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href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=ROC%E6%9B%B2%E7%BA%BF&returntoquery=diff%3Dprev%26oldid%3D85264872" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=ROC%E6%9B%B2%E7%BA%BF&returntoquery=diff%3Dprev%26oldid%3D85264872" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" 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">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-基本概念" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#基本概念"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>基本概念</span> </div> </a> <ul id="toc-基本概念-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ROC空間" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ROC空間"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>ROC空間</span> </div> </a> <ul id="toc-ROC空間-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ROC曲線" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ROC曲線"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>ROC曲線</span> </div> </a> <ul id="toc-ROC曲線-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-曲線下面積（AUC）" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#曲線下面積（AUC）"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>曲線下面積（AUC）</span> </div> </a> <button aria-controls="toc-曲線下面積（AUC）-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>开关曲線下面積（AUC）子章节</span> </button> <ul id="toc-曲線下面積（AUC）-sublist" class="vector-toc-list"> <li id="toc-意義" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#意義"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>意義</span> </div> </a> <ul id="toc-意義-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-計算" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#計算"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>計算</span> </div> </a> <ul id="toc-計算-sublist" class="vector-toc-list"> <li id="toc-梯形法" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#梯形法"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>梯形法</span> </div> </a> <ul id="toc-梯形法-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-ROC_AUCH法" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#ROC_AUCH法"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.2</span> <span>ROC AUCH法</span> </div> </a> <ul id="toc-ROC_AUCH法-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-潛在問題" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#潛在問題"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>潛在問題</span> </div> </a> <ul id="toc-潛在問題-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-分析軟體" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#分析軟體"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>分析軟體</span> </div> </a> <ul id="toc-分析軟體-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>参考文献</span> </div> </a> <button aria-controls="toc-参考文献-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>开关参考文献子章节</span> </button> <ul id="toc-参考文献-sublist" class="vector-toc-list"> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-来源" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#来源"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>来源</span> </div> </a> <ul id="toc-来源-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-外部链接" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部链接"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>外部链接</span> </div> </a> <ul id="toc-外部链接-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="目录" 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="开关目录" > <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">开关目录</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">ROC曲线：修订间差异</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="前往另一种语言写成的文章。21种语言可用" > <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-21" 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">21种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Corba_caracter%C3%ADstica_de_funcionament_del_receptor" title="Corba característica de funcionament del receptor – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Corba característica de funcionament del receptor" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/ROC_k%C5%99ivka" title="ROC křivka – 捷克语" lang="cs" hreflang="cs" data-title="ROC křivka" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/ROC-Kurve" title="ROC-Kurve – 德语" lang="de" hreflang="de" data-title="ROC-Kurve" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Receiver_operating_characteristic" title="Receiver operating characteristic – 英语" lang="en" hreflang="en" data-title="Receiver operating characteristic" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Curva_ROC" title="Curva ROC – 西班牙语" lang="es" hreflang="es" data-title="Curva ROC" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%86%D8%AD%D9%86%DB%8C_%D9%88%DB%8C%DA%98%DA%AF%DB%8C_%D8%B9%D9%85%D9%84%DB%8C%D8%A7%D8%AA%DB%8C_%DA%AF%DB%8C%D8%B1%D9%86%D8%AF%D9%87" title="منحنی ویژگی عملیاتی گیرنده – 波斯语" lang="fa" hreflang="fa" data-title="منحنی ویژگی عملیاتی گیرنده" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Courbe_ROC" title="Courbe ROC – 法语" lang="fr" hreflang="fr" data-title="Courbe ROC" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%A7%D7%95%D7%9E%D7%AA_ROC" title="עקומת ROC – 希伯来语" lang="he" hreflang="he" data-title="עקומת ROC" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Receiver_operating_characteristic" title="Receiver operating characteristic – 意大利语" lang="it" hreflang="it" data-title="Receiver operating characteristic" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8F%97%E4%BF%A1%E8%80%85%E6%93%8D%E4%BD%9C%E7%89%B9%E6%80%A7" title="受信者操作特性 – 日语" lang="ja" hreflang="ja" data-title="受信者操作特性" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98%EC%8B%A0%EC%9E%90_%EC%A1%B0%EC%9E%91_%ED%8A%B9%EC%84%B1" title="수신자 조작 특성 – 韩语" lang="ko" hreflang="ko" data-title="수신자 조작 특성" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/ROC_kreiv%C4%97" title="ROC kreivė – 立陶宛语" lang="lt" hreflang="lt" data-title="ROC kreivė" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/ROC-curve" title="ROC-curve – 荷兰语" lang="nl" hreflang="nl" data-title="ROC-curve" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Krzywa_ROC" title="Krzywa ROC – 波兰语" lang="pl" hreflang="pl" data-title="Krzywa ROC" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Caracter%C3%ADstica_de_Opera%C3%A7%C3%A3o_do_Receptor" title="Característica de Operação do Receptor – 葡萄牙语" lang="pt" hreflang="pt" data-title="Característica de Operação do Receptor" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/ROC-%D0%BA%D1%80%D0%B8%D0%B2%D0%B0%D1%8F" title="ROC-кривая – 俄语" lang="ru" hreflang="ru" data-title="ROC-кривая" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/ROC" title="ROC – 土耳其语" lang="tr" hreflang="tr" data-title="ROC" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/ROC-%D0%BA%D1%80%D0%B8%D0%B2%D0%B0" title="ROC-крива – 乌克兰语" lang="uk" hreflang="uk" data-title="ROC-крива" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%C6%B0%E1%BB%9Dng_cong_ROC" title="Đường cong ROC – 越南语" lang="vi" hreflang="vi" data-title="Đường cong ROC" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/ROC%E6%9B%B2%E7%BA%BF" title="ROC曲线 – 吴语" lang="wuu" hreflang="wuu" data-title="ROC曲线" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/ROC_%E6%9B%B2%E7%B7%9A" title="ROC 曲線 – 粤语" lang="yue" hreflang="yue" data-title="ROC 曲線" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</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/Q327120#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div 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hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&variant=zh-sg&diff=prev&oldid=85264872" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&variant=zh-tw&diff=prev&oldid=85264872" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <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/ROC%E6%9B%B2%E7%BA%BF"><span>阅读</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a 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accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/ROC%E6%9B%B2%E7%BA%BF" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E4%BC%A0" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E7%89%B9%E6%AE%8A%E9%A1%B5%E9%9D%A2" title="全部特殊页面的列表[q]" accesskey="q"><span>特殊页面</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&oldid=85264872" title="此页面该修订版本的固定链接"><span>固定链接</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&action=info" title="关于此页面的更多信息"><span>页面信息</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=ROC%E6%9B%B2%E7%BA%BF&id=85264872&wpFormIdentifier=titleform" title="有关如何引用此页面的信息"><span>引用此页</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DROC%25E6%259B%25B2%25E7%25BA%25BF%26diff%3Dprev%26oldid%3D85264872"><span>获取短链接</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrKodu&url=https%3A%2F%2Fzh.wikipedia.org%2Fw%2Findex.php%3Ftitle%3DROC%25E6%259B%25B2%25E7%25BA%25BF%26diff%3Dprev%26oldid%3D85264872"><span>下载二维码</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/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</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"> 在其他项目中 </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:Receiver_operating_characteristic" hreflang="en"><span>维基共享资源</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/Q327120" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</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="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <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">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button 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class="mw-usertoollinks-contribs" title="Special:用户贡献/UjuiUjuMandan">贡献</a>）</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:%E5%B7%A1%E6%9F%A5%E8%B1%81%E5%85%8D%E8%80%85" class="mw-redirect" title="Wikipedia:巡查豁免者">巡查豁免者</a>、<a href="/wiki/Wikipedia:%E5%BB%B6%E4%BC%B8%E7%A1%AE%E8%AE%A4%E7%94%A8%E6%88%B7" class="mw-redirect" title="Wikipedia:延伸确认用户">延伸确认用户</a></div><div class="mw-diff-usereditcount"><span>24,586</span>次编辑</div></div></div><div id="mw-diff-otitle3"> <span class="comment comment--without-parentheses">加入{{<a href="/wiki/Template:Expand_language" title="Template:Expand language">Expand language</a>}}标记</span></div><div id="mw-diff-otitle5"><span class="mw-tag-markers"><a href="/wiki/Special:%E6%A0%87%E7%AD%BE" title="Special:标签">标签</a>：<span class="mw-tag-marker mw-tag-marker-Twinkle"><a href="/wiki/Wikipedia:TW" class="mw-redirect" title="Wikipedia:TW">TW</a></span></span></div><div id="mw-diff-otitle4"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&diff=prev&oldid=85264668" title="ROC曲线" id="differences-prevlink">←上一版本</a></div></td> <td colspan="2" class="diff-ntitle diff-side-added"><div id="mw-diff-ntitle1"><strong><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&oldid=85264872" title="ROC曲线">2024年12月10日 (二) 15:05的版本</a> <span class="mw-diff-edit"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&action=edit&oldid=85264872" title="ROC曲线">编辑</a></span><span class="mw-diff-timestamp" data-timestamp="2024-12-10T15:05:07Z"></span> <span class="mw-diff-undo"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&action=edit&undoafter=85264668&undo=85264872" title="“撤销”可以恢复该编辑并在预览模式下打开编辑表单。它允许在摘要中加入原因。">撤销</a></span></strong></div><div id="mw-diff-ntitle2"><a href="/wiki/User:UjuiUjuMandan" class="mw-userlink" title="User:UjuiUjuMandan" data-mw-revid="85264872"><bdi>UjuiUjuMandan</bdi></a><span class="mw-usertoollinks">（<a href="/wiki/User_talk:UjuiUjuMandan" class="mw-usertoollinks-talk" 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href="https://www.mediawiki.org/wiki/Special:MyLanguage/2017_wikitext_editor">2017年版源代码编辑</a></span></span></div><div id="mw-diff-ntitle4"><a href="/w/index.php?title=ROC%E6%9B%B2%E7%BA%BF&diff=next&oldid=85264872" title="ROC曲线" id="differences-nextlink">下一版本→</a></div></td> </tr><tr> <td colspan="2" class="diff-lineno">第88行：</td> <td colspan="2" class="diff-lineno">第88行：</td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>在这条线的以上的点代表了一个好的分类结果（勝過隨機分類），而在这条线以下的点代表了差的分类结果（劣於隨機分類）。</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>在这条线的以上的点代表了一个好的分类结果（勝過隨機分類），而在这条线以下的点代表了差的分类结果（劣於隨機分類）。</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>'''完美的預測'''是一个在左上角的点，在ROC空间座标 (0,1)点，X=0 代表着没有偽阳性，Y=1 代表著沒有偽阴性（所有的陽性都是真陽性）；也就是說，不管分類器輸出結果是陽性或陰性，都是100%正確。一个'''随机的预测'''会得到位於从 (0, 0) 到 (1, 1) '''对角线'''（也叫'''无识别率线'''）上的一个点；<del class="diffchange diffchange-inline">最直观</del>的<del class="diffchange diffchange-inline">随机</del>预测<del class="diffchange diffchange-inline">的例子就是抛硬币</del>。</div></td> <td class="diff-marker" data-marker="+"></td> <td class="diff-addedline diff-side-added"><div>'''完美的預測'''是一个在左上角的点，在ROC空间座标 (0,1)点，X=0 代表着没有偽阳性，Y=1 代表著沒有偽阴性（所有的陽性都是真陽性）；也就是說，不管分類器輸出結果是陽性或陰性，都是100%正確。一个'''随机的预测'''会得到位於从 (0, 0) 到 (1, 1) '''对角线'''（也叫'''无识别率线'''）上的一个点；<ins class="diffchange diffchange-inline">如果分类器采用“抛硬币”</ins>的<ins class="diffchange diffchange-inline">设定，那么该</ins>预测<ins class="diffchange diffchange-inline">会在点(0.5, 0.5)上</ins>。</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><br /></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>让我们来看在實際有100个阳性和100个阴性的案例時，四種預測方法（可能是四種分類器，或是同一分類器的四種閾值設定）的結果差異：</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>让我们来看在實際有100个阳性和100个阴性的案例時，四種預測方法（可能是四種分類器，或是同一分類器的四種閾值設定）的結果差異：</div></td> </tr>  </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>2024年12月10日 (二) 15:05的版本</h2> <div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r83732972">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output 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.ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Expand_language plainlinks metadata ambox ambox-notice" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span class="skin-invert" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/50px-Translation_to_zh_arrow.svg.png" decoding="async" width="50" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/75px-Translation_to_zh_arrow.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/100px-Translation_to_zh_arrow.svg.png 2x" data-file-width="60" data-file-height="20" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目<b>可参照<a href="https://en.wikipedia.org/wiki/Receiver_operating_characteristic" class="extiw" title="en:Receiver operating characteristic">英語維基百科</a>相應條目来扩充</b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2024年12月10日</span>)</i></small><span class="hide-when-compact"><br /><small>若您熟悉来源语言和主题，请协助<a href="/wiki/Wikipedia:%E7%BF%BB%E8%AF%91%E5%AE%88%E5%88%99" class="mw-redirect" title="Wikipedia:翻译守则">参考外语维基百科扩充条目</a>。请勿直接提交机械翻译，也不要翻译不可靠、低品质内容。依<a href="/wiki/Wikipedia:%E5%9C%A8%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E5%86%85%E5%A4%8D%E5%88%B6%E5%86%85%E5%AE%B9" title="Wikipedia:在维基百科内复制内容">版权协议</a>，译文需<a href="/wiki/Wikipedia:%E7%B7%A8%E8%BC%AF%E6%91%98%E8%A6%81#翻譯文章" title="Wikipedia:編輯摘要">在编辑摘要注明来源</a>，或于讨论页顶部标记<code>{{<a href="/wiki/Template:Translated_page" title="Template:Translated page">Translated page</a>}}</code>标签。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <div id="noteTA-60ef224e" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="IT"></div><div data-noteta-group-source="module" data-noteta-group="Math"></div></div></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Roccurves.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Roccurves.png/220px-Roccurves.png" decoding="async" width="220" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Roccurves.png/330px-Roccurves.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Roccurves.png/440px-Roccurves.png 2x" data-file-width="500" data-file-height="485" /></a><figcaption>3条ROC曲线</figcaption></figure> <p>在<a href="/wiki/%E4%BF%A1%E5%8F%B7%E6%A3%80%E6%B5%8B%E7%90%86%E8%AE%BA" title="信号检测理论">信号检测理论</a>中，<b>接收者操作特征曲線</b>，或者叫<b>ROC曲线</b>（英語：<span lang="en">Receiver operating characteristic curve</span>），是一种坐標圖式的分析工具，用於选择最佳的信號偵測模型、捨棄次佳的模型或者在同一模型中設定最佳<a href="/wiki/%E9%98%88%E5%80%BC" class="mw-redirect mw-disambig" title="阈值">閾值</a>。 </p><p>在做決策時，ROC分析能不受成本／效益的影響，給出客觀中立的建議。 </p><p>ROC曲线首先是由二战中的电子工程师和雷达工程师发明的，用来偵测战场上的敌军載具（飛機、船艦），也就是信号检测理论。之后很快就被引入了<a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%A6" title="心理学">心理学</a>来进行信号的<a href="/wiki/%E7%9F%A5%E8%A7%89" title="知觉">知觉</a>检测。數十年來，ROC分析被用於<a href="/wiki/%E5%8C%BB%E5%AD%A6" title="医学">医学</a>、<a href="/wiki/%E6%97%A0%E7%BA%BF%E7%94%B5" title="无线电">无线电</a>、<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8" class="mw-redirect" title="生物學">生物學</a>、<a href="/wiki/%E7%8A%AF%E7%BD%AA%E5%BF%83%E7%90%86%E5%AD%B8" title="犯罪心理學">犯罪心理學</a>领域中，而且最近在<a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a>（machine learning）和<a href="/wiki/%E6%95%B0%E6%8D%AE%E6%8C%96%E6%8E%98" title="数据挖掘">数据挖掘</a>（data mining）领域也得到了很好的发展。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="基本概念"><span id=".E5.9F.BA.E6.9C.AC.E6.A6.82.E5.BF.B5"></span>基本概念</h2></div> <table class="wikitable" align="right" width="40%" style="font-size:90%; margin-left:0.5em; padding:0.25em; background:#f1f5fc;"> <caption>术语 </caption> <tbody><tr valign="top"> <td> <dl><dt>陽性 (P, positive)</dt> <dt>陰性 (N, Negative)</dt> <dt>真阳性 (TP, true positive)</dt> <dd>正确的肯定。又稱：命中 (hit)</dd> <dt>真阴性 (TN, true negative)</dt> <dd>正确的否定。又稱：正確拒絕 (correct rejection)</dd> <dt>偽阳性 (FP, false positive)</dt> <dd>错误的肯定，又稱：假警報 (false alarm)，<a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E5%8F%8A%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" class="mw-redirect" title="第一型及第二型錯誤">第一型错误</a></dd> <dt>偽阴性 (FN, false negative)</dt> <dd>错误的否定，又稱：未命中 (miss)，<a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E5%8F%8A%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" class="mw-redirect" title="第一型及第二型錯誤">第二型错误</a></dd> <dt>真阳性率 (TPR, true positive rate)</dt> <dd>又稱：命中率 (hit rate)、敏感度(sensitivity)</dd> <dd>TPR = TP / P = TP / (TP+FN)</dd> <dt>偽阳性率(FPR, false positive rate)</dt> <dd>又稱：错误命中率，假警報率 (false alarm rate)</dd> <dd>FPR = FP / N = FP / (FP + TN)</dd> <dt><a href="/wiki/%E6%BA%96%E7%A2%BA%E5%BA%A6" class="mw-redirect" title="準確度">準确度</a> (ACC, accuracy)</dt> <dd>ACC = (TP + TN) / (P + N)</dd> <dd>即：(真陽性+真陰性) / 總樣本數</dd> <dt>真阴性率 (TNR)</dt> <dd>又稱：特異度 (SPC, specificity)</dd> <dd>SPC = TN / N = TN / (FP + TN) = 1 - FPR</dd> <dt>阳性预测值 (PPV)</dt> <dd>PPV = TP / (TP + FP)</dd> <dt>阴性预测值 (NPV)</dt> <dd>NPV = TN / (TN + FN)</dd> <dt>假發现率 (FDR)</dt> <dd>FDR = FP / (FP + TP)</dd> <dt><a href="/w/index.php?title=Matthews%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0&action=edit&redlink=1" class="new" title="Matthews相关系数（页面不存在）">Matthews相关系数</a> (MCC)，即 <a href="/wiki/Phi%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8" title="Phi相關係數">Phi相關係數</a></dt> <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 MCC={\frac {(TP*TN-FP*FN)}{\sqrt {PNP'N'}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mi>C</mi> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mi>P</mi> <mo>∗</mo> <mi>T</mi> <mi>N</mi> <mo>−</mo> <mi>F</mi> <mi>P</mi> <mo>∗</mo> <mi>F</mi> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> <msqrt> <mi>P</mi> <mi>N</mi> <msup> <mi>P</mi> <mo>′</mo> </msup> <msup> <mi>N</mi> <mo>′</mo> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle MCC={\frac {(TP*TN-FP*FN)}{\sqrt {PNP'N'}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c874f2a688a844a3409b7028407bc0ed6d4e361" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:33.321ex; height:6.676ex;" alt="{\displaystyle MCC={\frac {(TP*TN-FP*FN)}{\sqrt {PNP'N'}}}}"></span></dd> <dt><a href="/w/index.php?title=F1%E8%AF%84%E5%88%86&action=edit&redlink=1" class="new" title="F1评分（页面不存在）">F1评分</a></dt> <dd>F1 = 2TP/(P+P')</dd></dl> </td></tr> <tr> <td><span style="font-size:90%;"><i>Source: Fawcett (2006).</i></span> </td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">参见：<a href="/wiki/%E7%AC%AC%E4%B8%80%E5%9E%8B%E5%8F%8A%E7%AC%AC%E4%BA%8C%E5%9E%8B%E9%8C%AF%E8%AA%A4" class="mw-redirect" title="第一型及第二型錯誤">第一型及第二型錯誤</a>和<a href="/wiki/%E9%9D%88%E6%95%8F%E5%BA%A6%E5%92%8C%E7%89%B9%E7%95%B0%E5%BA%A6" title="靈敏度和特異度">靈敏度和特異度</a></div> <p><b>分类模型</b>（又稱<a href="/w/index.php?title=%E5%88%86%E7%B1%BB%E5%99%A8&action=edit&redlink=1" class="new" title="分类器（页面不存在）">分类器</a>，或<a href="/wiki/%E8%A8%BA%E6%96%B7" class="mw-redirect" title="診斷">診斷</a>）是将一个实例映射到一个特定类的过程。ROC分析的是<a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E5%88%86%E9%A1%9E%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="二元分類模型（页面不存在）">二元分類模型</a>，也就是輸出結果只有兩種類別的模型，例如：（陽性／陰性）（有病／沒病）（垃圾郵件／非垃圾郵件）（敵軍／非敵軍）。 </p><p>當<b>訊號偵測</b>（或<b>變數測量</b>）的结果是一個<a href="/w/index.php?title=%E9%80%A3%E7%BA%8C%E5%80%BC&action=edit&redlink=1" class="new" title="連續值（页面不存在）">連續值</a>時，類與類的邊界必须用一个<a href="/wiki/%E9%98%88%E5%80%BC" class="mw-redirect mw-disambig" title="阈值">阈值</a>（英語：<span lang="en">threshold</span>）來界定。举例来说，用血压值来检测一个人是否有<a href="/wiki/%E9%AB%98%E8%A1%80%E5%8E%8B" class="mw-redirect" title="高血压">高血压</a>，測出的血壓值是連續的實數（從0~200都有可能），以收縮壓140／舒張壓90為閾值，閾值以上便診斷為有高血壓，閾值未滿者診斷為無高血壓。二元分類模型的個案預測有四種結局： </p> <ol><li><b>真陽性</b>（TP）：<b>診斷為有</b>，<b>實際上也有</b>高血壓。</li> <li><b>偽阳性</b>（FP）：<b>診斷為有</b>，<b>实际卻没有</b>高血壓。</li> <li><b>真陰性</b>（TN）：<b>診斷為沒有</b>，<b>實際上也沒有</b>高血壓。</li> <li><b>偽阴性</b>（FN）：<b>診斷為沒有</b>，<b>实际却有</b>高血壓。</li></ol> <p>這四種結局可以畫成2 × 2的<a href="/wiki/%E6%B7%B7%E6%B7%86%E7%9F%A9%E9%98%B5" title="混淆矩阵">混淆矩阵</a>： </p> <table class="wikitable" align="center" style="border: thin solid"> <tbody><tr> <th colspan="2" rowspan="2"> </th> <th colspan="2" align="center">真实值</th> <th rowspan="2">總<br />數 </th></tr> <tr> <th><i>p</i></th> <th><i>n</i> </th></tr> <tr> <th rowspan="2" valign="middle">预<br />测<br />输<br />出 </th> <th valign="middle" style="padding:0.5em;"><i>p'</i></th> <th style="padding:0.5em;">真阳性<br />(TP)</th> <th style="padding:0.5em;">偽阳性<br />(FP)</th> <th style="padding:0.5em;">P' </th></tr> <tr> <th valign="middle" style="padding:0.5em;"><i>n'</i></th> <th style="padding: 0.5em;">偽阴性<br />(FN)</th> <th style="padding:0.5em;">真阴性<br />(TN)</th> <th style="padding:0.5em;">N' </th></tr> <tr> <th colspan="2" style="padding:0.5em;">總數</th> <th align="center">P</th> <th align="center">N</th> <th> </th></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="ROC空間"><span id="ROC.E7.A9.BA.E9.96.93"></span>ROC空間</h2></div> <p>ROC空间将偽陽性率（FPR）定義為 <i>X</i> 軸，真陽性率（TPR）定义为 <i>Y</i> 轴。 </p> <ul><li>TPR：在所有實際為陽性的樣本中，被<b>正確地</b>判斷為陽性之比率。（相当于<a href="/wiki/%E9%9D%88%E6%95%8F%E5%BA%A6%E5%92%8C%E7%89%B9%E7%95%B0%E5%BA%A6" title="靈敏度和特異度">灵敏度</a>。）</li></ul> <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 TPR=TP/(TP+FN)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mi>P</mi> <mi>R</mi> <mo>=</mo> <mi>T</mi> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>T</mi> <mi>P</mi> <mo>+</mo> <mi>F</mi> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle TPR=TP/(TP+FN)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7fbc69a0bf8dcae28fc8fa12b65e868ed91bdb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.624ex; height:2.843ex;" alt="{\displaystyle TPR=TP/(TP+FN)}"></span></dd></dl> <ul><li>FPR：在所有實際為阴性的样本中，被<b>錯誤地</b>判斷為陽性之比率。</li></ul> <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 FPR=FP/(FP+TN)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mi>P</mi> <mi>R</mi> <mo>=</mo> <mi>F</mi> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mi>P</mi> <mo>+</mo> <mi>T</mi> <mi>N</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle FPR=FP/(FP+TN)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26b32536ee324e37e5118aaa1d4af6d62dfcd536" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.833ex; height:2.843ex;" alt="{\displaystyle FPR=FP/(FP+TN)}"></span></dd></dl> <p><b>給定</b>一個二元分類<b>模型</b>和它的<b>閾值</b>，就能從所有樣本的（陽性／陰性）真實值和預測值計算出一個 (X=FPR, Y=TPR) 座標點。在这条线的以上的点代表了一个好的分类结果（勝過隨機分類），而在这条线以下的点代表了差的分类结果（劣於隨機分類）。 </p><p><b>完美的預測</b>是一个在左上角的点，在ROC空间座标 (0,1)点，X=0 代表着没有偽阳性，Y=1 代表著沒有偽阴性（所有的陽性都是真陽性）；也就是說，不管分類器輸出結果是陽性或陰性，都是100%正確。一个<b>随机的预测</b>会得到位於从 (0, 0) 到 (1, 1) <b>对角线</b>（也叫<b>无识别率线</b>）上的一个点；如果分类器采用“抛硬币”的设定，那么该预测会在点(0.5, 0.5)上。 </p><p>让我们来看在實際有100个阳性和100个阴性的案例時，四種預測方法（可能是四種分類器，或是同一分類器的四種閾值設定）的結果差異： </p> <table style="font-size:90%; margin-left:0.5em;"> <tbody><tr> <th>A</th> <th>B</th> <th>C</th> <th>C' </th></tr> <tr> <td> <table style="text-align:center;"> <tbody><tr> <td style="border:thin solid; padding:1em;">TP=63</td> <td style="border:thin solid; padding:1em;">FP=28</td> <td>91 </td></tr> <tr> <td style="border:thin solid; padding:1em;">FN=37</td> <td style="border:thin solid; padding:1em;">TN=72</td> <td>109 </td></tr> <tr> <td>100</td> <td>100</td> <td>200 </td></tr></tbody></table> </td> <td style="padding-left:1em;"> <table style="text-align:center;"> <tbody><tr> <td style="border:thin solid; padding:1em;">TP=77</td> <td style="border:thin solid; padding:1em;">FP=77</td> <td>154 </td></tr> <tr> <td style="border:thin solid; padding:1em;">FN=23</td> <td style="border:thin solid; padding:1em;">TN=23</td> <td>46 </td></tr> <tr> <td>100</td> <td>100</td> <td>200 </td></tr></tbody></table> </td> <td style="padding-left:1em;"> <table style="text-align:center;"> <tbody><tr> <td style="border:thin solid; padding:1em;">TP=24</td> <td style="border:thin solid; padding:1em;">FP=88</td> <td>112 </td></tr> <tr> <td style="border:thin solid; padding:1em;">FN=76</td> <td style="border:thin solid; padding:1em;">TN=12</td> <td>88 </td></tr> <tr> <td>100</td> <td>100</td> <td>200 </td></tr></tbody></table> </td> <td style="padding-left:1em;"> <table style="text-align:center;"> <tbody><tr> <td style="border:thin solid; padding:1em;">TP=76</td> <td style="border:thin solid; padding:1em;">FP=12</td> <td>88 </td></tr> <tr> <td style="border:thin solid; padding:1em;">FN=24</td> <td style="border:thin solid; padding:1em;">TN=88</td> <td>112 </td></tr> <tr> <td>100</td> <td>100</td> <td>200 </td></tr></tbody></table> </td></tr> <tr> <td style="padding-left:1em;">TPR = 0.63</td> <td style="padding-left:2em;">TPR = 0.77</td> <td style="padding-left:2em;">TPR = 0.24</td> <td style="padding-left:2em;">TPR = 0.76 </td></tr> <tr> <td style="padding-left:1em;">FPR = 0.28</td> <td style="padding-left:2em;">FPR = 0.77</td> <td style="padding-left:2em;">FPR = 0.88</td> <td style="padding-left:2em;">FPR = 0.12 </td></tr> <tr> <td style="padding-left:1em;">ACC = 0.675</td> <td style="padding-left:2em;">ACC = 0.500</td> <td style="padding-left:2em;">ACC = 0.180</td> <td style="padding-left:2em;">ACC = 0.820 </td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:ROC_space-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/ROC_space-2.png/350px-ROC_space-2.png" decoding="async" width="350" height="350" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/ROC_space-2.png/525px-ROC_space-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/ROC_space-2.png/700px-ROC_space-2.png 2x" data-file-width="1093" data-file-height="1094" /></a><figcaption>ROC空间的4个例子</figcaption></figure> <p>將這4種结果畫在ROC空间裡： </p> <ul><li>點與随机猜测线的距離，是預測力的指標：<b>离左上角越近的點預測（診斷）準確率越高</b>。離右下角越近的點，预测越不準。</li> <li>在<b>A</b>、<b>B</b>、<b>C</b>三者當中，最好的結果是<b>A</b>方法。</li> <li><b>B</b>方法的结果位於随机猜测线（對角線）上，在例子中我们可以看到<b>B</b>的準確度（ACC，定義見前面表格）是50%。</li> <li><b>C</b>雖然預測準確度最差，甚至劣於隨機分類，也就是低於0.5（低於對角線）。然而，当将<b>C</b>以 (0.5, 0.5) 為中點作一个镜像后，<b>C'</b>的结果甚至要比<b>A</b>还要好。这个作镜像的方法，简单說，不管<b>C</b>（或任何ROC點低於對角線的情況）预测了什么，就做相反的結論。</li></ul> <div class="mw-heading mw-heading2"><h2 id="ROC曲線"><span id="ROC.E6.9B.B2.E7.B7.9A"></span>ROC曲線</h2></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:ROCfig.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/ROCfig.PNG/350px-ROCfig.PNG" decoding="async" width="350" height="569" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/5c/ROCfig.PNG 1.5x" data-file-width="361" data-file-height="587" /></a><figcaption>隨著閾值調整，ROC座標系裡的點如何移動</figcaption></figure> <p>上述ROC空間裡的單點，是給定分類模型且給定閾值後得出的。但同一個<a href="/w/index.php?title=%E4%BA%8C%E5%85%83%E5%88%86%E9%A1%9E%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="二元分類模型（页面不存在）">二元分類模型</a>的<a href="/wiki/%E9%98%88%E5%80%BC" class="mw-redirect mw-disambig" title="阈值">閾值</a>可能設定為高或低，每種閾值的設定會得出不同的FPR和TPR。 </p> <ul><li>將<b>同一模型每個閾值</b> 的 (FPR, TPR) 座標都畫在ROC空間裡，就成為<b>特定模型的ROC曲線</b>。</li></ul> <p>例如右圖，人體的血液蛋白濃度是呈正态分布的連續變數，病人的分布是紅色，平均值為A <a href="/wiki/%E5%85%AC%E5%85%8B" class="mw-redirect" title="公克">g</a>/<a href="/wiki/%E5%85%AC%E5%8D%87#-{公升}-配合國際單位制的詞頭" title="公升">dL</a>，健康人的分布是藍色，平均值是C g/dL。健康檢查會測量血液樣本中的某種蛋白質濃度，達到某個值（閾值，threshold）以上診斷為有疾病徵兆。研究者可以調整閾值的高低（將左上圖的B垂直線往左或右移動），便會得出不同的偽陽性率與真陽性率，總之即得出不同的預測準確率。 </p><p>1. 由於每個不同的分類器（診斷工具、偵測工具）有各自的測量標準和測量值的單位（標示為：「健康人－病人分佈圖」的橫軸），所以不同分類器的「健康人－病人分佈圖」都長得不一樣。 </p><p>2. <b>比較不同分類器時，ROC曲線的實際形狀，便視兩個實際分佈的重疊範圍而定，沒有規律可循。</b> </p><p>3. 但<b>在同一個分類器之內</b>，閾值的不同設定對ROC曲線的影響，仍有一些規律可循： </p> <ul><li><b>當閾值設定為最高時</b>，亦即所有樣本都被預測為陰性，<b>沒有樣本被預測為陽性</b>，此時在偽陽性率 FPR = FP / ( FP + TN ) 算式中的 FP = 0，所以 FPR = 0%。同時在真陽性率（TPR）算式中， TPR = TP / ( TP + FN ) 算式中的 TP = 0，所以 TPR = 0%</li></ul> <dl><dd>→ <b>當閾值設定為最高時，必得出ROC座標系左下角的點 (0, 0)。</b></dd></dl> <ul><li><b>當閾值設定為最低時</b>，亦即所有樣本都被預測為陽性，<b>沒有樣本被預測為陰性</b>，此時在偽陽性率FPR = FP / ( FP + TN ) 算式中的 TN = 0，所以 <b>FPR = 100%</b>。同時在真陽性率 TPR = TP / ( TP + FN ) 算式中的 FN = 0，所以 <b>TPR=100%</b></li></ul> <dl><dd>→ <b>當閾值設定為最低時，必得出ROC座標系右上角的點 (1, 1)。</b></dd></dl> <ul><li>因為TP、FP、TN、FN都是累積次數，TN和FN隨著閾值調低而減少（或持平），TP和FP隨著閾值調低而增加（或持平），所以FPR和TPR皆必隨著閾值調低而增加（或持平）。</li></ul> <dl><dd>→ <b>隨著閾值調低，ROC點</b> 往右上（或右／或上）移動，或不動；但<b>絕不會往左下(或左／或下)移動</b>。</dd></dl> <div class="mw-heading mw-heading2"><h2 id="曲線下面積（AUC）"><span id=".E6.9B.B2.E7.B7.9A.E4.B8.8B.E9.9D.A2.E7.A9.8D.EF.BC.88AUC.EF.BC.89"></span>曲線下面積（AUC）</h2></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Curvas.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Curvas.png/350px-Curvas.png" decoding="async" width="350" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Curvas.png/525px-Curvas.png 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b9/Curvas.png 2x" data-file-width="568" data-file-height="281" /></a><figcaption>例示三種AUC值（曲線下面積）</figcaption></figure> <p>在比較不同的分類模型時，可以將每個模型的ROC曲線都畫出來，比較曲線下面積做為模型優劣的指標。 </p> <div class="mw-heading mw-heading3"><h3 id="意義"><span id=".E6.84.8F.E7.BE.A9"></span>意義</h3></div> <p>ROC曲線下方的面積（英語：<span lang="en">Area under the Curve of ROC (AUC ROC)</span>），其意義是： </p> <ul><li>因為是在1x1的方格裡求面積，AUC必在0~1之間。</li> <li>假設閾值以上是陽性，以下是陰性；</li> <li>若隨機抽取一個陽性樣本和一個陰性樣本，分類器<b>正確判斷</b>陽性樣本的值高於陰性樣本之<b>機率</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 =AUC}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mi>A</mi> <mi>U</mi> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =AUC}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fa6081560fcd9458a42c8400e7b50085101a486" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.745ex; height:2.176ex;" alt="{\displaystyle =AUC}"></span><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。</li> <li>簡單說：<b>AUC值越大的分類器，正確率越高。</b></li></ul> <p>從AUC判斷分類器（預測模型）優劣的標準： </p> <ul><li>AUC = 1，是完美分類器，採用這個預測模型時，存在至少一個閾值能得出完美預測。絕大多數預測的場合，不存在完美分類器。</li> <li>0.5 < AUC < 1，優於隨機猜測。這個分類器（模型）妥善設定閾值的話，能有預測價值。</li> <li>AUC = 0.5，跟隨機猜測一樣（例：丟銅板），模型沒有預測價值。</li> <li>AUC < 0.5，比隨機猜測還差；但只要總是反預測而行，就優於隨機猜測。</li></ul> <div class="mw-heading mw-heading3"><h3 id="計算"><span id=".E8.A8.88.E7.AE.97"></span>計算</h3></div> <p>AUC的計算有兩種方式，都是以逼近法求近似值。 </p> <div class="mw-heading mw-heading4"><h4 id="梯形法"><span id=".E6.A2.AF.E5.BD.A2.E6.B3.95"></span>梯形法</h4></div> <p><b>梯形法</b>（英語：<span lang="en">trapezoid method</span>）：簡單地將每個相鄰的點以直線連接，計算連線下方的總面積。因為每一線段下方都是一個梯形，所以叫<b>梯形法</b>。 </p> <ul><li>優點：簡單，所以常用。</li> <li>缺點：傾向於低估AUC。</li></ul> <div class="mw-heading mw-heading4"><h4 id="ROC_AUCH法"><span id="ROC_AUCH.E6.B3.95"></span>ROC AUCH法</h4></div> <div class="mw-heading mw-heading3"><h3 id="潛在問題"><span id=".E6.BD.9B.E5.9C.A8.E5.95.8F.E9.A1.8C"></span>潛在問題</h3></div> <p>AUC of ROC是<a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">機器學習</a>的社群最常使用來比較不同模型優劣的方法<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> 。然而近來這個做法開始受到質疑，因為有些機器學習的研究指出，AUC的杂訊太多，並且很常求不出可信又有效的AUC值（此時便不能保證AUC傳達本節開頭所述之意義），使得AUC在模型比較時產生的問題比解釋的問題更多<sup id="cite_ref-Hanczar2010_3-0" class="reference"><a href="#cite_note-Hanczar2010-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lobo2008_4-0" class="reference"><a href="#cite_note-Lobo2008-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hand2009_5-0" class="reference"><a href="#cite_note-Hand2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> 。 </p> <div class="mw-heading mw-heading2"><h2 id="分析軟體"><span id=".E5.88.86.E6.9E.90.E8.BB.9F.E9.AB.94"></span>分析軟體</h2></div> <p>所有常用於統計分析的軟體（例：SPSS、SAS、SYSTAT、S-Plus、ROCKIT、RscorePlus）都有依據不同閾值自動計算真陽性和偽陽性比率、並依此繪製ROC曲線的功能。 </p><p><b>离散分类器</b>（英語：<span lang="en">discrete</span>，或稱「間斷分類器」），如<a href="/wiki/%E5%86%B3%E7%AD%96%E6%A0%91" title="决策树">决策树</a>，产生的是离散的数值或者一个二元标签。应用到实例中，这样的分类器最后只会在ROC空间产生单一的点。而一些其他的分类器，如<a href="/wiki/%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E5%99%A8" title="朴素贝叶斯分类器">朴素贝叶斯分类器</a>，<a href="/wiki/%E9%82%8F%E8%BC%AF%E6%96%AF%E8%AB%A6%E8%BF%B4%E6%AD%B8" title="邏輯斯諦迴歸">邏輯斯諦迴歸</a>或者<a href="/wiki/%E4%BA%BA%E5%B7%A5%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C" title="人工神经网络">人工神经网络</a>，产生的是实例属于某一类的可能性，对于这些方法，一个阈值就决定了ROC空间中点的位置。举例来说，如果可能值低于或者等于0.8这个阈值就将其认为是阳性的类，而其他的值被认为是阴性类。这样就可以通过画每一个阈值的ROC点来生成一个生成一条曲线。MedCalc是较好的ROC曲线分析软件。 </p> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2></div> <div class="mw-heading mw-heading3"><h3 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h3></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Fawcett, Tom (2006); <i>An introduction to ROC analysis</i>, Pattern Recognition Letters, 27, 861–874.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation journal">Hanley, James A.; McNeil, 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(2010); <i>Small-sample precision of ROC-related estimates</i>, Bioinformatics 26 (6): 822–830</span> </li> <li id="cite_note-Lobo2008-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lobo2008_4-0">^</a></b></span> <span class="reference-text">Lobo, Jorge M.; Jiménez-Valverde, Alberto; and Real, Raimundo (2008), <i>AUC: a misleading measure of the performance of predictive distribution models</i>, Global Ecology and Biogeography, 17: 145–151</span> </li> <li id="cite_note-Hand2009-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hand2009_5-0">^</a></b></span> <span class="reference-text">Hand, David J. 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(2007). Receiver-operating characteristic analysis for evaluating diagnostic tests and predictive models. <i>Circulation</i>, 6;115(5):654–7.</li> <li><cite class="citation book">X. H., Zhou. <span></span><i>Statistical Methods in Diagnostic Medicine</i><span></span>. Wiley & Sons. 2002. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780471347729" title="Special:网络书源/9780471347729"><span title="国际标准书号">ISBN</span> 9780471347729</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AROC%E6%9B%B2%E7%BA%BF&rft.aufirst=Zhou&rft.aulast=X.+H.&rft.btitle=Statistical+Methods+in+Diagnostic+Medicine&rft.date=2002&rft.genre=book&rft.isbn=9780471347729&rft.pub=Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li>Lasko, T.A., J.G. Bhagwat, K.H. Zou and Ohno-Machado, L. (2005). The use of receiver operating characteristic curves in biomedical informatics. <i>Journal of Biomedical Informatics</i>, 38(5):404–415.</li> <li>Balakrishnan, N., (1991) <i>Handbook of the Logistic Distribution</i>, Marcel Dekker, Inc., <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780824785871" class="internal mw-magiclink-isbn">ISBN 978-0824785871</a>.</li> <li>Gonen M., (2007) <i>Analyzing Receiver Operating Characteristic Curves Using SAS</i>, SAS Press, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9781599942981" class="internal mw-magiclink-isbn">ISBN 978-1-59994-298-1</a>.</li> <li>Green, W.H., (2003) <i>Econometric Analysis</i>, fifth edition, <a href="/wiki/Prentice_Hall" class="mw-redirect" title="Prentice Hall">Prentice Hall</a>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0130661899" class="internal mw-magiclink-isbn">ISBN 0-13-066189-9</a>.</li> <li>Heagerty, P.J., Lumley, T., Pepe, M. S. (2000) Time-dependent ROC Curves for Censored Survival Data and a Diagnostic Marker <i>Biometrics</i>, <b>56</b>:337–344</li> <li>Hosmer, D.W. and Lemeshow, S., (2000) <i>Applied Logistic Regression</i>, 2nd ed., New York; Chichester, <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">Wiley</a>, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0471356328" class="internal mw-magiclink-isbn">ISBN 0-471-35632-8</a>.</li> <li>Brown, C.D., and Davis, H.T. (2006) Receiver operating characteristic curves and related decision measures: a tutorial, <i>Chemometrics and Intelligent Laboratory Systems</i>, <b>80</b>:24–38</li> <li>Mason, S.J. and Graham, N.E. (2002) Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation. <i>Q.J.R. Meteorol. Soc.</i>, 128:2145–2166.</li> <li>Pepe, M.S. (2003). <i>The statistical evaluation of medical tests for classification and prediction</i>. <a href="/wiki/Oxford_University_Press" class="mw-redirect" title="Oxford University Press">Oxford</a>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0198565828" class="internal mw-magiclink-isbn">ISBN 0198565828</a>.</li> <li>Carsten, S. Wesseling, S., Schink, T., and Jung, K. (2003) Comparison of Eight Computer Programs for Receiver-Operating Characteristic Analysis. <i>Clinical Chemistry</i>, <b>49</b>:433–439</li> <li>Swets, J.A. (1995). <i>Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers.</i> Lawrence Erlbaum Associates.</li> <li>Swets, J.A., Dawes, R., and Monahan, J. (2000) Better Decisions through Science. <i><a href="/wiki/Scientific_American" class="mw-redirect" title="Scientific American">Scientific American</a></i>, October, pages 82–87.</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="外部链接"><span id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5"></span>外部链接</h2></div> <ul><li><a rel="nofollow" class="external text" href="http://www.gpa.etsmtl.ca/cours/sys828/REFS/A1/Fawcett_PRL2006.pdf">An introduction to ROC analysis</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100702020856/http://www-psych.stanford.edu/~lera/psych115s/notes/signal/">A more thorough treatment of ROC curves and signal detection theory</a></li> <li><a rel="nofollow" class="external text" href="http://home.comcast.net/~tom.fawcett/public_html/ROCCH/index.html">Tom Fawcett's ROC Convex Hull: tutorial, program and papers</a>（<a rel="nofollow" class="external text" href="//web.archive.org/web/20090615110133/http://home.comcast.net/~tom.fawcett/public_html/ROCCH/index.html">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20100715035231/http://www.cs.bris.ac.uk/~flach/ICML04tutorial/index.html">Peter Flach's tutorial on ROC analysis in machine learning</a></li> <li><a rel="nofollow" class="external text" href="http://www.anaesthetist.com/mnm/stats/roc/">The magnificent ROC</a>（<a rel="nofollow" class="external text" href="//web.archive.org/web/20100529080209/http://www.anaesthetist.com/mnm/stats/roc/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） — An explanation and interactive demonstration of the connection of ROCs to archetypal bi-normal test result plots</li></ul> <div class="navbox-styles"><style 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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%A6%82%E7%8E%87%E5%88%86%E5%B8%83" title="概率分布">连续概率</a></th><td class="navbox-list-with-group 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/%E9%9B%86%E4%B8%AD%E8%B6%8B%E5%8A%BF" title="集中趋势">集中趋势</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B0" title="平均数">平均数</a> <ul><li><a href="/wiki/%E5%B9%B3%E6%96%B9%E5%B9%B3%E5%9D%87%E6%95%B0" title="平方平均数">平方</a></li> <li><a href="/wiki/%E7%AE%97%E6%9C%AF%E5%B9%B3%E5%9D%87%E6%95%B0" title="算术平均数">算術</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0" title="几何平均数">幾何</a></li> <li><a href="/wiki/%E8%B0%83%E5%92%8C%E5%B9%B3%E5%9D%87%E6%95%B0" title="调和平均数">調和</a></li> <li><a href="/wiki/%E7%AE%97%E6%9C%AF-%E5%87%A0%E4%BD%95%E5%B9%B3%E5%9D%87%E6%95%B0" title="算术-几何平均数">算术-几何</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95-%E8%B0%83%E5%92%8C%E5%B9%B3%E5%9D%87%E6%95%B0" title="几何-调和平均数">几何-调和</a></li> <li><a href="/wiki/%E5%B8%8C%E7%BE%85%E5%B9%B3%E5%9D%87%E6%95%B8" title="希羅平均數">希羅</a>／<a href="/wiki/%E5%B9%B3%E5%9D%87%E6%95%B0%E4%B8%8D%E7%AD%89%E5%BC%8F" title="平均数不等式">平均数不等式</a></li></ul></li> <li><a href="/wiki/%E4%B8%AD%E4%BD%8D%E6%95%B8" title="中位數">中位數</a></li> <li><a href="/wiki/%E4%BC%97%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="众数 (数学)">眾數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%A6%BB%E6%95%A3%E7%A8%8B%E5%BA%A6" title="离散程度">离散程度</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%85%A8%E8%B7%9D" title="全距">全距</a></li> <li><a href="/wiki/%E5%8F%98%E5%BC%82%E7%B3%BB%E6%95%B0" title="变异系数">变异系数</a></li> <li><a href="/wiki/%E7%99%BE%E5%88%86%E4%BD%8D%E6%95%B0" title="百分位数">百分位數</a></li> <li><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/%E5%9B%9B%E5%88%86%E4%BD%8D%E6%95%B0" title="四分位数">四分位数</a></li> <li><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/%E6%96%B9%E5%B7%AE" title="方差">方差</a></li> <li><a href="/wiki/%E5%B9%B3%E5%9D%87%E5%B7%AE" title="平均差">平均差</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/%E5%88%87%E6%AF%94%E9%9B%AA%E5%A4%AB%E4%B8%8D%E7%AD%89%E5%BC%8F" title="切比雪夫不等式">切比雪夫不等式</a></li> <li><a href="/wiki/%E5%9F%BA%E5%B0%BC%E7%B3%BB%E6%95%B0" title="基尼系数">基尼系数</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="ilh-all" data-orig-title="分布形态" data-lang-code="en" data-lang-name="英语" data-foreign-title="Shape of the distribution"><span class="ilh-page"><a href="/w/index.php?title=%E5%88%86%E5%B8%83%E5%BD%A2%E6%80%81&action=edit&redlink=1" class="new" title="分布形态（页面不存在）">分布形态</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Shape_of_the_distribution" class="extiw" title="en:Shape of the distribution"><span lang="en" dir="auto">Shape of the distribution</span></a></span>）</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%B8%AD%E5%BF%83%E6%9E%81%E9%99%90%E5%AE%9A%E7%90%86" title="中心极限定理">中心极限定理</a></li> <li><a href="/wiki/%E7%9F%A9_(%E6%95%B8%E5%AD%B8)" title="矩 (數學)">矩</a> <ul><li><a href="/wiki/%E5%81%8F%E5%BA%A6" title="偏度">偏態</a></li> <li><a href="/wiki/%E5%B3%B0%E5%BA%A6" title="峰度">峰態</a></li></ul></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%A6%82%E7%8E%87%E5%88%86%E5%B8%83" title="概率分布">离散概率</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="次數 (統計學)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Count data"><span class="ilh-page"><a href="/w/index.php?title=%E6%AC%A1%E6%95%B8_(%E7%B5%B1%E8%A8%88%E5%AD%B8)&action=edit&redlink=1" class="new" title="次數 (統計學)（页面不存在）">次數</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Count_data" class="extiw" title="en:Count data"><span lang="en" dir="auto">Count data</span></a></span>）</span></span></li> <li>· <span class="nowrap"><span class="ilh-all" data-orig-title="列聯表" data-lang-code="en" data-lang-name="英语" data-foreign-title="Contingency table"><span class="ilh-page"><a href="/wiki/%E5%88%97%E8%81%94%E8%A1%A8" title="列联表">列聯表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Contingency_table" class="extiw" title="en:Contingency table"><span lang="en" dir="auto">Contingency table</span></a></span>）</span></span></span></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="5" 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/120px-Fisher_iris_versicolor_sepalwidth.svg.png" decoding="async" width="120" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/180px-Fisher_iris_versicolor_sepalwidth.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/240px-Fisher_iris_versicolor_sepalwidth.svg.png 2x" data-file-width="822" data-file-height="567" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><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><br />和<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-with-group 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%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></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BF%A1%E8%B3%B4%E5%8D%80%E9%96%93" title="信賴區間">置信区间</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></li> <li><a href="/wiki/%E6%98%BE%E8%91%97%E6%80%A7%E5%B7%AE%E5%BC%82" title="显著性差异">显著性差异</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/%E8%B4%9D%E5%8F%B6%E6%96%AF%E6%8E%A8%E6%96%AD" title="贝叶斯推断">贝叶斯推断</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AF%95%E9%AA%8C%E8%AE%BE%E8%AE%A1" title="试验设计">实验设计</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%80%BB%E4%BD%93" title="总体">总体</a></li> <li><a href="/wiki/%E6%8A%BD%E6%A8%A3" title="抽樣">抽樣</a></li> <li><a href="/wiki/%E9%87%8D%E6%8A%BD%E6%A0%B7" title="重抽样">重抽样</a> <ul><li><a href="/wiki/%E5%88%80%E5%88%87%E6%B3%95" title="刀切法">刀切法</a></li> <li><a href="/wiki/%E8%87%AA%E5%8A%A9%E6%B3%95" title="自助法">自助法</a></li> <li><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></ul></li> <li><span class="ilh-all" data-orig-title="重複 (統計學)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Replication (statistics)"><span class="ilh-page"><a href="/w/index.php?title=%E9%87%8D%E8%A4%87_(%E7%B5%B1%E8%A8%88%E5%AD%B8)&action=edit&redlink=1" class="new" title="重複 (統計學)（页面不存在）">重复</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Replication_(statistics)" class="extiw" title="en:Replication (statistics)"><span lang="en" dir="auto">Replication (statistics)</span></a></span>）</span></span></li> <li><a href="/w/index.php?title=%E9%98%BB%E7%A2%8D&action=edit&redlink=1" class="new" title="阻碍（页面不存在）">阻碍</a></li> <li><a href="/wiki/%E9%9D%88%E6%95%8F%E5%BA%A6%E5%92%8C%E7%89%B9%E7%95%B0%E5%BA%A6" title="靈敏度和特異度">靈敏度和特異度</a></li> <li><span class="ilh-all" data-orig-title="區集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Blocking (statistics)"><span class="ilh-page"><a href="/w/index.php?title=%E5%8D%80%E9%9B%86&action=edit&redlink=1" class="new" title="區集（页面不存在）">區集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Blocking_(statistics)" class="extiw" title="en:Blocking (statistics)"><span lang="en" dir="auto">Blocking (statistics)</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%BC%BA%E5%A4%B1%E6%95%B0%E6%8D%AE" title="缺失数据">缺失数据</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="ilh-all" data-orig-title="样本量" data-lang-code="en" data-lang-name="英语" data-foreign-title="Sample size"><span class="ilh-page"><a href="/w/index.php?title=%E6%A0%B7%E6%9C%AC%E9%87%8F&action=edit&redlink=1" class="new" title="样本量（页面不存在）">样本量</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Sample_size" class="extiw" title="en:Sample size"><span lang="en" dir="auto">Sample size</span></a></span>）</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%A0%87%E5%87%86%E8%AF%AF%E5%B7%AE" title="标准误差">標準誤</a></li> <li><a href="/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說">零假设</a></li> <li><a href="/wiki/%E5%B0%8D%E7%AB%8B%E5%81%87%E8%AA%AA" title="對立假說">备择假设</a></li> <li><a href="/wiki/%E5%9E%8B%E4%B8%80%E9%8C%AF%E8%AA%A4%E8%88%87%E5%9E%8B%E4%BA%8C%E9%8C%AF%E8%AA%A4" title="型一錯誤與型二錯誤">第一类错误与第二类错误</a></li> <li><a href="/wiki/%E6%AA%A2%E5%AE%9A%E5%8A%9B" title="檢定力">统计功效</a></li> <li><a href="/wiki/%E6%95%88%E5%BA%94%E5%80%BC" title="效应值">效应值</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">常规估计</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%B4%9D%E5%8F%B6%E6%96%AF%E6%8E%A8%E6%96%AD" title="贝叶斯推断">贝叶斯推断</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></li> <li><a href="/wiki/%E6%9C%80%E5%A4%A7%E4%BC%BC%E7%84%B6%E4%BC%B0%E8%AE%A1" title="最大似然估计">最大似然估计</a></li> <li><span class="ilh-all" data-orig-title="最小距離估計" data-lang-code="en" data-lang-name="英语" data-foreign-title="Minimum distance estimation"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%80%E5%B0%8F%E8%B7%9D%E9%9B%A2%E4%BC%B0%E8%A8%88&action=edit&redlink=1" class="new" title="最小距離估計（页面不存在）">最小距離估計</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Minimum_distance_estimation" class="extiw" title="en:Minimum distance estimation"><span lang="en" dir="auto">Minimum distance estimation</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%9F%A9%E4%BC%B0%E8%AE%A1" title="矩估计">矩估计</a></li> <li><a href="/w/index.php?title=%E6%9C%80%E5%A4%A7%E9%97%B4%E8%B7%9D&action=edit&redlink=1" class="new" title="最大间距（页面不存在）">最大间距</a></li></ul> </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">假设检验</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Z%E6%A3%80%E9%AA%8C" title="Z检验">Z檢驗</a></li> <li><a href="/wiki/%E5%8F%B8%E5%BE%92%E9%A0%93t%E6%AA%A2%E5%AE%9A" title="司徒頓t檢定">学生t检验</a></li> <li><a href="/wiki/F%E6%A3%80%E9%AA%8C" title="F检验">F檢定</a></li> <li><a href="/wiki/%E5%8D%A1%E6%96%B9%E6%A3%80%E9%AA%8C" title="卡方检验">卡方检验</a></li> <li><span class="ilh-all" data-orig-title="Wald檢定" data-lang-code="en" data-lang-name="英语" data-foreign-title="Wald test"><span class="ilh-page"><a href="/w/index.php?title=Wald%E6%AA%A2%E5%AE%9A&action=edit&redlink=1" class="new" title="Wald檢定（页面不存在）">Wald檢定</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Wald_test" class="extiw" title="en:Wald test"><span lang="en" dir="auto">Wald test</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="曼-惠特尼檢定" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mann–Whitney U test"><span class="ilh-page"><a href="/w/index.php?title=%E6%9B%BC-%E6%83%A0%E7%89%B9%E5%B0%BC%E6%AA%A2%E5%AE%9A&action=edit&redlink=1" class="new" title="曼-惠特尼檢定（页面不存在）">曼-惠特尼檢定</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test" class="extiw" title="en:Mann–Whitney U test"><span lang="en" dir="auto">Mann–Whitney U test</span></a></span>）</span></span></li> <li><a href="/w/index.php?title=%E7%A7%A9%E5%92%8C%E6%A3%80%E9%AA%8C&action=edit&redlink=1" class="new" title="秩和检验（页面不存在）">秩和检验</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%94%9F%E5%AD%98%E5%88%86%E6%9E%90" title="生存分析">生存分析</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%94%9F%E5%AD%98%E5%87%BD%E6%95%B0" title="生存函数">生存函数</a></li> <li><a href="/w/index.php?title=%E4%B9%98%E7%A9%8D%E6%A5%B5%E9%99%90%E4%BC%B0%E8%A8%88%E9%87%8F&action=edit&redlink=1" class="new" title="乘積極限估計量（页面不存在）">乘積極限估計量</a></li> <li><a href="/w/index.php?title=%E5%B0%8D%E6%95%B8%E7%A7%A9%E5%92%8C%E6%AA%A2%E5%AE%9A&action=edit&redlink=1" class="new" title="對數秩和檢定（页面不存在）">對數秩和檢定</a></li> <li><a href="/wiki/%E5%A4%B1%E6%95%88%E7%8E%87" title="失效率">失效率</a></li> <li><a href="/w/index.php?title=%E5%8D%B1%E9%9A%AA%E6%AF%94%E4%BE%8B%E6%A8%A1%E5%BC%8F&action=edit&redlink=1" class="new" title="危險比例模式（页面不存在）">危險比例模式</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%9B%B8%E5%85%B3_(%E6%A6%82%E7%8E%87%E8%AE%BA)" title="相关 (概率论)">相關</a>及<br /><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></th><td class="navbox-list-with-group 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%">相关性</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%B9%B2%E6%93%BE%E5%9B%A0%E7%B4%A0" title="干擾因素">干擾因素</a></li> <li><a href="/wiki/%E7%9A%AE%E5%B0%94%E9%80%8A%E7%A7%AF%E7%9F%A9%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0" title="皮尔逊积矩相关系数">皮尔逊積矩相關係數</a></li> <li><span class="ilh-all" data-orig-title="等級相關" data-lang-code="en" data-lang-name="英语" data-foreign-title="Rank correlation"><span class="ilh-page"><a href="/w/index.php?title=%E7%AD%89%E7%B4%9A%E7%9B%B8%E9%97%9C&action=edit&redlink=1" class="new" title="等級相關（页面不存在）">等級相關</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Rank_correlation" class="extiw" title="en:Rank correlation"><span lang="en" dir="auto">Rank correlation</span></a></span>）</span></span> (<a href="/wiki/%E6%96%AF%E7%9A%AE%E5%B0%94%E6%9B%BC%E7%AD%89%E7%BA%A7%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0" title="斯皮尔曼等级相关系数">斯皮尔曼等级相关系数</a></li> <li><span class="ilh-all" data-orig-title="肯德等級相關係數" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kendall tau rank correlation coefficient"><span class="ilh-page"><a href="/w/index.php?title=%E8%82%AF%E5%BE%B7%E7%AD%89%E7%B4%9A%E7%9B%B8%E9%97%9C%E4%BF%82%E6%95%B8&action=edit&redlink=1" class="new" title="肯德等級相關係數（页面不存在）">肯德等級相關係數</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient" class="extiw" title="en:Kendall tau rank correlation coefficient"><span lang="en" dir="auto">Kendall tau rank correlation coefficient</span></a></span>）</span></span>)</li> <li><a href="/wiki/%E8%87%AA%E7%94%B1%E5%BA%A6_(%E7%BB%9F%E8%AE%A1%E5%AD%A6)" title="自由度 (统计学)">自由度</a></li> <li><a href="/wiki/%E8%AF%AF%E5%B7%AE" title="误差">误差和残差</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B7%9A%E6%80%A7%E5%9B%9E%E6%AD%B8" title="線性回歸">線性回歸</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="線性模型" data-lang-code="en" data-lang-name="英语" data-foreign-title="Linear model"><span class="ilh-page"><a href="/w/index.php?title=%E7%B7%9A%E6%80%A7%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="線性模型（页面不存在）">線性模型</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Linear_model" class="extiw" title="en:Linear model"><span lang="en" dir="auto">Linear model</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%B8%80%E8%88%AC%E7%BA%BF%E6%80%A7%E6%A8%A1%E5%9E%8B" title="一般线性模型">一般线性模型</a></li> <li><a href="/wiki/%E5%BB%A3%E7%BE%A9%E7%B7%9A%E6%80%A7%E6%A8%A1%E5%9E%8B" title="廣義線性模型">廣義線性模型</a></li> <li><a href="/wiki/%E7%B0%A1%E5%96%AE%E7%B7%9A%E6%80%A7%E8%BF%B4%E6%AD%B8" title="簡單線性迴歸">簡單線性迴歸</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><span class="ilh-all" data-orig-title="贝叶斯回归" data-lang-code="en" data-lang-name="英语" data-foreign-title="Bayesian linear regression"><span class="ilh-page"><a href="/w/index.php?title=%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%9B%9E%E5%BD%92&action=edit&redlink=1" class="new" title="贝叶斯回归（页面不存在）">贝叶斯回归</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Bayesian_linear_regression" class="extiw" title="en:Bayesian linear regression"><span lang="en" dir="auto">Bayesian linear regression</span></a></span>）</span></span></li> <li><a href="/wiki/%E6%96%B9%E5%B7%AE%E5%88%86%E6%9E%90" title="方差分析">方差分析</a></li> <li><span class="ilh-all" data-orig-title="共變異數分析" data-lang-code="en" data-lang-name="英语" data-foreign-title="Analysis of covariance"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%B1%E8%AE%8A%E7%95%B0%E6%95%B8%E5%88%86%E6%9E%90&action=edit&redlink=1" class="new" title="共變異數分析（页面不存在）">协方差分析</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Analysis_of_covariance" class="extiw" title="en:Analysis of covariance"><span lang="en" dir="auto">Analysis of covariance</span></a></span>）</span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%9B%9E%E5%BD%92" title="非线性回归">非线性回归</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="非参数回归模型" data-lang-code="en" data-lang-name="英语" data-foreign-title="Nonparametric regression"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E5%8F%82%E6%95%B0%E5%9B%9E%E5%BD%92%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="非参数回归模型（页面不存在）">非参数回归模型</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Nonparametric_regression" class="extiw" title="en:Nonparametric regression"><span lang="en" dir="auto">Nonparametric regression</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="半参数回归模型" data-lang-code="en" data-lang-name="英语" data-foreign-title="Semiparametric regression"><span class="ilh-page"><a href="/w/index.php?title=%E5%8D%8A%E5%8F%82%E6%95%B0%E5%9B%9E%E5%BD%92%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="半参数回归模型（页面不存在）">半参数回归模型</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Semiparametric_regression" class="extiw" title="en:Semiparametric regression"><span lang="en" dir="auto">Semiparametric regression</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E6%96%AF%E8%AB%A6%E8%BF%B4%E6%AD%B8" title="邏輯斯諦迴歸">邏輯斯諦迴歸</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%BB%9F%E8%AE%A1%E5%9B%BE%E5%BD%A2" title="统计图形">统计图形</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%A5%BC%E5%9B%BE" title="饼图">饼图</a></li> <li><a href="/wiki/%E6%9D%A1%E5%BD%A2%E5%9B%BE" title="条形图">条形图</a></li> <li><a href="/wiki/%E5%8F%8C%E6%A0%87%E5%9B%BE" title="双标图">双标图</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/%E7%AE%A1%E5%88%B6%E5%9C%96" title="管制圖">管制圖</a></li> <li><span class="ilh-all" data-orig-title="森林圖" data-lang-code="en" data-lang-name="英语" data-foreign-title="Forest plot"><span class="ilh-page"><a href="/w/index.php?title=%E6%A3%AE%E6%9E%97%E5%9C%96&action=edit&redlink=1" class="new" title="森林圖（页面不存在）">森林圖</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Forest_plot" class="extiw" title="en:Forest plot"><span lang="en" dir="auto">Forest plot</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%9B%B4%E6%96%B9%E5%9B%BE" title="直方图">直方图</a></li> <li><a href="/wiki/%E5%88%86%E4%BD%8D%E5%9C%96" title="分位圖">分位圖</a></li> <li><a href="/wiki/%E8%B6%8B%E5%8A%BF%E5%9B%BE" title="趋势图">趋势图</a></li> <li><a href="/wiki/%E6%95%A3%E5%B8%83%E5%9C%96" title="散布圖">散点图</a></li> <li><a href="/wiki/%E5%B9%B9%E8%91%89%E5%9C%96" title="幹葉圖">莖葉圖</a></li> <li><span class="ilh-all" data-orig-title="雷达图" data-lang-code="en" data-lang-name="英语" data-foreign-title="Radar chart"><span class="ilh-page"><a href="/w/index.php?title=%E9%9B%B7%E8%BE%BE%E5%9B%BE&action=edit&redlink=1" class="new" title="雷达图（页面不存在）">雷达图</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Radar_chart" class="extiw" title="en:Radar chart"><span lang="en" dir="auto">Radar chart</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%A4%BA%E6%84%8F%E5%9C%B0%E5%9C%96" title="示意地圖">示意地圖</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其他</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="统计类型" data-lang-code="d" data-lang-name="維基數據" data-foreign-title="Q47103999"><span class="ilh-page"><a href="/w/index.php?title=%E7%BB%9F%E8%AE%A1%E7%B1%BB%E5%9E%8B&action=edit&redlink=1" class="new" title="统计类型（页面不存在）">统计类型</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">維基數據所列</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://www.wikidata.org/wiki/Q47103999" class="extiw" title="d:Q47103999"><span lang="d" dir="auto">Q47103999</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%9B%9E%E6%87%89%E9%81%8E%E7%A8%8B%E6%95%88%E5%BA%A6" title="回應過程效度">回應過程效度</a></li> <li><a href="/wiki/%E7%B5%B1%E8%A8%88%E8%AA%A4%E7%94%A8" title="統計誤用">統計誤用</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span 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