mw-cite-backlink"><a href="#cite_ref-74">↑</a></span> <span class="reference-text">experimental</span> </li> <li id="cite_note-76"><span class="mw-cite-backlink"><a href="#cite_ref-76">↑</a></span> <span class="reference-text">statistical correlation</span> </li> <li id="cite_note-77"><span class="mw-cite-backlink"><a href="#cite_ref-77">↑</a></span> <span class="reference-text">Pearson correlation coefficient</span> </li> <li id="cite_note-79"><span class="mw-cite-backlink"><a href="#cite_ref-79">↑</a></span> <span class="reference-text">causality</span> </li> <li id="cite_note-81"><span class="mw-cite-backlink"><a href="#cite_ref-81">↑</a></span> <span class="reference-text">correlation does not imply causation</span> </li> <li id="cite_note-82"><span class="mw-cite-backlink"><a href="#cite_ref-82">↑</a></span> <span class="reference-text">manipulate</span> </li> <li id="cite_note-85"><span class="mw-cite-backlink"><a href="#cite_ref-85">↑</a></span> <span class="reference-text">controlled environment</span> </li> <li id="cite_note-86"><span class="mw-cite-backlink"><a href="#cite_ref-86">↑</a></span> <span class="reference-text">experimental group</span> </li> <li id="cite_note-87"><span class="mw-cite-backlink"><a href="#cite_ref-87">↑</a></span> <span class="reference-text">control group</span> </li> <li id="cite_note-88"><span class="mw-cite-backlink"><a href="#cite_ref-88">↑</a></span> <span class="reference-text">Hawthorne effect</span> </li> <li id="cite_note-90"><span class="mw-cite-backlink"><a href="#cite_ref-90">↑</a></span> <span class="reference-text">hypothesis testing</span> </li> <li id="cite_note-92"><span class="mw-cite-backlink"><a href="#cite_ref-92">↑</a></span> <span class="reference-text">parameter</span> </li> <li id="cite_note-93"><span class="mw-cite-backlink"><a href="#cite_ref-93">↑</a></span> <span class="reference-text">estimator</span> </li> <li id="cite_note-95"><span class="mw-cite-backlink"><a href="#cite_ref-95">↑</a></span> <span class="reference-text">confidence interval，CI</span> </li> <li id="cite_note-97"><span class="mw-cite-backlink"><a href="#cite_ref-97">↑</a></span> <span class="reference-text">null hypothesis</span> </li> <li id="cite_note-98"><span class="mw-cite-backlink"><a href="#cite_ref-98">↑</a></span> <span class="reference-text">alternative hypothesis</span> </li> <li id="cite_note-102"><span class="mw-cite-backlink"><a href="#cite_ref-102">↑</a></span> <span class="reference-text">Type I Error</span> </li> <li id="cite_note-103"><span class="mw-cite-backlink"><a href="#cite_ref-103">↑</a></span> <span class="reference-text">false positive</span> </li> <li id="cite_note-104"><span class="mw-cite-backlink"><a href="#cite_ref-104">↑</a></span> <span class="reference-text">Type II Error</span> </li> <li id="cite_note-105"><span class="mw-cite-backlink"><a href="#cite_ref-105">↑</a></span> <span class="reference-text">false negative</span> </li> <li id="cite_note-107"><span class="mw-cite-backlink"><a href="#cite_ref-107">↑</a></span> <span class="reference-text">statistical significance</span> </li> <li id="cite_note-112"><span class="mw-cite-backlink"><a href="#cite_ref-112">↑</a></span> <span class="reference-text">reject the null hypothesis</span> </li> <li id="cite_note-113"><span class="mw-cite-backlink"><a href="#cite_ref-113">↑</a></span> <span class="reference-text">comparison of means</span> </li> <li id="cite_note-114"><span class="mw-cite-backlink"><a href="#cite_ref-114">↑</a></span> <span class="reference-text">Student's t-test</span> </li> <li id="cite_note-115"><span class="mw-cite-backlink"><a href="#cite_ref-115">↑</a></span> <span class="reference-text">independent samples t-test</span> </li> <li id="cite_note-120"><span class="mw-cite-backlink"><a href="#cite_ref-120">↑</a></span> <span class="reference-text">paired samples t-test / repeated-measure t-test</span> </li> <li id="cite_note-121"><span class="mw-cite-backlink"><a href="#cite_ref-121">↑</a></span> <span class="reference-text">analysis of variance，ANOVA</span> </li> <li id="cite_note-122"><span class="mw-cite-backlink"><a href="#cite_ref-122">↑</a></span> <span class="reference-text">one-way ANOVA</span> </li> <li id="cite_note-125"><span class="mw-cite-backlink"><a href="#cite_ref-125">↑</a></span> <span class="reference-text">Darrell Huff</span> </li> <li id="cite_note-129"><span class="mw-cite-backlink"><a href="#cite_ref-129">↑</a></span> <span class="reference-text">英：Manuscript on Deciphering Cryptographic Messages</span> </li> <li id="cite_note-132"><span class="mw-cite-backlink"><a href="#cite_ref-132">↑</a></span> <span class="reference-text">Giovanni Villani</span> </li> <li id="cite_note-133"><span class="mw-cite-backlink"><a href="#cite_ref-133">↑</a></span> <span class="reference-text">John Graunt</span> </li> </ol></div> <p>篇文引用咗以下呢啲<a href="/wiki/%E6%96%87%E7%8D%BB" title="文獻">文獻</a>同<a href="/wiki/%E7%B6%B2%E9%A0%81" title="網頁">網頁</a>： </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2020813"><div class="reflist reflist-columns references-column-width reflist-columns-3"> <ol class="references"> <li id="cite_note-hays-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-hays_1-0">1.0</a></sup> <sup><a href="#cite_ref-hays_1-1">1.1</a></sup> <sup><a href="#cite_ref-hays_1-2">1.2</a></sup></span> <span class="reference-text">Hays, William Lee, (1973) <i>Statistics for the Social Sciences</i>, Holt, Rinehart and Winston, p.xii, <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9780030779459" class="internal mw-magiclink-isbn">ISBN 978-0-03-077945-9</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Moses, Lincoln E. (1986) <i>Think and Explain with Statistics</i>, Addison-Wesley, <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9780201156195" class="internal mw-magiclink-isbn">ISBN 978-0-201-15619-5</a> . pp. 1-3</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Etikan, I., & Bala, K. (2017). Sampling and sampling methods. <i>Biometrics & Biostatistics International Journal</i>, 5(6), 00149.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Stevens, S. S. (7 June 1946). "On the Theory of Scales of Measurement". <i>Science</i>. 103 (2684): 677–680.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Michell, J (1986). "Measurement scales and statistics: a clash of paradigms". <i>Psychological Bulletin</i>. 100 (3): 398–407.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Dodge, Y. (2006) <i>The Oxford Dictionary of Statistical Terms</i>, Oxford University Press. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/0199206139" class="internal mw-magiclink-isbn">ISBN 0-19-920613-9</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Romijn, Jan-Willem (2014). "Philosophy of statistics". <i>Stanford Encyclopedia of Philosophy</i>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">Halvorson, H. O., & Ziegler, N. R. (1933). Application of statistics to problems in bacteriology: I. A means of determining bacterial population by the dilution method. <i>Journal of Bacteriology</i>, 25(2), 101.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">Lumb, P. (1974). Application of statistics in soil mechanics. <i>Soil Mechanics New Horizons</i>. IK Lee, ed.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text">Stanovich, Keith E. (2007). <i>How to Think Straight About Psychology</i>. Boston: Pearson Education. p. 123</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">Crawford S., Stucki L. (1990), "Peer review and the changing research record", <i>J Am Soc Info Science</i>, vol. 41, pp. 223–28</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">Godfrey-Smith 2003, Chapter 14: "<i>Bayesianism and Modern Theories of Evidence</i>".</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text">Sklar, L. (1992). <i>Philosophy of physics</i>. Dimensions of Philosophy S.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text">Brigandt, Ingo; Love, Alan (2017), "Reductionism in Biology", in Zalta, Edward N. (ed.), <i>The Stanford Encyclopedia of Philosophy</i> (Spring 2017 ed.), Metaphysics Research Lab, Stanford University.</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><a href="#cite_ref-18">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.iep.utm.edu/ded-ind">Deductive and Inductive Arguments</a>.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><a href="#cite_ref-19">↑</a></span> <span class="reference-text">Sextus Empiricus, <i>Outlines of Pyrrhonism</i>. Trans. R.G. Bury, Harvard University Press, Cambridge, Massachusetts, 1933, p. 283.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><a href="#cite_ref-20">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.forbes.com/sites/quora/2017/12/14/theres-no-such-thing-as-proof-in-the-scientific-world-theres-only-evidence/?sh=1f14c9cf5392">There's No Such Thing As Proof In The Scientific World - There's Only Evidence</a>. <i>Forbes</i>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><a href="#cite_ref-21">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r2190673">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output 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a[href$=".PDF?"].external>span[aria-label]>.syu1ming4>.saan1,.mw-parser-output a[href$=".PDF#"].external>span[aria-label]>.syu1ming4>.saan1{width:unset;font-size:unset}.mw-parser-output .zyun1ming4 .hai2tau4ge3.zit3 .hai2tau4ge3.zi6:after{overflow:hidden}.mw-parser-output .zyun1ming4 .hai2tau4ge3.hai2zeoi3mei1ge3.zit3{clip-path:inset(0 0 0 0)}.mw-parser-output .zyun1ming4 .hai2tau4ge3.hai2zeoi3mei1ge3.zit3 .hai2tau4ge3.hai2zeoi3mei1ge3.zi6:after{clip-path:inset(0.14em 0 0 0)}.mw-parser-output .zyun1ming4 .hai2zeoi3mei1ge3.zit3 .hai2zeoi3mei1ge3.zi6:after{transform:rotate(90deg)translate(-0.25em,0.5em)}.mw-parser-output .fan1gaak3+.zi6:after{clip-path:inset(0 0 0 0.1em)}.mw-parser-output .pin1ming4 .zi6:after,.mw-parser-output .syu1ming4 .zi6:after,.mw-parser-output .zyun1ming4 .zi6:after,.mw-parser-output .zoek6zung6 .zi6:after{position:absolute;align-self:baseline;margin-left:-1em}.mw-parser-output .pin1ming4 .zi6:after,.mw-parser-output .syu1ming4 .zi6:after{padding-top:1em;content:"﹋"}.mw-parser-output .zyun1ming4 .zi6:after{content:"︳";transform-origin:bottom left;transform:rotate(90deg)translate(-0.25em,0.35em)}.mw-parser-output .zoek6zung6 .zi6:after{padding-top:0.6em;content:"·";width:1em;text-align:center}.mw-parser-output .koen1zo2,.mw-parser-output .pin1ming4-b .hoi1-adj,.mw-parser-output .syu1ming4-b .hoi1-adj{margin-left:-0.4em}.mw-parser-output .koen1jau6,.mw-parser-output .pin1ming4-b .saan1-adj,.mw-parser-output .syu1ming4-b .saan1-adj{margin-right:-0.4em}.mw-parser-output .zyun1ming4-b{white-space:nowrap;border-bottom:0.05em solid currentColor}.mw-parser-output .zyun1ming4-b+link+.zyun1ming4-b,.mw-parser-output .zyun1ming4-b+.zyun1ming4-b{margin-left:0.083em}.mw-parser-output .references-small>ul{margin-left:0}.mw-parser-output .references-small>ul>li{margin-left:3em;text-indent:-3em;list-style:none}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFChanceRossman2005" class="citation book cs1">Chance, Beth L.; Rossman, Allan J. (2005). "Preface". <a rel="nofollow" class="external text" href="http://www.rossmanchance.com/iscam/preface.pdf"><i>Investigating Statistical Concepts, Applications, and Methods</i></a> <span class="cs1-format">(PDF)</span>. Duxbury Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/978-0-495-05064-3" title="Special:書本來源/978-0-495-05064-3"><bdi>978-0-495-05064-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Preface&rft.btitle=Investigating+Statistical+Concepts%2C+Applications%2C+and+Methods&rft.pub=Duxbury+Press&rft.date=2005&rft.isbn=978-0-495-05064-3&rft.aulast=Chance&rft.aufirst=Beth+L.&rft.au=Rossman%2C+Allan+J.&rft_id=http%3A%2F%2Fwww.rossmanchance.com%2Fiscam%2Fpreface.pdf&rfr_id=info%3Asid%2Fzh-yue.wikipedia.org%3A%E7%B5%B1%E8%A8%88%E5%AD%B8" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><a href="#cite_ref-22">↑</a></span> <span class="reference-text">Moore, David (1992). "Teaching Statistics as a Respectable Subject". In F. Gordon and S. Gordon. <i>Statistics for the Twenty-First Century</i>. Washington, DC: The Mathematical Association of America. pp. 14-25. </span> </li> <li id="cite_note-feller1968-24"><span class="mw-cite-backlink"><a href="#cite_ref-feller1968_24-0">↑</a></span> <span class="reference-text">William Feller, <i>An Introduction to Probability Theory and Its Applications</i>, (Vol 1), 3rd Ed, (1968), Wiley.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><a href="#cite_ref-25">↑</a></span> <span class="reference-text">Hays, William Lee, (1973) <i>Statistics for the Social Sciences</i>, Holt, Rinehart and Winston</span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><a href="#cite_ref-26">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2190673"><cite id="CITEREFMoore1992" class="citation book cs1">Moore, David (1992). "Teaching Statistics as a Respectable Subject". <a rel="nofollow" class="external text" href="https://archive.org/details/statisticsfortwe0000unse"><i>Statistics for the Twenty-First Century</i></a>. Washington, DC: The Mathematical Association of America. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/statisticsfortwe0000unse/page/14">14</a>–25. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/978-0-88385-078-7" title="Special:書本來源/978-0-88385-078-7"><bdi>978-0-88385-078-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Teaching+Statistics+as+a+Respectable+Subject&rft.btitle=Statistics+for+the+Twenty-First+Century&rft.place=Washington%2C+DC&rft.pages=14-25&rft.pub=The+Mathematical+Association+of+America&rft.date=1992&rft.isbn=978-0-88385-078-7&rft.aulast=Moore&rft.aufirst=David&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fstatisticsfortwe0000unse&rfr_id=info%3Asid%2Fzh-yue.wikipedia.org%3A%E7%B5%B1%E8%A8%88%E5%AD%B8" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" class="mw-redirect" title="Template:Cite book">cite book</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Unknown parameter <code class="cs1-code">|editors=</code> ignored (<code class="cs1-code">|editor=</code> suggested) (<a href="/wiki/Help:CS1_errors#parameter_ignored_suggest" title="Help:CS1 errors">help</a>)</span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><a href="#cite_ref-27">↑</a></span> <span class="reference-text">Moses, Lincoln E. (1986). <i>Think and Explain with Statistics</i>, Addison-Wesley.</span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><a href="#cite_ref-30">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://study.com/academy/lesson/descriptive-and-inferential-statistics.html">Descriptive & Inferential Statistics: Definition, Differences & Examples</a>.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><a href="#cite_ref-31">↑</a></span> <span class="reference-text">Pearcey, S. M., & De Castro, J. M. (2002). Food intake and meal patterns of weight-stable and weight-gaining persons. <i>The American journal of clinical nutrition</i>, 76(1), 107-112.</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><a href="#cite_ref-33">↑</a></span> <span class="reference-text">Lescroël, A. L.; Ballard, G.; Grémillet, D.; Authier, M.; Ainley, D. G. (2014). Descamps, Sébastien (ed.). "Antarctic Climate Change: Extreme Events Disrupt Plastic Phenotypic Response in Adélie Penguins". <i>PLoS ONE</i>. 9 (1): e85291.</span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><a href="#cite_ref-35">↑</a></span> <span class="reference-text">Michell, J. (1993). The origins of the representational theory of measurement: Helmholtz, Hölder, and Russell. <i>Studies in History and Philosophy of Science</i>, <i>24</i>, 185-206.</span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><a href="#cite_ref-38">↑</a></span> <span class="reference-text">K.D. Joshi, <i>Foundations of Discrete Mathematics</i>, 1989, New Age International Limited, [1], page 7.</span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><a href="#cite_ref-43">↑</a></span> <span class="reference-text">Stuart, A. (1962). <i>Basic Ideas of Scientific Sampling</i>. New York: Hafner Publishing Company.</span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><a href="#cite_ref-45">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2190673"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170706190224/https://psychcentral.com/blog/archives/2010/08/26/psychology-secrets-most-psychology-studies-are-college-student-biased/">"Psychology Secrets: Most Psychology Studies Are College Student Biased"</a>. <a rel="nofollow" class="external text" href="https://psychcentral.com/blog/archives/2010/08/26/psychology-secrets-most-psychology-studies-are-college-student-biased/">原著</a>喺2017年7月6號歸檔<span class="reference-accessdate">. 喺2017年12月3號搵到</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Psychology+Secrets%3A+Most+Psychology+Studies+Are+College+Student+Biased&rft_id=https%3A%2F%2Fpsychcentral.com%2Fblog%2Farchives%2F2010%2F08%2F26%2Fpsychology-secrets-most-psychology-studies-are-college-student-biased%2F&rfr_id=info%3Asid%2Fzh-yue.wikipedia.org%3A%E7%B5%B1%E8%A8%88%E5%AD%B8" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><a href="#cite_ref-48">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2190673"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20171127132820/http://psc.dss.ucdavis.edu/sommerb/sommerdemo/scaling/levels.htm">"Levels of measurement"</a>. <a rel="nofollow" class="external text" href="http://psc.dss.ucdavis.edu/sommerb/sommerdemo/scaling/levels.htm">原著</a>喺2017年11月27號歸檔<span class="reference-accessdate">. 喺2017年11月26號搵到</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Levels+of+measurement&rft_id=http%3A%2F%2Fpsc.dss.ucdavis.edu%2Fsommerb%2Fsommerdemo%2Fscaling%2Flevels.htm&rfr_id=info%3Asid%2Fzh-yue.wikipedia.org%3A%E7%B5%B1%E8%A8%88%E5%AD%B8" class="Z3988"></span><a href="/wiki/Wayback_Machine" title="Wayback Machine">互聯網檔案館</a>嘅<a rel="nofollow" class="external text" href="https://web.archive.org/web/20171127132820/http://psc.dss.ucdavis.edu/sommerb/sommerdemo/scaling/levels.htm">歸檔</a>，歸檔日期2017年11月27號，.</span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><a href="#cite_ref-49">↑</a></span> <span class="reference-text">Kirch, W., ed. (2008). "Level of Measurement". <i>Encyclopedia of Public Health</i>. Springer. pp. 851–852. </span> </li> <li id="cite_note-furr2017-56"><span class="mw-cite-backlink"><a href="#cite_ref-furr2017_56-0">↑</a></span> <span class="reference-text">Furr, R. M. (2017). <i>Psychometrics: an introduction</i>. Sage Publications.</span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><a href="#cite_ref-57">↑</a></span> <span class="reference-text">Nunnally, J.C. (1978). <i>Psychometric theory</i> (2nd ed.). New York: McGraw-Hill.</span> </li> <li id="cite_note-data1988-59"><span class="mw-cite-backlink"><a href="#cite_ref-data1988_59-0">↑</a></span> <span class="reference-text">Data, C. E., & Using Descriptive Statistics Bartz, A. E. (1988). <i>Basic statistical concepts</i>. New York: Macmillan. Devore, J., and Peck.</span> </li> <li id="cite_note-65"><span class="mw-cite-backlink"><a href="#cite_ref-65">↑</a></span> <span class="reference-text">B. S. Everitt: The Cambridge Dictionary of Statistics, Cambridge University Press, Cambridge (3rd edition, 2006).</span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><a href="#cite_ref-69">↑</a></span> <span class="reference-text">Bryc, Wlodzimierz (1995). <i>The Normal Distribution: Characterizations with Applications</i>. Springer-Verlag.</span> </li> <li id="cite_note-dinov2008-72"><span class="mw-cite-backlink"><a href="#cite_ref-dinov2008_72-0">↑</a></span> <span class="reference-text">Dinov, Ivo; Christou, Nicolas; Sanchez, Juana (2008). "Central Limit Theorem: New SOCR Applet and Demonstration Activity". <i>Journal of Statistics Education</i>. ASA. 16 (2).</span> </li> <li id="cite_note-75"><span class="mw-cite-backlink"><a href="#cite_ref-75">↑</a></span> <span class="reference-text">Freedman, D.A. (2005). <i>Statistical Models: Theory and Practice</i>, Cambridge University Press.</span> </li> <li id="cite_note-rodgers1988-78"><span class="mw-cite-backlink"><a href="#cite_ref-rodgers1988_78-0">↑</a></span> <span class="reference-text">Rodgers, J. L.; Nicewander, W. A. (1988). "Thirteen ways to look at the correlation coefficient". <i>The American Statistician</i>. 42 (1): 59-66.</span> </li> <li id="cite_note-80"><span class="mw-cite-backlink"><a href="#cite_ref-80">↑</a></span> <span class="reference-text">Aldrich, John (1995). "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20060219042545/http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf">Correlations Genuine and Spurious in Pearson and Yule</a>" (PDF). <i>Statistical Science</i>. 10 (4): 364–376.</span> </li> <li id="cite_note-Roth2002-83"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Roth2002_83-0">42.0</a></sup> <sup><a href="#cite_ref-Roth2002_83-1">42.1</a></sup></span> <span class="reference-text">Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," <i>Econometrica</i>, 70(4), pp. 1341–1378.</span> </li> <li id="cite_note-84"><span class="mw-cite-backlink"><a href="#cite_ref-84">↑</a></span> <span class="reference-text">See, e.g., Grechenig, K., Nicklisch, A., & Thöni, C. (2010). Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty. <i>Journal of Empirical Legal Studies</i>, 7(4), 847-867.</span> </li> <li id="cite_note-89"><span class="mw-cite-backlink"><a href="#cite_ref-89">↑</a></span> <span class="reference-text">McCarney R, Warner J, Iliffe S, van Haselen R, Griffin M, Fisher P (2007). "The Hawthorne Effect: a randomised, controlled trial". <i>BMC Med Res Methodol</i>. 7 (1): 30.</span> </li> <li id="cite_note-myers2010-91"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-myers2010_91-0">45.0</a></sup> <sup><a href="#cite_ref-myers2010_91-1">45.1</a></sup></span> <span class="reference-text">Myers, Jerome L.; Well, Arnold D.; Lorch Jr., Robert F. (2010). "Developing fundamentals of hypothesis testing using the binomial distribution". <i>Research design and statistical analysis</i> (3rd ed.). New York, NY: Routledge. pp. 65–90.</span> </li> <li id="cite_note-94"><span class="mw-cite-backlink"><a href="#cite_ref-94">↑</a></span> <span class="reference-text">Jaynes, E. T. (2007), <i>Probability Theory: The logic of science</i> (5 ed.), Cambridge University Press,</span> </li> <li id="cite_note-96"><span class="mw-cite-backlink"><a href="#cite_ref-96">↑</a></span> <span class="reference-text">Zar, J. H. (1984). <i>Biostatistical Analysis</i>. Prentice-Hall International, New Jersey, pp 43–45.</span> </li> <li id="cite_note-Adetal2007-99"><span class="mw-cite-backlink"><a href="#cite_ref-Adetal2007_99-0">↑</a></span> <span class="reference-text">Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007). <i>Advising on research methods: A consultant's companion</i>. Huizen, The Netherlands: Johannes van Kessel Publishing.</span> </li> <li id="cite_note-100"><span class="mw-cite-backlink"><a href="#cite_ref-100">↑</a></span> <span class="reference-text">Everitt, B. (1998). <i>The Cambridge Dictionary of Statistics</i>. Cambridge, UK New York: Cambridge University Press. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/0521593468" class="internal mw-magiclink-isbn">ISBN 0521593468</a>.</span> </li> <li id="cite_note-101"><span class="mw-cite-backlink"><a href="#cite_ref-101">↑</a></span> <span class="reference-text">Rubin, D. B.; Little, R. J. A. (2002). <i>Statistical analysis with missing data</i>. New York: Wiley.</span> </li> <li id="cite_note-106"><span class="mw-cite-backlink"><a href="#cite_ref-106">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.thoughtco.com/difference-between-type-i-and-type-ii-errors-3126414">The Difference Between Type I and Type II Errors</a>.</span> </li> <li id="cite_note-108"><span class="mw-cite-backlink"><a href="#cite_ref-108">↑</a></span> <span class="reference-text">Lydia Denworth, <b>A Significant Problem: Standard scientific methods are under fire. Will anything change?</b>, <i>Scientific American</i>, vol. 321, no. 4 (October 2019), pp. 62–67. "The use of p values for nearly a century [since 1925] to determine statistical significance of experimental results has contributed to an illusion of certainty and [to] reproducibility crises in many scientific fields... Some [researchers] suggest changing statistical methods, whereas others would do away with a threshold for defining "significant" results." (p. 63.)，呢篇文講到：「（自從 1925 年）近一個世紀以嚟，用 <i>p</i> 值決定一個實驗結果係咪顯著，搞到我哋有種肯定嘅錯覺（有種錯覺以為可以肯定啲實驗結果係啱嘅）同引起咗好多科學領域嘅<a href="/wiki/%E5%86%8D%E7%8F%BE" title="再現">再現</a>危機（指實驗結果做唔到再現）... 有啲研究者主張改變用緊嘅統計方法，而其他就會放棄唔再用門檻值嚟界定『顯著』嘅結果。」</span> </li> <li id="cite_note-109"><span class="mw-cite-backlink"><a href="#cite_ref-109">↑</a></span> <span class="reference-text">Piazza E. (2007). <i>Probabilità e Statistica</i>. Esculapio.</span> </li> <li id="cite_note-ttestthingies-116"><span class="mw-cite-backlink"><a href="#cite_ref-ttestthingies_116-0">↑</a></span> <span class="reference-text">O'Mahony, M. (1986). <i>Sensory Evaluation of Food: Statistical Methods and Procedures</i>. CRC Press. p. 487. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/0824773373" class="internal mw-magiclink-isbn">ISBN 0-82477337-3</a>.</span> </li> <li id="cite_note-derrick2017-117"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-derrick2017_117-0">55.0</a></sup> <sup><a href="#cite_ref-derrick2017_117-1">55.1</a></sup> <sup><a href="#cite_ref-derrick2017_117-2">55.2</a></sup></span> <span class="reference-text">Derrick, B; Toher, D; White, P (2017). "How to compare the means of two samples that include paired observations and independent observations: A companion to Derrick, Russ, Toher and White (2017)". <i>The Quantitative Methods for Psychology</i>. 13 (2): 120–126. </span> </li> <li id="cite_note-118"><span class="mw-cite-backlink"><a href="#cite_ref-118">↑</a></span> <span class="reference-text">McCulloch, J. Huston (1985). "On Heteroscedasticity". <i>Econometrica</i>. 53 (2): 483.</span> </li> <li id="cite_note-123"><span class="mw-cite-backlink"><a href="#cite_ref-123">↑</a></span> <span class="reference-text">Howell, David (2002). <i>Statistical Methods for Psychology</i>. Duxbury. pp. 324–325.</span> </li> <li id="cite_note-124"><span class="mw-cite-backlink"><a href="#cite_ref-124">↑</a></span> <span class="reference-text">英文段原文："There are three kinds of lies: lies, damned lies, and statistics."</span> </li> <li id="cite_note-126"><span class="mw-cite-backlink"><a href="#cite_ref-126">↑</a></span> <span class="reference-text">Huff, D. (1954). <i>How to Lie With Statistics</i>, WW Norton & Company, Inc. New York, NY. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9780393310726" class="internal mw-magiclink-isbn">ISBN 978-0-393-31072-6</a></span> </li> <li id="cite_note-127"><span class="mw-cite-backlink"><a href="#cite_ref-127">↑</a></span> <span class="reference-text">Drennan, R. D. <i>Statistics in archaeology</i>. (Edit) Pearsall, Deborah M. Encyclopedia of Archaeology. Elsevier Inc. 2008: 2093–2100.</span> </li> <li id="cite_note-128"><span class="mw-cite-backlink"><a href="#cite_ref-128">↑</a></span> <span class="reference-text">Cohen, J. B. Misuse of Statistics. <i>Journal of the American Statistical Association</i> (JSTOR). 1938年12月, 33 (204): 657–674.</span> </li> <li id="cite_note-130"><span class="mw-cite-backlink"><a href="#cite_ref-130">↑</a></span> <span class="reference-text">Al-Kadi, I. A. (1992) "The origins of cryptology: The Arab contributions", <i>Cryptologia</i>, 16(2) 97–126. doi:10.1080/0161-119291866801</span> </li> <li id="cite_note-131"><span class="mw-cite-backlink"><a href="#cite_ref-131">↑</a></span> <span class="reference-text">Singh, S. (2000). <i>The code book : the science of secrecy from ancient Egypt to quantum cryptography</i> (1st Anchor Books ed.). New York: Anchor Books.</span> </li> <li id="cite_note-134"><span class="mw-cite-backlink"><a href="#cite_ref-134">↑</a></span> <span class="reference-text">Willcox, W. (1938) "The Founder of Statistics". <i>Review of the International Statistical Institute</i>, 5(4):321–328.</span> </li> <li id="cite_note-135"><span class="mw-cite-backlink"><a href="#cite_ref-135">↑</a></span> <span class="reference-text">《文明小史．第四八回》：「所賺雖只毫釐，積少成多，一年統計，卻也不在少數。」</span> </li> <li id="cite_note-136"><span class="mw-cite-backlink"><a href="#cite_ref-136">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2190673"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200328044058/http://pedia.cloud.edu.tw/Entry/Detail/?title=%E7%B5%B1%E8%A8%88&search=%E7%A9%8D%E5%B0%91%E6%88%90%E5%A4%9A"><span class="pin1ming4-b" aria-label="〈詞條名稱：統計〉"><span class="zit3"><span class="koen1zo2">〈</span>詞</span><span class="zit3">條名稱：統計</span><span class="zit3"><span class="koen1jau6">〉</span></span></span></a>。<span class="syu1ming4-b" aria-label="《教育部重編國語辭典修訂本》"><span class="zit3"><span class="koen1zo2">《</span>教</span><span class="zit3">育部重編國語辭典修訂本</span><span class="zit3"><span class="koen1jau6">》</span></span></span>。臺灣教育部。<a rel="nofollow" class="external text" href="http://pedia.cloud.edu.tw/Entry/Detail/?title=%E7%B5%B1%E8%A8%88&search=%E7%A9%8D%E5%B0%91%E6%88%90%E5%A4%9A">原著</a>喺2020年3月28號歸檔<span class="reference-accessdate">。喺2018年5月15號搵到</span>。</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=%E6%95%99%E8%82%B2%E9%83%A8%E9%87%8D%E7%B7%A8%E5%9C%8B%E8%AA%9E%E8%BE%AD%E5%85%B8%E4%BF%AE%E8%A8%82%E6%9C%AC&rft.atitle=%E8%A9%9E%E6%A2%9D%E5%90%8D%E7%A8%B1%EF%BC%9A%E7%B5%B1%E8%A8%88&rft_id=http%3A%2F%2Fpedia.cloud.edu.tw%2FEntry%2FDetail%2F%3Ftitle%3D%25E7%25B5%25B1%25E8%25A8%2588%26search%3D%25E7%25A9%258D%25E5%25B0%2591%25E6%2588%2590%25E5%25A4%259A&rfr_id=info%3Asid%2Fzh-yue.wikipedia.org%3A%E7%B5%B1%E8%A8%88%E5%AD%B8" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="拎"><span id=".E6.8B.8E"></span>拎</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%B5%B1%E8%A8%88%E5%AD%B8&action=edit&section=29" title="編輯小節: 拎"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2018312">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r2018311">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><a href="https://commons.wikimedia.org/wiki/%E9%A0%AD%E7%89%88" class="extiw" title="commons:頭版">維基同享</a>有多媒體嘅嘢：<br /><b><a href="https://commons.wikimedia.org/wiki/Category:statistics" class="extiw" title="commons:Category:statistics"><span style="">統計學 / Stats</span></a></b></div></div> </div> <ul><li><span style="font-family: sans-serif; cursor: default; color: var(--color-subtle, #555); font-size: 0.8em; position: relative; bottom: 0.1em; font-weight: bold;" title="連到英文網頁">（英文）</span> <a rel="nofollow" class="external text" href="https://www.forbes.com/sites/forbestechcouncil/2022/08/23/understanding-the-4-vs-of-big-data/?sh=382827205f0a">理解大數據嘅 4V</a>，講<a href="/wiki/%E5%95%86%E5%AD%B8" title="商學">商學</a>嘢嘅<a href="/wiki/%E9%9B%9C%E8%AA%8C" title="雜誌">雜誌</a><a href="/wiki/%E7%A6%8F%E5%B8%83%E6%96%AF" title="福布斯">福布斯</a>出咗篇文，講<a href="/wiki/%E5%A4%A7%E6%95%B8%E6%93%9A" title="大數據">大數據</a>嘅 <b>4V</b> 問題—即係話數據量大（<b>v</b>olume）、花款多（<b>v</b>ariety）、攞得快（<b>v</b>elocity）、而且有時難核實（<b>v</b>eracity）。</li> <li><span style="font-family: sans-serif; cursor: default; color: var(--color-subtle, #555); font-size: 0.8em; position: relative; bottom: 0.1em; font-weight: bold;" title="連到英文網頁">（英文）</span> TIBCO Software Inc. (2020). <a rel="nofollow" class="external text" href="https://docs.tibco.com/data-science/textbook">數據科學教科書</a></li> <li><span style="font-family: sans-serif; cursor: default; color: var(--color-subtle, #555); font-size: 0.8em; position: relative; bottom: 0.1em; font-weight: bold;" title="連到英文網頁">（英文）</span> <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/statistics/">統計學嘅哲學</a>，<a href="/wiki/%E5%8F%B2%E4%B8%B9%E7%A6%8F%E5%93%B2%E5%AD%B8%E7%99%BE%E7%A7%91%E5%85%A8%E6%9B%B8" title="史丹福哲學百科全書">史丹福哲學百科全書</a>講統計學。</li></ul> <div role="navigation" class="navbox" aria-labelledby="統計學" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:%E7%B5%B1%E8%A8%88%E5%AD%B8" title="Template:統計學"><abbr title="去睇呢個模" 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title="數據集">數據集</a>）</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a></li> <li><a href="/wiki/%E6%A8%A3%E6%9C%AC" title="樣本">樣本</a>（<a href="/wiki/%E6%A8%A3%E6%9C%AC%E5%A4%A7%E7%B4%B0" title="樣本大細">大細</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A8%A3%E6%9C%AC%E4%BB%A3%E8%A1%A8%E6%80%A7" class="mw-redirect" title="樣本代表性">代表性</a>）</li> <li><a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%8A%BD%E6%A8%A3" title="隨機抽樣">隨機抽樣</a></li> <li><a href="/wiki/%E7%B3%BB%E7%B5%B1%E6%8A%BD%E6%A8%A3" title="系統抽樣">系統抽樣</a></li> <li><a href="/wiki/%E6%8A%BD%E6%A8%A3%E8%AA%A4%E5%B7%AE" title="抽樣誤差">抽樣誤差</a></li> <li><a href="/wiki/%E5%A4%A7%E6%95%B8%E5%AE%9A%E5%BE%8B" title="大數定律">大數定律</a></li> <li><a href="/wiki/%E5%80%96%E5%AD%98%E5%81%8F%E8%A6%8B" class="mw-redirect" title="倖存偏見">倖存偏見</a></li> <li><a href="/wiki/%E8%BF%94%E5%8E%BB%E5%B9%B3%E5%9D%87" title="返去平均">返去平均</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%87%8F%E5%BA%A6" title="量度">量度</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%93%8D%E4%BD%9C%E5%8C%96" title="操作化">操作化</a>同<a href="/wiki/%E9%87%8F%E5%BA%A6%E5%B1%A4%E6%AC%A1" title="量度層次">層次</a></li> <li><a href="/wiki/%E9%80%A3%E7%BA%8C%E5%90%8C%E9%9B%A2%E6%95%A3%E8%AE%8A%E6%95%B8" title="連續同離散變數">連續同離散變數</a>（<a href="/wiki/%E9%9B%A2%E6%95%A3%E5%8C%96" title="離散化">離散化</a>）</li> <li><a href="/wiki/%E5%85%B1%E5%90%8C%E6%96%B9%E6%B3%95%E8%AE%8A%E7%95%B0" title="共同方法變異">共同方法變異</a>（<a href="/wiki/%E5%93%88%E6%9B%BC%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="哈曼測試">哈曼測試</a>）</li> <li><a href="/wiki/%E6%99%82%E9%96%93%E8%A7%A3%E5%83%8F%E5%BA%A6" title="時間解像度">時間</a>同<a href="/wiki/%E7%A9%BA%E9%96%93%E8%A7%A3%E5%83%8F%E5%BA%A6" title="空間解像度">空間</a>解像度</li> <li><a href="/wiki/%E9%9D%88%E6%95%8F%E5%BA%A6%E5%90%8C%E7%89%B9%E7%95%B0%E5%BA%A6" title="靈敏度同特異度">靈敏度同特異度</a></li> <li><a href="/wiki/%E6%99%82%E9%96%93%E5%BA%8F%E5%88%97" title="時間序列">時間序列</a></li> <li><a href="/wiki/%E5%90%8D%E6%AC%A1" title="名次">名次</a></li> <li><a href="/wiki/%E5%A4%A9%E8%8A%B1%E6%9D%BF%E6%95%88%E6%87%89" title="天花板效應">天花板</a>同<a href="/wiki/%E5%9C%B0%E6%9D%BF%E6%95%88%E6%87%89" title="地板效應">地板</a>效應</li> <li><a href="/wiki/%E6%95%B8%E6%95%B8%E6%93%9A" title="數數據">數數據</a></li> <li><a href="/wiki/%E5%88%AA%E5%A4%B1" title="刪失">刪失</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/%E4%BF%A1%E5%BA%A6" title="信度">信度</a><a href="/wiki/%E6%95%88%E5%BA%A6" title="效度">效度</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%A9%95%E5%88%86%E8%80%85%E9%96%93%E4%BF%A1%E5%BA%A6" title="評分者間信度">評分者間</a>同<a href="/wiki/%E8%A9%95%E5%88%86%E8%80%85%E5%85%A7%E4%BF%A1%E5%BA%A6" title="評分者內信度">評分者內</a>信度</li> <li><a href="/wiki/%E9%87%8D%E6%B8%AC%E8%A9%A6%E4%BF%A1%E5%BA%A6" title="重測試信度">重測試信度</a></li> <li><a href="/wiki/%E5%85%A7%E9%83%A8%E4%B8%80%E8%87%B4%E5%BA%A6" title="內部一致度">內部一致度</a></li> <li><a href="/wiki/%E5%8D%A1%E9%9A%86%E5%B7%B4%E7%B3%BB%E6%95%B8" title="卡隆巴系數">卡隆巴系數</a></li> <li><a href="/wiki/%E5%BB%BA%E6%A7%8B%E6%95%88%E5%BA%A6" title="建構效度">建構效度</a></li> <li><a href="/wiki/%E6%95%88%E6%A8%99%E6%95%88%E5%BA%A6" title="效標效度">效標效度</a></li> <li><a href="/wiki/%E5%88%86%E6%AD%A7%E6%95%88%E5%BA%A6" title="分歧效度">分歧效度</a></li> <li><a href="/wiki/%E5%85%A7%E5%AE%B9%E6%95%88%E5%BA%A6" title="內容效度">內容效度</a></li> <li><a href="/wiki/%E8%81%9A%E5%90%88%E6%95%88%E5%BA%A6" title="聚合效度">聚合效度</a></li> <li><a href="/wiki/%E8%A1%A8%E9%9D%A2%E6%95%88%E5%BA%A6" title="表面效度">表面效度</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AF%A6%E9%A9%97%E6%93%8D%E4%BD%9C" class="mw-redirect" title="實驗操作">實驗操作</a></li> <li><a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84%E5%90%8C%E5%B0%8D%E7%85%A7%E7%B5%84" title="實驗組同對照組">實驗組同對照組</a></li> <li><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%B0%8D%E7%85%A7" title="科學對照">科學對照</a></li> <li><a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%8C%96%E5%AF%A6%E9%A9%97" title="隨機化實驗">隨機化實驗</a></li> <li><a href="/wiki/%E5%AF%A6%E9%A9%97%E8%A8%AD%E8%A8%88" title="實驗設計">實驗設計</a></li> <li><a href="/wiki/%E5%8F%97%E8%A9%A6%E9%96%93%E8%A8%AD%E8%A8%88" title="受試間設計">受試間</a>同<a href="/wiki/%E5%8F%97%E8%A9%A6%E5%85%A7%E8%A8%AD%E8%A8%88" title="受試內設計">受試內</a>設計</li> <li><a href="/wiki/%E6%9E%90%E5%9B%A0%E5%AF%A6%E9%A9%97" title="析因實驗">析因實驗</a></li> <li><a href="/wiki/%E8%87%AA%E7%84%B6%E5%AF%A6%E9%A9%97" title="自然實驗">自然實驗</a></li> <li><a href="/wiki/%E5%87%86%E5%AF%A6%E9%A9%97" class="mw-redirect" title="准實驗">准實驗</a></li> <li><a href="/wiki/%E8%87%A8%E5%BA%8A%E7%A0%94%E7%A9%B6" title="臨床研究">臨床研究</a>（<a href="/wiki/%E8%87%A8%E5%BA%8A%E8%A9%A6%E9%A9%97" title="臨床試驗">臨床試驗</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%B0%8D%E7%85%A7%E8%A9%A6%E9%A9%97" title="隨機對照試驗">隨機對照試驗</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">第啲方法</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%A7%80%E5%AF%9F%E7%A0%94%E7%A9%B6" title="觀察研究">觀察研究</a>（<a href="/wiki/%E6%A9%AB%E5%88%87%E9%9D%A2%E7%A0%94%E7%A9%B6" title="橫切面研究">橫切面</a>同<a href="/wiki/%E7%B8%B1%E5%90%91%E7%A0%94%E7%A9%B6" title="縱向研究">縱向</a>研究<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%8A%E5%88%97%E7%A0%94%E7%A9%B6" title="隊列研究">隊列研究</a>）</li> <li><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%B5%B1%E8%A8%88%E8%AA%BF%E6%9F%A5" title="社會統計調查">社會統計調查</a>（<a href="/wiki/%E8%87%AA%E6%88%91%E5%A0%B1%E5%91%8A%E7%A0%94%E7%A9%B6" title="自我報告研究">自我報告研究</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%95%8F%E5%8D%B7%E8%AA%BF%E6%9F%A5" title="問卷調查">問卷調查</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%9D%8E%E5%8D%A1%E7%89%B9%E9%87%8F%E8%A1%A8" title="李卡特量表">李卡特量表</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%B0%91%E6%84%8F%E8%AA%BF%E6%9F%A5" title="民意調查">民意調查</a>）</li> <li><a href="/wiki/%E6%AA%94%E6%A1%88%E7%A0%94%E7%A9%B6" title="檔案研究">檔案研究</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td><td class="navbox-image" rowspan="6" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Fisher_iris_versicolor_sepalwidth.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/150px-Fisher_iris_versicolor_sepalwidth.svg.png" decoding="async" width="150" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/225px-Fisher_iris_versicolor_sepalwidth.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/300px-Fisher_iris_versicolor_sepalwidth.svg.png 2x" data-file-width="822" data-file-height="567" /></a></span></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="描述統計學" style="font-size:114%;margin:0 4em"><a href="/wiki/%E6%8F%8F%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" title="描述統計學">描述統計學</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="連續數據" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%80%A3%E7%BA%8C%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" class="mw-redirect" title="連續概率分佈">連續數據</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/%E9%9B%86%E4%B8%AD%E8%B6%A8%E5%8B%A2" title="集中趨勢">集中趨勢</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B9%B3%E5%9D%87" title="平均">平均</a></li> <li><a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B8" class="mw-redirect" title="平均數">Mean</a>（<a href="/wiki/%E7%AE%97%E8%A1%93%E5%B9%B3%E5%9D%87%E5%80%BC" title="算術平均值">算術</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%B9%BE%E4%BD%95%E5%B9%B3%E5%9D%87%E5%80%BC" title="幾何平均值">幾何</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%AA%BF%E5%92%8C%E5%B9%B3%E5%9D%87%E5%80%BC" title="調和平均值">調和</a>）</li> <li><a href="/wiki/%E4%B8%AD%E4%BD%8D%E6%95%B8" title="中位數">Median</a></li> <li><a href="/wiki/%E7%9C%BE%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="眾數 (統計學)">Mode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/%E9%9B%A2%E6%95%A3%E7%A8%8B%E5%BA%A6" title="離散程度">離散程度</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%96%B9%E5%B7%AE" title="方差">方差</a>同<a href="/wiki/%E6%A8%99%E6%BA%96%E5%B7%AE" title="標準差">標準差</a></li> <li><a href="/wiki/%E5%85%A8%E8%B7%9D" title="全距">全距</a></li> <li><a href="/wiki/%E7%99%BE%E5%88%86%E4%BD%8D%E6%95%B8" title="百分位數">百分位數</a>（<a href="/wiki/%E5%9B%9B%E5%88%86%E4%BD%8D%E8%B7%9D" title="四分位距">四分位距</a>）</li> <li><a href="/wiki/%E8%AE%8A%E7%95%B0%E7%B3%BB%E6%95%B8" title="變異系數">變異系數</a></li> <li><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%8C%87%E6%95%B8" title="離散指數">離散指數</a></li> <li><a href="/wiki/%E5%8D%94%E6%96%B9%E5%B7%AE%E7%9F%A9%E9%99%A3" title="協方差矩陣">協方差矩陣</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">分佈形狀</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8B%95%E5%B7%AE" title="動差">動差</a>（<a href="/wiki/%E5%81%8F%E5%BA%A6" title="偏度">偏度</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%B3%B0%E5%BA%A6" title="峰度">峰度</a>）</li> <li><a href="/wiki/%E6%A8%99%E6%BA%96%E8%AA%A4%E5%B7%AE" title="標準誤差">標準誤差</a></li> <li><a href="/wiki/%E4%B8%AD%E5%A4%AE%E6%A5%B5%E9%99%90%E5%AE%9A%E7%90%86" title="中央極限定理">中央極限定理</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B5%B1%E8%A8%88%E7%9B%B8%E9%97%9C" title="統計相關">統計相關</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AD%A3%E7%9B%B8%E9%97%9C" class="mw-redirect" title="正相關">正相關</a>同<a href="/wiki/%E8%B2%A0%E7%9B%B8%E9%97%9C" class="mw-redirect" title="負相關">負相關</a></li> <li><a href="/wiki/%E7%9A%AE%E4%BA%9E%E9%81%9C%E7%A9%8D%E5%B7%AE%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8" title="皮亞遜積差相關係數">皮亞遜積差相關係數</a></li> <li><a href="/wiki/%E5%8D%94%E6%96%B9%E5%B7%AE" title="協方差">協方差</a></li> <li><a href="/wiki/%E7%AD%89%E7%B4%9A%E7%9B%B8%E9%97%9C" title="等級相關">等級相關</a>（<a href="/wiki/%E6%96%AF%E7%9A%AE%E4%BA%9E%E6%9B%BC%E7%AD%89%E7%B4%9A%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8" title="斯皮亞曼等級相關係數">斯皮亞曼</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%CE%A4_%E7%AD%89%E7%B4%9A%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8" title="Τ 等級相關係數">τ</a>）</li> <li><a href="/wiki/%E5%B1%80%E9%83%A8%E7%9B%B8%E9%97%9C" title="局部相關">局部相關</a></li> <li><a href="/wiki/%E7%B5%84%E5%85%A7%E7%9B%B8%E9%97%9C" title="組內相關">組內相關</a></li> <li><a href="/wiki/%E8%87%AA%E7%9B%B8%E9%97%9C" title="自相關">自相關</a></li> <li><a href="/wiki/%E4%BA%A4%E5%8F%89%E7%9B%B8%E9%97%9C" title="交叉相關">交叉相關</a></li> <li><a href="/wiki/%E7%9B%B8%E9%97%9C%E5%94%94%E8%98%8A%E5%90%AB%E5%9B%A0%E6%9E%9C" title="相關唔蘊含因果">相關唔蘊含因果</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%9C%96" title="統計圖">統計圖</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%A3%92%E5%BD%A2%E5%9C%96" title="棒形圖">棒形圖</a></li> <li><a href="/wiki/%E5%9C%93%E5%BD%A2%E5%9C%96" title="圓形圖">圓形圖</a></li> <li><a href="/wiki/%E6%8A%98%E7%B7%9A%E5%9C%96" title="折線圖">折線圖</a></li> <li><a href="/wiki/%E7%B5%84%E7%B9%94%E5%9C%96" title="組織圖">組織圖</a></li> <li><a href="/wiki/%E7%AE%B1%E5%BD%A2%E5%9C%96" title="箱形圖">箱形圖</a></li> <li><a href="/wiki/%E6%95%A3%E4%BD%88%E5%9C%96" title="散佈圖">散佈圖</a></li> <li><a href="/wiki/%E8%B1%A1%E5%BD%A2%E5%9C%96" title="象形圖">象形圖</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%9C%96%E5%BD%A2" title="統計圖形">統計圖形</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">相關概念</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="頻率 (統計學)">頻率</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E9%87%8F" title="統計量">統計量</a></li> <li><a href="/wiki/%E6%A8%99%E6%BA%96%E5%88%86%E6%95%B8" title="標準分數">標準分數</a></li> <li><a href="/wiki/%E7%BC%BA%E5%A4%B1%E6%95%B8%E6%93%9A" title="缺失數據">缺失數據</a></li> <li><a href="/wiki/%E7%B5%90%E5%90%88%E6%95%B8%E6%93%9A" title="結合數據">結合數據</a></li> <li><a href="/wiki/%E8%AA%A4%E5%B7%AE%E7%A9%8D%E8%81%9A" title="誤差積聚">誤差積聚</a></li> <li><a href="/wiki/%E7%8F%AD%E4%BD%9B%E5%AE%9A%E5%BE%8B" title="班佛定律">班佛定律</a></li> <li><a href="/wiki/%E6%95%B8%E6%93%9A%E8%A6%96%E8%A6%BA%E5%8C%96" title="數據視覺化">數據視覺化</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="推論統計學" style="font-size:114%;margin:0 4em"><a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">推論統計學</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B5%B1%E8%A8%88%E7%90%86%E8%AB%96" class="mw-redirect" title="統計理論">統計理論</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B8%BD%E9%AB%94" title="總體">總體</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E9%87%8F" title="統計量">統計量</a></li> <li><a href="/wiki/%E7%8D%A8%E7%AB%8B%E5%90%8C%E5%88%86%E4%BD%88" title="獨立同分佈">獨立同分佈</a></li> <li><a href="/wiki/%E5%AF%A6%E8%AD%89%E5%88%86%E4%BD%88%E5%87%BD%E6%95%B8" title="實證分佈函數">實證分佈函數</a></li> <li><a href="/wiki/%E9%87%8D%E6%8A%BD%E6%A8%A3" title="重抽樣">重抽樣</a>（<a href="/wiki/%E8%87%AA%E5%8A%A9%E6%8A%BD%E6%A8%A3%E6%B3%95" title="自助抽樣法">自助抽樣法</a>）</li> <li><a href="/wiki/%E6%90%8D%E5%A4%B1%E5%87%BD%E6%95%B8" title="損失函數">損失函數</a></li> <li><a href="/wiki/%E6%95%88%E7%8E%87_(%E7%B5%B1%E8%A8%88%E5%AD%B8)" title="效率 (統計學)">效率</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E8%B7%9D%E9%9B%A2" title="統計距離">統計距離</a></li> <li><a href="/wiki/%E7%89%B9%E5%BE%B5%E5%80%BC" title="特徵值">特徵值</a>同<a href="/wiki/%E7%89%B9%E5%BE%B5%E5%90%91%E9%87%8F" title="特徵向量">特徵向量</a></li> <li><a href="/wiki/%E9%A0%91%E5%81%A5%E7%B5%B1%E8%A8%88" title="頑健統計">頑健統計</a></li> <li><a href="/wiki/%E5%86%8D%E7%8F%BE" title="再現">再現</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" class="mw-redirect" title="離散概率分佈">離散</a>定<a href="/wiki/%E9%80%A3%E7%BA%8C%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" class="mw-redirect" title="連續概率分佈">連續</a></li> <li><a href="/wiki/%E5%B0%8D%E7%A8%B1%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="對稱概率分佈">對稱</a></li> <li><a href="/wiki/%E6%A6%82%E7%8E%87%E8%B3%AA%E9%87%8F%E5%87%BD%E6%95%B8" title="概率質量函數">概率質量函數</a>同<a href="/wiki/%E6%A6%82%E7%8E%87%E5%AF%86%E5%BA%A6%E5%87%BD%E6%95%B8" title="概率密度函數">概率密度函數</a></li> <li><a href="/wiki/%E7%B4%AF%E8%A8%88%E5%87%BD%E6%95%B8" class="mw-redirect" title="累計函數">累計函數</a></li> <li><a href="/wiki/%E5%B8%B8%E6%85%8B%E5%88%86%E4%BD%88" title="常態分佈">常態分佈</a>（<a href="/wiki/%E9%90%98%E5%BD%A2%E7%B7%9A" class="mw-redirect" title="鐘形線">鐘形線</a>）</li> <li><a href="/wiki/%E9%A0%BB%E7%8E%87%E5%88%86%E4%BD%88" title="頻率分佈">頻率分佈</a></li> <li><a href="/wiki/%E6%8A%BD%E6%A8%A3%E5%88%86%E4%BD%88" title="抽樣分佈">抽樣分佈</a>（<a href="/wiki/%E9%A0%86%E5%BA%8F%E7%B5%B1%E8%A8%88%E9%87%8F" title="順序統計量">順序統計量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%85%85%E5%88%86%E7%B5%B1%E8%A8%88%E9%87%8F" title="充分統計量">充分統計量</a>）</li> <li><a href="/wiki/%E8%81%AF%E5%90%88%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="聯合概率分佈">聯合分佈</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">學派詮釋</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%A0%BB%E7%8E%87%E5%AD%B8%E6%B4%BE%E6%8E%A8%E8%AB%96" title="頻率學派推論">頻率學派推論</a></li> <li><a href="/wiki/%E8%B2%9D%E8%91%89%E6%96%AF%E6%8E%A8%E8%AB%96" title="貝葉斯推論">貝葉斯推論</a></li> <li><a href="/wiki/%E8%B2%9D%E8%91%89%E6%96%AF%E6%A6%82%E7%8E%87" title="貝葉斯概率">貝葉斯概率</a>（<a href="/wiki/%E5%85%88%E9%A9%97%E6%A6%82%E7%8E%87" title="先驗概率">先驗</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BE%8C%E9%A9%97%E6%A6%82%E7%8E%87" title="後驗概率">後驗</a>）</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%81%87%E8%AA%AA%E6%AA%A2%E5%AE%9A" title="假說檢定">假說檢定</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%81%87%E8%AA%AA" title="假說">假說</a>（<a href="/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說">虛無假說</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%82%99%E6%93%87%E5%81%87%E8%AA%AA" title="備擇假說">備擇假說</a>）</li> <li><a href="/wiki/%E5%96%AE%E5%81%B4%E5%90%8C%E9%9B%99%E5%81%B4%E6%AA%A2%E5%AE%9A" title="單側同雙側檢定">單側同雙側檢定</a></li> <li><a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E5%90%8C%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" title="第一型同第二型錯誤">第一型同第二型錯誤</a></li> <li><a href="/wiki/%E9%A1%AF%E8%91%97%E5%B7%AE%E7%95%B0" title="顯著差異">顯著差異</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%8A%9F%E6%95%88" title="統計功效">統計功效</a></li> <li><a href="/wiki/%E8%87%AA%E8%AE%8A%E6%95%B8%E5%90%8C%E6%87%89%E8%AE%8A%E6%95%B8" title="自變數同應變數">自變數同應變數</a></li> <li><a href="/wiki/%E5%9B%A0%E6%9E%9C%E9%97%9C%E4%BF%82" title="因果關係">因果關係</a></li> <li><a href="/wiki/%E6%95%88%E6%87%89%E5%80%BC" title="效應值">效應值</a></li> <li><a href="/wiki/%E5%88%86%E6%9E%90%E5%B1%A4%E6%AC%A1" title="分析層次">分析層次</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%BC%B0%E8%A8%88%E7%90%86%E8%AB%96" title="估計理論">估計理論</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%BB%9E%E4%BC%B0%E8%A8%88" title="點估計">點估計</a>（<a href="/wiki/%E6%9C%80%E5%A4%A7%E4%BC%BC%E7%84%B6%E4%BC%B0%E8%A8%88" title="最大似然估計">最大似然估計</a>）</li> <li><a href="/wiki/%E5%8D%80%E9%96%93%E4%BC%B0%E8%A8%88" title="區間估計">區間估計</a>（<a href="/wiki/%E4%BF%A1%E5%BF%83%E5%8D%80%E9%96%93" title="信心區間">信心區間</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%A0%90%E6%B8%AC%E5%8D%80%E9%96%93" title="預測區間">預測區間</a>）</li> <li><a href="/wiki/%E9%87%8D%E6%8A%BD%E6%A8%A3" title="重抽樣">重抽樣</a>（<a href="/wiki/%E8%87%AA%E5%8A%A9%E6%8A%BD%E6%A8%A3%E6%B3%95" title="自助抽樣法">自助抽樣法</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%A4%E5%8F%89%E9%A9%97%E8%AD%89" title="交叉驗證">交叉驗證</a>）</li> <li><a href="/wiki/%E8%92%99%E5%9C%B0%E5%8D%A1%E7%BE%85%E6%96%B9%E6%B3%95" title="蒙地卡羅方法">蒙地卡羅方法</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%AF%94%E8%BC%83%E5%B9%B3%E5%9D%87%E5%80%BC" class="mw-redirect" title="比較平均值">平均比較</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AD%B8%E7%94%9F_t_%E6%B8%AC%E8%A9%A6" title="學生 t 測試">學生 t 測試</a>（<a href="/wiki/%E7%8D%A8%E7%AB%8B%E6%A8%A3%E6%9C%AC_t_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="獨立樣本 t 測試">獨立樣本</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%85%8D%E5%B0%8D%E6%A8%A3%E6%9C%AC_t_%E6%B8%AC%E8%A9%A6" class="mw-redirect" title="配對樣本 t 測試">配對樣本</a>）</li> <li><a href="/wiki/Z_%E6%B8%AC%E8%A9%A6" title="Z 測試">Z 測試</a></li> <li><a href="/wiki/F_%E6%B8%AC%E8%A9%A6" title="F 測試">F 測試</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E8%87%AA%E7%94%B1%E5%BA%A6" title="統計自由度">統計自由度</a></li> <li><a href="/wiki/%E5%A4%9A%E9%87%8D%E6%AF%94%E8%BC%83%E5%95%8F%E9%A1%8C" title="多重比較問題">多重比較問題</a>（<a href="/wiki/%E9%82%A6%E4%BD%9B%E6%9C%97%E5%B0%BC%E6%A0%A1%E6%AD%A3" title="邦佛朗尼校正">邦佛朗尼校正</a>）</li> <li><a href="/wiki/%E7%AD%89%E5%88%86%E6%95%A3%E6%80%A7" title="等分散性">等分散性</a>同<a href="/wiki/%E7%95%B0%E5%88%86%E6%95%A3%E6%80%A7" title="異分散性">異分散性</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="方差分析">ANOVA</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%96%AE%E5%9B%A0%E5%AD%90%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="單因子方差分析">單因子</a></li> <li><a href="/wiki/%E9%9B%99%E5%9B%A0%E5%AD%90%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="雙因子方差分析">雙因子</a></li> <li><a href="/wiki/%E9%87%8D%E8%A4%87%E9%87%8F%E6%95%B8%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" class="mw-redirect" title="重複量數方差分析">重複量數</a></li> <li><a href="/wiki/%E5%A4%9A%E8%AE%8A%E9%87%8F%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="多變量方差分析">多變量</a></li> <li><a href="/wiki/%E5%8D%94%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="協方差分析">協方差分析</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B5%B1%E8%A8%88%E6%A8%A1%E5%9E%8B" title="統計模型">統計模型</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%8E%A7%E5%88%B6%E8%AE%8A%E6%95%B8" title="控制變數">控制</a>、<a href="/wiki/%E4%B8%AD%E4%BB%8B%E8%AE%8A%E6%95%B8" title="中介變數">中介</a>、<a href="/wiki/%E8%AA%BF%E7%AF%80%E8%AE%8A%E6%95%B8" title="調節變數">調節</a>、<a href="/wiki/%E6%B7%B7%E6%B7%86%E8%AE%8A%E6%95%B8" title="混淆變數">混淆</a>同<a href="/wiki/%E5%A3%93%E5%88%B6%E8%AE%8A%E6%95%B8" title="壓制變數">壓制</a>變數</li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%8F%83%E6%95%B8" title="統計參數">參數</a></li> <li><a href="/wiki/%E5%96%AE%E8%AE%8A%E9%87%8F%E5%88%86%E6%9E%90" title="單變量分析">單變量</a>同<a href="/wiki/%E5%A4%9A%E8%AE%8A%E9%87%8F%E5%88%86%E6%9E%90" title="多變量分析">多變量</a>分析</li> <li>模型<a href="/wiki/%E7%B5%B1%E8%A8%88%E6%A8%A1%E5%9E%8B%E6%A8%99%E6%98%8E" title="統計模型標明">標明</a>同<a href="/wiki/%E7%B5%B1%E8%A8%88%E6%A8%A1%E5%9E%8B%E9%81%B8%E6%93%87" title="統計模型選擇">選擇</a></li> <li><a href="/wiki/%E5%A4%9A%E7%B5%84%E5%88%86%E6%9E%90" class="mw-redirect" title="多組分析">多組分析</a></li> <li><a href="/wiki/%E7%B4%84%E6%9D%9F_(%E6%95%B8%E5%AD%B8)" title="約束 (數學)">約束</a></li> <li><a href="/wiki/%E5%8F%AF%E8%A7%A3%E9%87%8B%E8%AE%8A%E7%95%B0" title="可解釋變異">可解釋變異</a></li> <li><a href="/wiki/%E6%95%8F%E6%84%9F%E5%BA%A6%E5%88%86%E6%9E%90" title="敏感度分析">敏感度分析</a></li> <li><a href="/wiki/%E6%8F%92%E5%80%BC" title="插值">插值</a>同<a href="/wiki/%E5%A4%96%E6%8E%A8" title="外推">外推</a></li> <li><a href="/wiki/%E6%B7%B7%E5%90%88%E7%89%A9%E6%A8%A1%E5%9E%8B" title="混合物模型">混合物</a></li> <li><a href="/wiki/%E5%8F%AF%E8%A9%AE%E9%87%8B%E5%BA%A6" class="mw-redirect" title="可詮釋度">可詮釋度</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">　<a href="/wiki/%E9%81%A9%E5%90%88%E5%BA%A6" title="適合度">適合度</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%81%A9%E5%90%88%E5%BA%A6%E6%8C%87%E6%A8%99" class="mw-redirect" title="適合度指標">適合度指標</a></li> <li><a href="/wiki/%E5%8D%A1%E6%96%B9%E6%AA%A2%E5%AE%9A" title="卡方檢定">卡方檢定</a></li> <li><a href="/wiki/%E8%B5%A4%E6%B1%A0%E8%B3%87%E8%A8%8A%E9%87%8F%E6%BA%96%E5%89%87" title="赤池資訊量準則">赤池資訊量準則</a></li> <li><a href="/wiki/%E8%B2%9D%E8%91%89%E6%96%AF%E8%B3%87%E8%A8%8A%E9%87%8F%E6%BA%96%E5%89%87" title="貝葉斯資訊量準則">貝葉斯資訊量準則</a></li> <li><a href="/wiki/%E8%BF%91%E4%BC%BC%E5%80%BC%E6%A0%B9%E5%9D%87%E6%96%B9%E8%AA%A4%E5%B7%AE" class="mw-redirect" title="近似值根均方誤差">RMSEA</a></li> <li><a href="/wiki/%E6%A8%99%E6%BA%96%E5%8C%96%E6%A0%B9%E5%9D%87%E6%AE%98%E5%B7%AE" class="mw-redirect" title="標準化根均殘差">SRMR</a></li> <li><a href="/wiki/%E6%AF%94%E8%BC%83%E9%81%A9%E5%90%88%E6%8C%87%E6%95%B8" class="mw-redirect" title="比較適合指數">CFI</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="迴歸分析同相關技術" style="font-size:114%;margin:0 4em"><a href="/wiki/%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="迴歸分析">迴歸分析</a>同相關技術</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">基礎</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AE%98%E5%B7%AE%E5%90%8C%E8%AA%A4%E5%B7%AE" title="殘差同誤差">殘差同誤差</a></li> <li><a href="/wiki/%E5%9B%BA%E5%AE%9A%E6%95%88%E6%87%89%E6%A8%A1%E5%9E%8B" title="固定效應模型">固定效應</a>、<a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%95%88%E6%87%89%E6%A8%A1%E5%9E%8B" title="隨機效應模型">隨機效應</a>同<a href="/wiki/%E6%B7%B7%E5%90%88%E6%A8%A1%E5%9E%8B" title="混合模型">混合</a>模型</li> <li><a href="/wiki/%E5%A4%9A%E9%87%8D%E8%BF%B4%E6%AD%B8%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="多重迴歸模型">多重迴歸模型</a>（<a href="/wiki/%E5%A4%9A%E9%87%8D%E5%85%B1%E7%B7%9A%E6%80%A7" title="多重共線性">多重共線性</a>）</li> <li><a href="/wiki/%E6%99%AE%E9%80%9A%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98%E6%B3%95" title="普通最小二乘法">普通最小二乘法</a></li> <li><a href="/wiki/%E6%AE%98%E5%B7%AE%E5%B9%B3%E6%96%B9%E5%92%8C" title="殘差平方和">殘差平方和</a></li> <li><a href="/wiki/%E5%9D%87%E6%96%B9%E8%AA%A4%E5%B7%AE" title="均方誤差">均方誤差</a></li> <li><a href="/wiki/%E6%A8%99%E6%BA%96%E8%AA%A4%E5%B7%AE" title="標準誤差">標準誤差</a></li> <li><a href="/wiki/%E6%B1%BA%E5%AE%9A%E7%B3%BB%E6%95%B8" title="決定系數">決定系數</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="線性迴歸分析">線性迴歸</a>（<a href="/wiki/%E7%B0%A1%E5%96%AE%E7%B7%9A%E6%80%A7%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" class="mw-redirect" title="簡單線性迴歸分析">簡單線性</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">進階模型</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9D%9E%E7%B7%9A%E6%80%A7%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="非線性迴歸分析">非線性迴歸分析</a></li> <li><a href="/wiki/Sigmoid_%E5%87%BD%E6%95%B8" title="Sigmoid 函數">Sigmoid 函數</a></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E8%BF%B4%E6%AD%B8" title="邏輯迴歸">邏輯迴歸</a></li> <li><a href="/wiki/%E4%B8%80%E8%88%AC%E7%B7%9A%E6%80%A7%E6%A8%A1%E5%9E%8B" title="一般線性模型">一般線性模型</a></li> <li><a href="/wiki/%E6%B3%8A%E6%B7%9E%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="泊淞迴歸分析">泊淞迴歸分析</a></li> <li><a href="/wiki/%E8%87%AA%E8%BF%B4%E6%AD%B8%E6%A8%A1%E5%9E%8B" title="自迴歸模型">自迴歸模型</a></li> <li><a href="/wiki/%E9%80%90%E6%AD%A5%E8%BF%B4%E6%AD%B8" title="逐步迴歸">逐步迴歸</a></li> <li><a href="/wiki/%E5%A4%9A%E8%AE%8A%E9%87%8F%E9%81%A9%E6%87%89%E6%80%A7%E8%BF%B4%E6%AD%B8%E6%A8%A1%E5%9E%8B" title="多變量適應性迴歸模型">多變量適應性迴歸模型</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">相關技術</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%94%9F%E9%82%84%E5%88%86%E6%9E%90" title="生還分析">生還分析</a>（<a href="/wiki/%E7%94%9F%E9%82%84%E5%87%BD%E6%95%B8" title="生還函數">函數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%B1%E6%95%88%E7%8E%87" title="失效率">失效率</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/K-M_%E4%BC%B0%E8%A8%88%E9%87%8F" title="K-M 估計量">K-M 估計量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/Log-rank_%E6%B8%AC%E8%A9%A6" title="Log-rank 測試">Log-rank 測試</a>同<a href="/wiki/%E6%AF%94%E4%BE%8B%E5%8D%B1%E6%A9%9F%E6%A8%A1%E5%9E%8B" title="比例危機模型">比例危機</a>）</li> <li><a href="/wiki/%E7%B5%90%E6%A7%8B%E6%96%B9%E7%A8%8B%E5%BC%8F%E6%A8%A1%E5%9E%8B" title="結構方程式模型">結構方程</a>同<a href="/wiki/%E9%80%9A%E5%BE%91%E5%88%86%E6%9E%90" title="通徑分析">通徑分析</a>（<a href="/wiki/%E9%87%8F%E5%BA%A6%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="量度模型">量度</a>同<a href="/wiki/%E7%B5%90%E6%A7%8B%E6%A8%A1%E5%9E%8B" class="mw-redirect" title="結構模型">結構</a>模型<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BF%AE%E6%94%B9%E6%8C%87%E6%95%B8" class="mw-redirect" title="修改指數">修改指數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%87%8F%E5%BA%A6%E4%B8%8D%E8%AE%8A%E7%89%B9%E6%80%A7" title="量度不變特性">量度不變特性</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%A4%E5%8F%89%E6%BB%AF%E5%BE%8C%E6%A8%A1%E5%9E%8B" title="交叉滯後模型">交叉滯後</a>）</li> <li><a href="/wiki/%E7%AD%89%E7%B4%9A%E7%B7%9A%E6%80%A7%E6%A8%A1%E5%9E%8B" title="等級線性模型">等級線性模型</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="第啲常用嘅分析技術" style="font-size:114%;margin:0 4em">第啲常用嘅分析技術</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="因素分析">因素分析</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8F%AF%E8%A7%80%E5%AF%9F%E8%AE%8A%E6%95%B8" title="可觀察變數">可觀察變數</a>同<a href="/wiki/%E6%BD%9B%E5%9C%A8%E8%AE%8A%E6%95%B8" title="潛在變數">潛在變數</a>（<a href="/wiki/%E5%BF%83%E7%90%86%E5%BB%BA%E6%A7%8B" title="心理建構">心理建構</a>）</li> <li><a href="/wiki/%E6%BD%9B%E5%9C%A8%E8%AE%8A%E6%95%B8%E6%A8%A1%E5%9E%8B" title="潛在變數模型">潛在變數模型</a></li> <li><a href="/wiki/%E9%99%8D%E7%B6%AD" title="降維">降維</a></li> <li><a href="/wiki/%E5%9B%A0%E7%B4%A0%E7%B5%90%E6%A7%8B" class="mw-redirect" title="因素結構">因素結構</a></li> <li><a href="/wiki/%E5%9B%A0%E7%B4%A0%E8%B2%A0%E8%8D%B7%E9%87%8F" class="mw-redirect" title="因素負荷量">因素負荷量</a></li> <li><a href="/wiki/%E6%8E%A2%E7%B4%A2%E5%9E%8B%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="探索型因素分析">探索型</a>同<a href="/wiki/%E7%A2%BA%E5%AE%9A%E5%9E%8B%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="確定型因素分析">確定型</a></li> <li><a href="/wiki/%E4%B8%BB%E6%88%90%E4%BB%BD%E5%88%86%E6%9E%90" title="主成份分析">主成份分析</a></li> <li><a href="/wiki/%E5%8D%A1%E9%9A%86%E5%B7%B4%E7%B3%BB%E6%95%B8" title="卡隆巴系數">卡隆巴系數</a></li> <li><a href="/wiki/%E5%BC%B5%E9%87%8F%E5%88%86%E8%A7%A3" title="張量分解">張量分解</a></li> <li><a href="/wiki/%E7%B5%90%E6%A7%8B%E6%96%B9%E7%A8%8B%E5%BC%8F%E6%A8%A1%E5%9E%8B" title="結構方程式模型">結構方程式模型</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%99%82%E9%96%93%E5%BA%8F%E5%88%97" title="時間序列">時間序列</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B9%B3%E7%A9%A9%E9%81%8E%E7%A8%8B" title="平穩過程">平穩過程</a></li> <li><a href="/wiki/%E9%A6%AC%E5%8F%AF%E5%A4%AB%E9%8F%88" title="馬可夫鏈">馬可夫鏈</a></li> <li><a href="/wiki/%E6%99%82%E5%9F%9F" title="時域">時域</a>（<a href="/wiki/%E8%87%AA%E7%9B%B8%E9%97%9C" title="自相關">自相關</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%A4%E5%8F%89%E7%9B%B8%E9%97%9C" title="交叉相關">交叉相關</a>）</li> <li><a href="/wiki/%E9%A0%BB%E5%9F%9F" title="頻域">頻域</a>（<a href="/wiki/%E5%82%85%E5%88%A9%E8%91%89%E5%88%86%E6%9E%90" title="傅利葉分析">傅利葉分析</a>）</li> <li><a href="/wiki/%E6%A0%BC%E8%98%AD%E5%82%91%E5%9B%A0%E6%9E%9C%E9%97%9C%E4%BF%82" title="格蘭傑因果關係">格蘭傑因果關係</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜技術</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%8E%A2%E7%B4%A2%E6%95%B8%E6%93%9A%E5%88%86%E6%9E%90" title="探索數據分析">探索分析</a></li> <li><a href="/wiki/%E9%AB%98%E6%B0%8F_kappa" title="高氏 kappa">高氏 kappa</a></li> <li><a href="/wiki/%E7%8D%A8%E7%AB%8B%E6%88%90%E4%BB%BD%E5%88%86%E6%9E%90" title="獨立成份分析">獨立成份分析</a></li> <li><a href="/wiki/%E8%81%9A%E9%A1%9E%E5%88%86%E6%9E%90" title="聚類分析">聚類分析</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%88%86%E9%A1%9E" title="統計分類">統計分類</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E5%88%A4%E5%88%A5%E5%88%86%E6%9E%90" title="線性判別分析">線性判別分析</a></li> <li><a href="/wiki/%E9%BB%9E%E9%81%8E%E7%A8%8B" title="點過程">點過程</a>（<a href="/wiki/%E9%BB%9E%E5%A0%B4" class="mw-redirect" title="點場">點場</a>）</li> <li><a href="/wiki/%E9%BA%A5%E5%80%AB%E7%91%AA%E6%B8%AC%E8%A9%A6" title="麥倫瑪測試">麥倫瑪測試</a></li> <li><a href="/wiki/%E9%9D%9E%E5%8F%83%E6%95%B8%E7%B5%B1%E8%A8%88%E5%AD%B8" title="非參數統計學">非參數統計學</a>（<a href="/wiki/MWU_%E6%B8%AC%E8%A9%A6" title="MWU 測試">MWU 測試</a>）</li> <li><a href="/wiki/%E4%BA%8B%E5%BE%8C%E5%88%86%E6%9E%90" title="事後分析">事後分析</a></li> <li><a href="/wiki/%E5%85%83%E5%88%86%E6%9E%90" title="元分析">元分析</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style=";"><div id="應用（誤用）" style="font-size:114%;margin:0 4em">應用（<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8%E5%98%85%E8%AA%A4%E7%94%A8" title="統計學嘅誤用">誤用</a>）</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%8A%9B%E5%AD%B8" title="統計力學">統計力學</a></li> <li><a href="/wiki/%E7%94%9F%E7%89%A9%E7%B5%B1%E8%A8%88%E5%AD%B8" title="生物統計學">生物統計學</a>（<a href="/wiki/%E7%94%9F%E7%89%A9%E8%B3%87%E8%A8%8A%E7%A7%91%E5%AD%B8" title="生物資訊科學">生物資訊科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%87%A8%E5%BA%8A%E8%A9%A6%E9%A9%97" title="臨床試驗">臨床試驗</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%82%B3%E6%9F%93%E7%97%85%E5%AD%B8" class="mw-redirect" title="傳染病學">傳染病學</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%B5%B1%E8%A8%88%E5%AD%B8" title="社會統計學">社會統計學</a>（<a href="/wiki/%E7%B2%BE%E7%AE%97%E5%AD%B8" title="精算學">精算學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B6%93%E6%BF%9F%E6%B8%AC%E9%87%8F%E5%AD%B8" title="經濟測量學">經濟測量學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%BA%E5%8F%A3%E7%B5%B1%E8%A8%88%E5%AD%B8" title="人口統計學">人口統計學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BF%83%E7%90%86%E6%B8%AC%E9%87%8F%E5%AD%B8" title="心理測量學">心理測量學</a>）</li> <li><a href="/wiki/%E5%9C%B0%E5%9C%96%E5%AD%B8" title="地圖學">地圖學</a></li> <li><a href="/wiki/%E5%B8%82%E5%A0%B4%E8%AA%BF%E6%9F%A5" class="mw-redirect" title="市場調查">市場調查</a></li> <li><a href="/wiki/%E8%AA%9E%E8%A8%80%E5%AD%B8" title="語言學">語言學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%B7%A5%E7%A8%8B" class="mw-redirect" title="工程">工程</a><a href="/wiki/%E7%A7%91%E6%8A%80" title="科技">科技</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B7%A5%E7%A8%8B%E7%B5%B1%E8%A8%88%E5%AD%B8" title="工程統計學">工程統計學</a>（<a href="/wiki/%E5%8F%AF%E9%9D%A0%E5%BA%A6%E5%B7%A5%E7%A8%8B" title="可靠度工程">可靠度工程</a>）</li> <li><a href="/wiki/%E6%A9%9F%E6%A2%B0%E5%AD%B8%E7%BF%92" title="機械學習">機械學習</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E5%88%86%E9%A1%9E" title="統計分類">統計分類</a></li> <li><a href="/wiki/%E5%81%8F%E5%A5%BD%E5%AD%B8%E7%BF%92" title="偏好學習">偏好學習</a></li> <li><a href="/wiki/%E6%93%AC%E4%BA%82%E6%95%B8%E7%94%A2%E7%94%9F" title="擬亂數產生">擬亂數產生</a></li> <li><a href="/wiki/%E7%95%B0%E5%B8%B8%E6%AA%A2%E6%B8%AC" title="異常檢測">異常檢測</a></li> <li><a href="/wiki/%E6%8E%A8%E8%96%A6%E7%B3%BB%E7%B5%B1" title="推薦系統">推薦系統</a></li> <li><a href="/wiki/%E8%87%AA%E7%84%B6%E8%AA%9E%E8%A8%80%E8%99%95%E7%90%86" title="自然語言處理">自然語言處理</a></li> <li><a href="/wiki/%E6%95%B8%E6%93%9A%E6%8E%A2%E5%8B%98" title="數據探勘">數據探勘</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><b><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, 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title="工程學">工程學</a>上嘅應用</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%95%B8%E5%AD%B8" title="離散數學">離散數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%91%BD%E9%A1%8C%E9%82%8F%E8%BC%AF" title="命題邏輯">命題邏輯</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" title="集合論">集合論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學">代數學</a>（<a href="/wiki/%E5%A0%B4_(%E6%95%B8%E5%AD%B8)" class="mw-redirect mw-disambig" title="場 (數學)">場</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學">組合數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%9C%96%E8%AB%96" title="圖論">圖論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%A2%E6%95%A3%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="離散幾何學">離散幾何學</a></div></td><td class="navbox-image" rowspan="8" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Aizerman2d.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/150px-Aizerman2d.jpg" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/225px-Aizerman2d.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/300px-Aizerman2d.jpg 2x" data-file-width="591" data-file-height="569" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數<br />學<br />分<br />析</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">分析基礎</div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%AF%A6%E6%95%B8" title="實數">實數</a>同<a href="/wiki/%E8%99%9B%E6%95%B8" title="虛數">虛數</a>（<a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>同<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%96%93%E8%B7%9D" title="間距">間距</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡">無窮盡</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">無窮小量</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E6%95%B8%E5%88%97" class="mw-redirect" title="數列">數列</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%AD%90%E6%95%B8%E5%88%97" title="子數列">子數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A2%9E%E6%B8%9B%E6%95%B8%E5%88%97" title="增減數列">增減數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%83%9D%E6%B0%8F%E6%95%B8%E5%88%97" title="郝氏數列">郝氏數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BF%9D%E8%A5%BF%E5%A5%B4-%E8%8F%AF%E5%AF%A6%E6%96%AF%E5%AE%9A%E7%90%86" title="保西奴-華實斯定理">保西奴-華實斯定理</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%87%BD%E6%95%B8" title="函數">函數</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%80%A3%E7%BA%8C%E5%87%BD%E6%95%B8" title="連續函數">連續函數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A5%B5%E9%99%90_(%E5%87%BD%E6%95%B8)" title="極限 (函數)">極限</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%80%BC%E8%BF%91%E7%90%86%E8%AB%96" title="逼近理論">逼近理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a>（<a href="/wiki/%E8%AE%8A%E5%88%86%E6%B3%95" title="變分法">變分法</a>）</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="微分" scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E5%88%86" title="微分">微分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a>（<a href="/wiki/%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="常微分方程">常</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%81%8F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="偏微分方程">偏</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="隨機微分方程">隨機</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%A4%87%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="複微分方程">複</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a></div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E7%A9%8D%E5%88%86" title="積分">積分</a>（<a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%A9%8D%E5%88%86" title="黎曼積分">黎曼積分</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A9%8D%E5%88%86%E6%96%B9%E7%A8%8B" title="積分方程">積分方程</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E5%85%83%E5%BE%AE%E7%A9%8D%E5%88%86" title="多元微積分">多元微積分</a>（<a href="/wiki/%E5%90%91%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="向量微積分">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="張量微積分">張量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E9%87%8D%E7%A9%8D%E5%88%86" title="多重積分">多重積分</a>）</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">第啲分析</div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%A4%9A%E9%87%8D%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="多重線性代數">多線代數</a>（<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%90%91%E9%87%8F%E7%A9%BA%E9%96%93" title="向量空間">向量空間</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F" title="張量">張量</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8B%95%E6%85%8B%E7%B3%BB%E7%B5%B1" title="動態系統">動態系統</a>（<a href="/wiki/%E6%B7%B7%E6%B2%8C%E7%90%86%E8%AB%96" title="混沌理論">混沌理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AB%96" title="控制理論">控制理論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%80%BC%E5%88%86%E6%9E%90" title="數值分析">數值分析</a></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E5%AD%B8" title="運算數學">運算數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E9%82%8F%E8%BC%AF" title="運算邏輯">運算邏輯</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%87%AA%E5%8B%95%E6%A9%9F%E7%90%86%E8%AB%96" title="自動機理論">自動機理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95" title="演算法">演算法</a>（<a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95%E5%88%86%E6%9E%90" title="演算法分析">分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%B3%87%E8%A8%8A%E7%90%86%E8%AB%96" title="資訊理論">資訊理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" title="密碼學">密碼學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E8%AB%96" title="運算數論">運算數論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E9%81%8B%E7%AE%97" title="科學運算">科學運算</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%BB%E8%85%A6%E4%BB%A3%E6%95%B8" title="電腦代數">電腦代數</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%9A%A8%E6%A9%9F%E8%AE%8A%E6%95%B8" title="隨機變數">隨機變數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E9%81%8E%E7%A8%8B" title="隨機過程">隨機過程</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%A6%AC%E5%8F%AF%E5%A4%AB%E9%8F%88" title="馬可夫鏈">馬可夫鏈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E7%A9%8D%E5%88%86" title="隨機微積分">隨機微積分</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%B1%BA%E7%AD%96%E8%AB%96" title="決策論">決策論</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a class="mw-selflink selflink">統計學</a>（<a href="/wiki/%E6%8F%8F%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" title="描述統計學">描述</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">推論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%9C%80%E4%BD%B3%E5%8C%96" title="最佳化">最佳化</a>（<a href="/wiki/%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="線性規劃">線性</a>同<a href="/wiki/%E9%9D%9E%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="非線性規劃">非線性</a>規劃）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%B6%93%E6%BF%9F%E5%AD%B8" title="數理經濟學">數理經濟學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E9%87%91%E8%9E%8D%E5%AD%B8" title="數理金融學">數理金融學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學">運籌學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B2%BE%E7%AE%97%E5%AD%B8" title="精算學">精算學</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E7%90%86%E7%89%A9%E7%90%86%E5%AD%B8" title="數理物理學">數理物理</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%88%86%E6%9E%90%E5%8A%9B%E5%AD%B8" title="分析力學">分析力學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A0%B4_(%E7%89%A9%E7%90%86)" title="場 (物理)">場</a>（<a href="/wiki/%E8%A6%8F%E7%AF%84%E5%A0%B4%E8%AB%96" title="規範場論">規範場論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%87%8F%E5%AD%90%E5%A0%B4%E8%AB%96" title="量子場論">量子場論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%87%8F%E5%AD%90%E7%BE%A3" title="量子羣">量子羣</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜應用</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%95%B8%E7%90%86%E5%8C%96%E5%AD%B8" title="數理化學">數理化學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">數理生物學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E5%BF%83%E7%90%86%E5%AD%B8" title="數理心理學">數理心理學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%A4%BE%E6%9C%83%E5%AD%B8" title="數理社會學">數理社會學</a>（<a href="/wiki/%E7%A4%BE%E6%9C%83%E9%81%B8%E6%93%87%E7%90%86%E8%AB%96" title="社會選擇理論">社會選擇理論</a>）</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜相關</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%95%B8%E5%AD%B8%E6%A8%A1%E5%9E%8B" title="數學模型">數學模型</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%B7%A5%E7%A8%8B%E6%95%B8%E5%AD%B8" title="工程數學">工程數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%87%89%E7%94%A8%E7%A7%91%E5%AD%B8" title="應用科學">應用科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A8%A1%E6%8E%A7%E5%AD%B8" title="模控學">模控學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B3%BB%E7%B5%B1" title="系統">系統</a>（<a href="/wiki/%E8%A4%87%E9%9B%9C%E7%B3%BB%E7%B5%B1" title="複雜系統">複雜系統</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%AD%B8%E5%96%BA%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8%E4%B8%8A%E5%98%85%E8%B6%85%E5%B8%B8%E6%95%88%E7%94%A8" title="數學喺自然科學上嘅超常效用">數學喺自然科學上嘅超常效用</a></div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div><b><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:%E6%95%B8%E5%AD%B8" title="Portal:數學">數學主題</a></b><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/Category:%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="Category:應用數學">應用數學類</a></div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="現代數學同數學各領域" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%95%B8%E5%AD%B8%E9%A0%98%E5%9F%9F" title="Template:數學領域"><abbr title="去睇呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">睇</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%95%B8%E5%AD%B8%E9%A0%98%E5%9F%9F" title="Template talk:數學領域"><abbr title="傾呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">傾</abbr></a></li><li 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style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E8%AD%89%E6%98%8E" title="數學證明">數學證明</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%B4%E6%8E%A5%E8%AD%89%E6%98%8E" title="直接證明">直接證明</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E6%AD%B8%E7%B4%8D%E6%B3%95" title="數學歸納法">數學歸納法</a></li> <li><a href="/wiki/%E5%90%A6%E5%AE%9A%E8%AD%89%E6%98%8E" title="否定證明">否定證明</a></li> <li><a href="/wiki/%E5%8F%8D%E8%AD%89%E6%B3%95" title="反證法">反證法</a></li> <li><a href="/wiki/%E6%A7%8B%E9%80%A0%E6%B3%95" title="構造法">構造法</a></li> <li><a href="/wiki/%E5%88%86%E9%A1%9E%E8%AD%89%E6%98%8E" title="分類證明">分類證明</a></li></ul> </div></td><td class="navbox-image" rowspan="10" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Mathematics.png" class="mw-file-description"><img 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href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" title="集合論">集合論</a></li> <li><a href="/wiki/%E9%A1%9E%E5%9E%8B%E8%AB%96" title="類型論">類型論</a></li> <li><a href="/wiki/%E8%B3%87%E8%A8%8A%E7%90%86%E8%AB%96" title="資訊理論">資訊理論</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E7%AC%A6%E8%99%9F" title="數學符號">數學符號</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E7%89%A9%E9%AB%94" title="數學物體">數學物體</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E8%AB%96" title="數論">數論</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B8" title="數">數</a>（<a href="/wiki/%E8%B3%AA%E6%95%B8" title="質數">質數</a>）</li> <li><a href="/wiki/%E7%AE%97%E8%A1%93" title="算術">算術</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8%E8%AB%96" title="代數數論">代數數論</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E6%95%B8%E8%AB%96" title="解析數論">解析數論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學">代數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9F%BA%E6%9C%AC%E4%BB%A3%E6%95%B8" title="基本代數">基本代數</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="線性代數">線性代數</a>（<a href="/wiki/%E5%A4%9A%E9%87%8D%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="多重線性代數">多重</a>）</li> <li><a href="/wiki/%E6%8A%BD%E8%B1%A1%E4%BB%A3%E6%95%B8" title="抽象代數">抽象代數</a>（<a href="/wiki/%E4%BA%A4%E6%8F%9B%E4%BB%A3%E6%95%B8" title="交換代數">交換代數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%BE%A3%E8%AB%96" title="羣論">羣論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BC%BD%E8%8F%AF%E7%90%86%E8%AB%96" title="伽華理論">伽華理論</a>）</li> <li><a href="/wiki/%E5%A0%B4%E8%AB%96" title="場論">場論</a></li> <li><a href="/wiki/%E6%B3%9B%E4%BB%A3%E6%95%B8" title="泛代數">泛代數</a></li> <li><a href="/wiki/%E5%90%8C%E8%AA%BF%E4%BB%A3%E6%95%B8" title="同調代數">同調代數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" title="幾何學">幾何學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97%E5%B9%BE%E4%BD%95" title="歐幾里得幾何">歐幾里得幾何</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E5%B9%BE%E4%BD%95" title="代數幾何">代數幾何</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%B9%BE%E4%BD%95" title="解析幾何">解析幾何</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a></li> <li><a href="/wiki/%E9%9B%A2%E6%95%A3%E5%B9%BE%E4%BD%95" title="離散幾何">離散幾何</a></li> <li><a href="/wiki/%E6%8B%93%E6%92%B2%E5%AD%B8" title="拓撲學">拓撲學</a>（<a href="/wiki/%E4%BB%A3%E6%95%B8%E6%8B%93%E6%92%B2" title="代數拓撲">代數拓撲</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a></li> <li><a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>同<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a></li> <li><a href="/wiki/%E6%B8%AC%E5%BA%A6" title="測度">測度</a></li> <li><a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a></li> <li><a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%95%B8%E5%AD%B8" title="離散數學">離散數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學">組合數學</a></li> <li><a href="/wiki/%E5%9C%96%E8%AB%96" title="圖論">圖論</a></li> <li><a href="/wiki/%E5%BA%8F%E7%90%86%E8%AB%96" title="序理論">序理論</a></li> <li><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="應用數學">應用數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B8%E7%90%86%E7%89%A9%E7%90%86%E5%AD%B8" title="數理物理學">數理物理學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E5%8C%96%E5%AD%B8" title="數理化學">數理化學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">數理生物學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E5%BF%83%E7%90%86%E5%AD%B8" title="數理心理學">數理心理學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%A4%BE%E6%9C%83%E5%AD%B8" title="數理社會學">數理社會學</a></li> <li><a href="/wiki/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AB%96" title="控制理論">控制理論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">　<a href="/wiki/%E6%B1%BA%E7%AD%96%E8%AB%96" title="決策論">決策論</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a>同<a class="mw-selflink selflink">統計學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%B6%93%E6%BF%9F%E5%AD%B8" title="數理經濟學">數理經濟學</a></li> <li><a href="/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學">運籌學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E9%87%91%E8%9E%8D%E5%AD%B8" title="數理金融學">數理金融學</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E5%AD%B8" title="運算數學">運算數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="電腦科學">電腦科學</a></li> <li><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a></li> <li><a href="/wiki/%E6%95%B8%E5%80%BC%E5%88%86%E6%9E%90" title="數值分析">數值分析</a></li> <li><a href="/wiki/%E6%9C%80%E4%BD%B3%E5%8C%96" title="最佳化">最佳化</a></li> <li><a href="/wiki/%E9%9B%BB%E8%85%A6%E4%BB%A3%E6%95%B8" title="電腦代數">電腦代數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜相關</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a></li> <li><a href="/wiki/%E7%90%86%E8%AB%96%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="理論電腦科學">理論電腦科學</a></li> <li><a href="/wiki/%E5%93%B2%E5%AD%B8" title="哲學">哲學</a>（<a href="/wiki/%E5%8F%A4%E5%B8%8C%E8%87%98%E5%93%B2%E5%AD%B8" title="古希臘哲學">古希臘哲學</a><span 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href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>嘅<a href="/wiki/%E7%A7%91%E5%AD%B8%E5%88%86%E6%94%AF" title="科學分支">各領域</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div id="科學哲學_·_科學家_·_科學教育_·_科學文獻_·_科學史"><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%93%B2%E5%AD%B8" title="科學哲學">科學哲學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E5%AE%B6" title="科學家">科學家</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E6%95%99%E8%82%B2" title="科學教育">科學教育</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%87%E7%8D%BB" title="科學文獻">科學文獻</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E5%8F%B2" title="科學史">科學史</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%A7%91%E5%AD%B8" title="形式科學">形式科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>（<a href="/wiki/%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="應用數學">應用數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a class="mw-selflink selflink">統計學</a>）</li> <li><a href="/wiki/%E7%90%86%E8%AB%96%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="理論電腦科學">理論電腦科學</a></li> <li><a href="/wiki/%E7%B3%BB%E7%B5%B1%E7%A7%91%E5%AD%B8" title="系統科學">系統科學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B4%94%E7%A7%91%E5%AD%B8" title="純科學">純科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%89%A9%E7%90%86%E7%A7%91%E5%AD%B8" title="物理科學">物理科學</a>（<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8" title="物理學">物理學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8C%96%E5%AD%B8" title="化學">化學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%9C%B0%E7%90%83%E7%A7%91%E5%AD%B8" title="地球科學">地球科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%A9%E6%96%87%E5%AD%B8" title="天文學">天文學</a>）</li> <li><a href="/wiki/%E7%94%9F%E5%91%BD%E7%A7%91%E5%AD%B8" title="生命科學">生命科學</a>（<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8" title="生物學">生物學</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E8%AA%8D%E7%9F%A5%E7%A7%91%E5%AD%B8" title="認知科學">認知科學</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AA%9E%E8%A8%80%E5%AD%B8" title="語言學">語言學</a></li> <li><a href="/wiki/%E4%BA%BA%E9%A1%9E%E5%AD%B8" title="人類學">人類學</a></li> <li><a href="/wiki/%E7%A5%9E%E7%B6%93%E7%A7%91%E5%AD%B8" title="神經科學">神經科學</a></li> <li><a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%B8" title="心理學">心理學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9C%B0%E7%90%86%E5%AD%B8" title="地理學">地理學</a></li> <li><a href="/wiki/%E8%80%83%E5%8F%A4%E5%AD%B8" title="考古學">考古學</a></li> <li><a href="/wiki/%E7%A4%BE%E6%9C%83%E5%AD%B8" title="社會學">社會學</a></li> <li><a href="/wiki/%E7%B6%93%E6%BF%9F%E5%AD%B8" title="經濟學">經濟學</a></li> <li><a href="/wiki/%E8%B3%87%E8%A8%8A%E7%A7%91%E5%AD%B8" title="資訊科學">資訊科學</a></li> <li><a href="/wiki/%E6%94%BF%E6%B2%BB%E5%AD%B8" title="政治學">政治學</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%87%89%E7%94%A8%E7%A7%91%E5%AD%B8" title="應用科學">應用科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%A8%88%E9%87%8F%E5%AD%B8" title="計量學">計量學</a></li> <li><a href="/wiki/%E8%BE%B2%E5%AD%B8" title="農學">農學</a>同<a href="/wiki/%E8%BE%B2%E6%A5%AD%E7%A7%91%E5%AD%B8" title="農業科學">農業科學</a></li> <li><a href="/wiki/%E5%B7%A5%E7%A8%8B%E5%AD%B8" title="工程學">工程學</a></li> <li><a href="/wiki/%E9%86%AB%E5%AD%B8" title="醫學">醫學</a></li> <li><a href="/wiki/%E9%81%8B%E5%8B%95%E7%A7%91%E5%AD%B8" title="運動科學">運動科學</a></li> <li><a href="/wiki/%E6%B3%95%E8%AD%89%E7%A7%91%E5%AD%B8" title="法證科學">法證科學</a></li> <li><a href="/wiki/%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="電腦科學">電腦科學</a>（<a href="/wiki/%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD" title="人工智能">AI</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜相關</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B2%BE%E5%AF%86%E7%A7%91%E5%AD%B8" title="精密科學">精密科學</a></li> <li><a href="/wiki/%E7%A1%AC%E5%90%8C%E8%BB%9F%E7%A7%91%E5%AD%B8" title="硬同軟科學">硬同軟科學</a></li> <li><a href="/wiki/%E8%B7%A8%E5%AD%B8%E7%A7%91%E7%A0%94%E7%A9%B6" title="跨學科研究">跨學科</a></li> <li><a href="/wiki/%E5%81%87%E7%A7%91%E5%AD%B8" title="假科學">假科學</a></li> <li><a href="/wiki/%E7%A7%91%E6%8A%80" title="科技">科技</a>同<a href="/wiki/%E7%A7%91%E5%B9%BB" title="科幻">科幻</a></li> <li><a href="/wiki/%E7%A7%91%E5%AD%B8%E8%AB%96" title="科學論">科學論</a></li> <li><a href="/wiki/%E9%96%8B%E6%94%BE%E7%A7%91%E5%AD%B8" title="開放科學">開放科學</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b>睇埋</b><br /> <a href="/wiki/%E7%9F%A5%E8%AD%98%E8%AB%96" title="知識論">知識論</a>（<a href="/wiki/%E7%B6%93%E9%A9%97%E4%B8%BB%E7%BE%A9" title="經驗主義">經驗主義</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%95%86%E5%AD%B8" title="商學">商學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%BA%E6%96%87%E5%AD%B8" title="人文學">人文學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AD%B8%E8%A1%93" title="學術">學術</a>同<a href="/wiki/%E5%AD%B8%E8%A1%93%E5%87%BA%E7%89%88" title="學術出版">學術出版</a></div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="研究" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:%E7%A0%94%E7%A9%B6" title="Template:研究"><abbr title="去睇呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">睇</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:%E7%A0%94%E7%A9%B6&action=edit&redlink=1" class="new" title="Template talk:研究 (無呢版)"><abbr title="傾呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">傾</abbr></a></li><li class="nv-edit"><a class="external text" href="https://zh-yue.wikipedia.org/w/index.php?title=Template:%E7%A0%94%E7%A9%B6&action=edit"><abbr title="編輯呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">改</abbr></a></li></ul></div><div id="研究" style="font-size:114%;margin:0 4em"><a href="/wiki/%E7%A0%94%E7%A9%B6" title="研究">研究</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div id="「用創意同有系統嘅方法嚟增進知識」嘅過程">「用<a href="/wiki/%E5%89%B5%E6%84%8F" title="創意">創意</a>同有系統嘅方法嚟增進<a href="/wiki/%E7%9F%A5%E8%AD%98" title="知識">知識</a>」嘅過程</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%AD%B8%E8%A1%93" title="學術">學術</a>領域</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a></li> <li><a href="/wiki/%E7%B4%94%E7%A7%91%E5%AD%B8" title="純科學">純科學</a>（<a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%A7%91%E5%AD%B8" title="形式科學">形式科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>）</li> <li><a href="/wiki/%E6%87%89%E7%94%A8%E7%A7%91%E5%AD%B8" title="應用科學">應用科學</a>（<a href="/wiki/%E7%A0%94%E7%A9%B6%E9%96%8B%E7%99%BC" title="研究開發">研究開發</a>）</li> <li><a href="/wiki/%E4%BA%BA%E6%96%87%E5%AD%B8" title="人文學">人文學</a></li> <li><a href="/wiki/%E5%95%86%E5%AD%B8" title="商學">商學</a></li> <li><a href="/wiki/%E5%B0%88%E6%A5%AD" title="專業">專業</a></li> <li><a href="/wiki/%E8%B7%A8%E5%AD%B8%E7%A7%91%E7%A0%94%E7%A9%B6" title="跨學科研究">跨學科</a></li></ul> </div></td><td class="navbox-image" rowspan="6" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:BookReader-favicon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/BookReader-favicon.svg/150px-BookReader-favicon.svg.png" decoding="async" width="150" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/BookReader-favicon.svg/225px-BookReader-favicon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/BookReader-favicon.svg/300px-BookReader-favicon.svg.png 2x" data-file-width="512" data-file-height="449" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">研究過程</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="研究設計" data-lang-code="en" data-lang-name="英文" data-foreign-title="Research design"><span class="ilh-page"><a href="/w/index.php?title=%E7%A0%94%E7%A9%B6%E8%A8%AD%E8%A8%88&action=edit&redlink=1" class="new" title="研究設計 (無呢版)">研究設計</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英文</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Research_design" class="extiw" title="en:Research design"><span lang="en" dir="auto">Research design</span></a></span>）</span></span>（<a href="/wiki/%E7%A0%94%E7%A9%B6%E8%A8%88%E5%8A%83%E6%9B%B8" title="研究計劃書">計劃書</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AE%9A%E6%80%A7%E7%A0%94%E7%A9%B6" title="定性研究">定性</a>同<a href="/wiki/%E5%AE%9A%E9%87%8F%E7%A0%94%E7%A9%B6" title="定量研究">定量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A0%94%E7%A9%B6%E5%95%8F%E9%A1%8C" title="研究問題">問題</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%81%87%E8%AA%AA" title="假說">假說</a>）</li> <li><a href="/wiki/%E5%AD%B8%E8%A1%93%E5%AF%AB%E4%BD%9C" title="學術寫作">學術寫作</a>（<a href="/wiki/%E6%96%87%E7%8D%BB%E7%B6%9C%E8%BF%B0" title="文獻綜述">文獻綜述</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8F%83%E8%80%83%E6%96%87%E7%8D%BB" title="參考文獻">參考文獻</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%92%E6%96%87%E6%80%A7" title="互文性">互文性</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%AB%96%E8%AD%89" title="論證">論證</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">研究方法</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E6%96%B9%E6%B3%95%E5%AD%B8" title="方法學">方法研究</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%B9%E6%B3%95" title="科學方法">科學方法</a></li> <li><a href="/wiki/%E6%95%98%E4%BA%8B%E5%88%86%E6%9E%90" title="敘事分析">敘事分析</a></li> <li><a href="/wiki/%E7%B4%AE%E6%A0%B9%E7%90%86%E8%AB%96" title="紮根理論">紮根理論</a></li> <li><a href="/wiki/%E6%89%B9%E5%88%A4%E7%90%86%E8%AB%96" title="批判理論">批判理論</a></li> <li><a href="/wiki/%E5%8F%B2%E5%AD%B8%E6%96%B9%E6%B3%95" title="史學方法">史學方法</a></li> <li><a href="/wiki/%E8%A7%A3%E9%87%8B%E5%AD%B8" title="解釋學">解釋學</a></li> <li><span class="ilh-all" data-orig-title="藝術方法學" data-lang-code="en" data-lang-name="英文" data-foreign-title="Art methodology"><span class="ilh-page"><a href="/w/index.php?title=%E8%97%9D%E8%A1%93%E6%96%B9%E6%B3%95%E5%AD%B8&action=edit&redlink=1" class="new" title="藝術方法學 (無呢版)">藝術方法學</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英文</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Art_methodology" class="extiw" title="en:Art methodology"><span lang="en" dir="auto">Art methodology</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%AF%A6%E7%94%A8%E4%B8%BB%E7%BE%A9" title="實用主義">實用主義</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%AF%A6%E9%A9%97" title="實驗">實驗</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%B0%8D%E7%85%A7" title="科學對照">對照</a></li> <li><a href="/wiki/%E5%AF%A6%E9%A9%97%E8%A8%AD%E8%A8%88" title="實驗設計">設計</a>（<a href="/wiki/%E5%AF%A6%E9%A9%97%E7%B5%84%E5%90%8C%E5%B0%8D%E7%85%A7%E7%B5%84" title="實驗組同對照組">實驗組同對照組</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%8C%96%E5%AF%A6%E9%A9%97" title="隨機化實驗">隨機化</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%9E%90%E5%9B%A0%E5%AF%A6%E9%A9%97" title="析因實驗">析因</a>）</li> <li><a href="/wiki/%E5%AF%A6%E5%9C%B0%E5%AF%A6%E9%A9%97" title="實地實驗">實地</a>同<a href="/wiki/%E8%87%AA%E7%84%B6%E5%AF%A6%E9%A9%97" title="自然實驗">自然</a>實驗</li> <li><a href="/wiki/%E7%9B%B2%E5%AF%A6%E9%A9%97" title="盲實驗">盲實驗</a></li> <li><a href="/wiki/%E6%BA%96%E5%AF%A6%E9%A9%97" title="準實驗">準實驗</a></li> <li><a href="/wiki/%E5%AF%A6%E9%A9%97%E5%AE%A4" title="實驗室">實驗室</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E4%BA%8C%E6%AC%A1%E7%A0%94%E7%A9%B6" title="二次研究">二次研究</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%96%87%E7%8D%BB%E7%B6%9C%E8%BF%B0" title="文獻綜述">文獻綜述</a>（<a href="/wiki/%E7%B3%BB%E7%B5%B1%E7%B6%9C%E8%BF%B0" title="系統綜述">系統綜述</a>）</li> <li><a href="/wiki/%E5%85%83%E5%88%86%E6%9E%90" title="元分析">元分析</a></li> <li><a href="/wiki/%E6%96%87%E7%8D%BB%E8%A8%88%E9%87%8F%E5%AD%B8" title="文獻計量學">文獻計量學</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A7%91%E5%AD%B8%E6%A8%A1%E5%9E%8B" title="科學模型">科學模型</a>（<a href="/wiki/%E6%A8%A1%E6%93%AC" title="模擬">模擬</a>）</li> <li><a href="/wiki/%E6%AA%94%E6%A1%88%E7%A0%94%E7%A9%B6" title="檔案研究">檔案</a></li> <li><a class="mw-selflink selflink">統計學</a></li> <li><a href="/wiki/%E8%A7%80%E5%AF%9F%E7%A0%94%E7%A9%B6" title="觀察研究">觀察</a></li> <li><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%B5%B1%E8%A8%88%E8%AA%BF%E6%9F%A5" title="社會統計調查">社會調查</a></li> <li><a href="/wiki/%E8%80%83%E5%AF%9F" title="考察">考察</a></li> <li><a href="/wiki/%E9%9D%A2%E8%A9%A6%E7%A0%94%E7%A9%B6" title="面試研究">面談</a></li> <li><a href="/wiki/%E5%85%A7%E5%AE%B9%E5%88%86%E6%9E%90" title="內容分析">內容分析</a></li> <li><a href="/wiki/%E5%B0%8D%E8%A9%B1%E5%88%86%E6%9E%90" title="對話分析">對話分析</a></li> <li><a href="/wiki/%E4%B8%BB%E9%A1%8C%E5%88%86%E6%9E%90" title="主題分析">主題分析</a></li> <li><a href="/wiki/%E5%80%8B%E6%A1%88%E7%A0%94%E7%A9%B6" title="個案研究">個案</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">機構制度</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%A4%A7%E5%AD%B8" title="大學">大學</a>同<a href="/wiki/%E7%A0%94%E7%A9%B6%E9%99%A2" title="研究院">研究院</a></li> <li><a href="/wiki/%E7%A2%A9%E5%A3%AB" title="碩士">碩士</a>同<a href="/wiki/%E5%8D%9A%E5%A3%AB" title="博士">博士</a></li> <li><a href="/wiki/%E5%AD%B8%E8%80%85" title="學者">學者</a></li> <li><a href="/wiki/%E7%A0%94%E7%A9%B6%E5%8A%A9%E7%90%86" title="研究助理">研究助理</a></li> <li><a href="/wiki/%E8%AB%96%E6%96%87" class="mw-redirect" title="論文">論文</a>（<a href="/wiki/%E5%8D%9A%E5%A3%AB%E8%AB%96%E6%96%87" title="博士論文">博士論文</a>）</li> <li><a href="/wiki/%E5%AD%B8%E8%A1%93%E5%87%BA%E7%89%88" title="學術出版">出版</a>（<a href="/wiki/%E5%AD%B8%E8%A1%93%E6%9C%9F%E5%88%8A" title="學術期刊">期刊</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AD%B8%E8%A1%93%E5%90%8C%E5%84%95%E4%BA%92%E8%A9%95" title="學術同儕互評">同儕互評</a>）</li> <li><a href="/wiki/%E5%AD%B8%E8%A1%93%E7%A0%94%E8%A8%8E%E6%9C%83" title="學術研討會">研討會</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%93%B2%E5%AD%B8" title="哲學">哲學</a>相關</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9F%A5%E8%AD%98%E8%AB%96" title="知識論">知識論</a>（<a href="/wiki/%E5%85%88%E9%A9%97%E5%90%8C%E5%BE%8C%E9%A9%97" title="先驗同後驗">先驗同後驗</a>）</li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a>同<a href="/wiki/%E5%93%B2%E5%AD%B8%E9%82%8F%E8%BC%AF" title="哲學邏輯">哲學邏輯</a></li> <li><a href="/wiki/%E5%BD%A2%E8%80%8C%E4%B8%8A%E5%AD%B8" title="形而上學">形而上學</a>、<a href="/wiki/%E7%90%86%E6%80%A7%E4%B8%BB%E7%BE%A9" title="理性主義">理性主義</a>同<a href="/wiki/%E7%B6%93%E9%A9%97%E4%B8%BB%E7%BE%A9" title="經驗主義">經驗主義</a></li> <li><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%93%B2%E5%AD%B8" 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