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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="Sivusto"> <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="Sisällysluettelo" 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">Sisällysluettelo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">siirrä sivupalkkiin</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">piilota</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">Johdanto</div> </a> </li> <li id="toc-Nollahypoteesin_käyttö" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Nollahypoteesin_käyttö"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Nollahypoteesin käyttö</span> </div> </a> <ul id="toc-Nollahypoteesin_käyttö-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ongelmia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ongelmia"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Ongelmia</span> </div> </a> <ul id="toc-Ongelmia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lähteet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lähteet"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lähteet</span> </div> </a> <ul id="toc-Lähteet-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="Sisällysluettelo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Sisällysluettelo" > <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="Vaihda sisällysluettelo" > <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">Vaihda sisällysluettelo</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">Nollahypoteesi</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="Mene artikkeliin toisella kielellä. Saatavilla 36 kielellä" > <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-36" 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">36 kieltä</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%B1%D8%B6%D9%8A%D8%A9_%D8%A7%D9%84%D8%B9%D8%AF%D9%85" title="فرضية العدم — arabia" lang="ar" hreflang="ar" data-title="فرضية العدم" data-language-autonym="العربية" data-language-local-name="arabia" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/S%C4%B1f%C4%B1r_hipotezi" title="Sıfır hipotezi — azeri" lang="az" hreflang="az" data-title="Sıfır hipotezi" data-language-autonym="Azərbaycanca" data-language-local-name="azeri" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Hipotesis_nol" title="Hipotesis nol — indonesia" lang="id" hreflang="id" data-title="Hipotesis nol" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A8%E0%A6%BE%E0%A6%B8%E0%A7%8D%E0%A6%A4%E0%A6%BF_%E0%A6%95%E0%A6%B2%E0%A7%8D%E0%A6%AA%E0%A6%A8%E0%A6%BE" title="নাস্তি কল্পনা — bengali" lang="bn" hreflang="bn" data-title="নাস্তি কল্পনা" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Hip%C3%B2tesi_nul%C2%B7la" title="Hipòtesi nul·la — katalaani" lang="ca" hreflang="ca" data-title="Hipòtesi nul·la" data-language-autonym="Català" data-language-local-name="katalaani" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhagdybiaeth_nwl" title="Rhagdybiaeth nwl — kymri" lang="cy" hreflang="cy" data-title="Rhagdybiaeth nwl" data-language-autonym="Cymraeg" data-language-local-name="kymri" 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/Nulhypotese" title="Nulhypotese — tanska" lang="da" hreflang="da" data-title="Nulhypotese" data-language-autonym="Dansk" data-language-local-name="tanska" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Nullhypothese" title="Nullhypothese — saksa" lang="de" hreflang="de" data-title="Nullhypothese" data-language-autonym="Deutsch" data-language-local-name="saksa" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Nullh%C3%BCpotees" title="Nullhüpotees — viro" lang="et" hreflang="et" data-title="Nullhüpotees" data-language-autonym="Eesti" data-language-local-name="viro" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Null_hypothesis" title="Null hypothesis — englanti" lang="en" hreflang="en" data-title="Null hypothesis" data-language-autonym="English" data-language-local-name="englanti" 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/Hip%C3%B3tesis_nula" title="Hipótesis nula — espanja" lang="es" hreflang="es" data-title="Hipótesis nula" data-language-autonym="Español" data-language-local-name="espanja" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hipotesi_nulu" title="Hipotesi nulu — baski" lang="eu" hreflang="eu" data-title="Hipotesi nulu" data-language-autonym="Euskara" data-language-local-name="baski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B1%D8%B6_%D8%B5%D9%81%D8%B1" title="فرض صفر — persia" lang="fa" hreflang="fa" data-title="فرض صفر" data-language-autonym="فارسی" data-language-local-name="persia" 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/Hypoth%C3%A8se_nulle" title="Hypothèse nulle — ranska" lang="fr" hreflang="fr" data-title="Hypothèse nulle" data-language-autonym="Français" data-language-local-name="ranska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%80%EB%AC%B4_%EA%B0%80%EC%84%A4" title="귀무 가설 — korea" lang="ko" hreflang="ko" data-title="귀무 가설" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%8D%E0%A4%A4_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A4%B2%E0%A5%8D%E0%A4%AA%E0%A4%A8%E0%A4%BE" title="रिक्त परिकल्पना — hindi" lang="hi" hreflang="hi" data-title="रिक्त परिकल्पना" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ipotesi_nulla" title="Ipotesi nulla — italia" lang="it" hreflang="it" data-title="Ipotesi nulla" data-language-autonym="Italiano" data-language-local-name="italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A9%D7%A2%D7%A8%D7%AA_%D7%94%D7%90%D7%A4%D7%A1" title="השערת האפס — heprea" lang="he" hreflang="he" data-title="השערת האפס" data-language-autonym="עברית" data-language-local-name="heprea" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Null_hypothesis" title="Null hypothesis — jaava" lang="jv" hreflang="jv" data-title="Null hypothesis" data-language-autonym="Jawa" data-language-local-name="jaava" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Nullhipot%C3%A9zis" title="Nullhipotézis — unkari" lang="hu" hreflang="hu" data-title="Nullhipotézis" data-language-autonym="Magyar" data-language-local-name="unkari" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B8%B0%E7%84%A1%E4%BB%AE%E8%AA%AC" title="帰無仮説 — japani" lang="ja" hreflang="ja" data-title="帰無仮説" data-language-autonym="日本語" data-language-local-name="japani" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Nullhypotese" title="Nullhypotese — norjan bokmål" lang="nb" hreflang="nb" data-title="Nullhypotese" data-language-autonym="Norsk bokmål" data-language-local-name="norjan bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Hip%C3%B3tese_nula" title="Hipótese nula — portugali" lang="pt" hreflang="pt" data-title="Hipótese nula" data-language-autonym="Português" data-language-local-name="portugali" 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/%D0%9D%D1%83%D0%BB%D0%B5%D0%B2%D0%B0%D1%8F_%D0%B3%D0%B8%D0%BF%D0%BE%D1%82%D0%B5%D0%B7%D0%B0" title="Нулевая гипотеза — venäjä" lang="ru" hreflang="ru" data-title="Нулевая гипотеза" data-language-autonym="Русский" data-language-local-name="venäjä" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Null_hypothesis" title="Null hypothesis — Simple English" lang="en-simple" hreflang="en-simple" data-title="Null hypothesis" 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-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%D8%B1%DB%8C%D9%85%D8%A7%D9%86%DB%95%DB%8C_%D8%A8%DB%95%D8%AA%D8%A7%DA%B5" title="گریمانەی بەتاڵ — soranî" lang="ckb" hreflang="ckb" data-title="گریمانەی بەتاڵ" data-language-autonym="کوردی" data-language-local-name="soranî" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9D%D1%83%D0%BB%D1%82%D0%B0_%D1%85%D0%B8%D0%BF%D0%BE%D1%82%D0%B5%D0%B7%D0%B0" title="Нулта хипотеза — serbia" lang="sr" hreflang="sr" data-title="Нулта хипотеза" data-language-autonym="Српски / srpski" data-language-local-name="serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Null_hypothesis" title="Null hypothesis — sunda" lang="su" hreflang="su" data-title="Null hypothesis" data-language-autonym="Sunda" data-language-local-name="sunda" 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/Nollhypotes" title="Nollhypotes — ruotsi" lang="sv" hreflang="sv" data-title="Nollhypotes" data-language-autonym="Svenska" data-language-local-name="ruotsi" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%82%E0%AE%9C%E0%AF%8D%E0%AE%AF_%E0%AE%95%E0%AE%B1%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%A4%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%8A%E0%AE%B3%E0%AF%8D%E0%AE%95%E0%AF%88" title="பூஜ்ய கற்பிதக் கொள்கை — tamili" lang="ta" hreflang="ta" data-title="பூஜ்ய கற்பிதக் கொள்கை" data-language-autonym="தமிழ்" data-language-local-name="tamili" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%A1%E0%B8%A1%E0%B8%B8%E0%B8%95%E0%B8%B4%E0%B8%90%E0%B8%B2%E0%B8%99%E0%B8%A7%E0%B9%88%E0%B8%B2%E0%B8%87" title="สมมุติฐานว่าง — thai" lang="th" hreflang="th" data-title="สมมุติฐานว่าง" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%E1%BA%A3_thuy%E1%BA%BFt_kh%C3%B4ng" title="Giả thuyết không — vietnam" lang="vi" hreflang="vi" data-title="Giả thuyết không" data-language-autonym="Tiếng Việt" data-language-local-name="vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bo%C5%9F_hipotez" title="Boş hipotez — turkki" lang="tr" hreflang="tr" data-title="Boş hipotez" data-language-autonym="Türkçe" data-language-local-name="turkki" 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/%D0%9D%D1%83%D0%BB%D1%8C%D0%BE%D0%B2%D0%B0_%D0%B3%D1%96%D0%BF%D0%BE%D1%82%D0%B5%D0%B7%D0%B0" title="Нульова гіпотеза — ukraina" lang="uk" hreflang="uk" data-title="Нульова гіпотеза" data-language-autonym="Українська" data-language-local-name="ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%99%9B%E7%84%A1%E5%81%87%E8%AA%AA" title="虛無假說 — kantoninkiina" lang="yue" hreflang="yue" data-title="虛無假說" data-language-autonym="粵語" data-language-local-name="kantoninkiina" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%9B%B6%E5%81%87%E8%AE%BE" title="零假设 — kiina" lang="zh" hreflang="zh" data-title="零假设" data-language-autonym="中文" data-language-local-name="kiina" class="interlanguage-link-target"><span>中文</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/Q628374#sitelinks-wikipedia" title="Muokkaa kieltenvälisiä linkkejä" class="wbc-editpage">Muokkaa linkkejä</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="Nimiavaruudet"> <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/Nollahypoteesi" title="Näytä sisältösivu [c]" accesskey="c"><span>Artikkeli</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Keskustelu:Nollahypoteesi" rel="discussion" title="Keskustele sisällöstä [t]" accesskey="t"><span>Keskustelu</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="Valitse kieliversio" > <label id="vector-variants-dropdown-label" 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Hypoteesit ovat aina <a href="/wiki/Falsifiointi" title="Falsifiointi">falsifioitavissa</a> eli kokeelliset tiedot voivat osoittaa hypoteesin vääräksi. <b>Nollahypoteesi</b> vastaa tavallisesti tyypillistä, odotettavissa olevaa tulosta; esimerkiksi ettei kahden mitatun ilmiön välillä ole yhteyttä<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> tai että tietty hoito on tehotonta<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>. Termin esitti ensimmäisenä englantilainen geneetikko ja tilastotieteilijä <a href="/wiki/Ronald_Fisher" title="Ronald Fisher">Ronald Fisher</a>.<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><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> </p><p>Tyypillisesti nollahypoteesin yhteydessä käytetään toista, vaihtoehtoista hypoteesia, jossa oletetaan yhteys ilmiöiden välillä. <a href="/w/index.php?title=Jerzy_Neyman&action=edit&redlink=1" class="new" title="Jerzy Neyman (sivua ei ole)">Jerzy Neyman</a> ja <a href="/w/index.php?title=Egon_Pearson&action=edit&redlink=1" class="new" title="Egon Pearson (sivua ei ole)">Egon Pearson</a> ovat formalisoineet vaihtoehtohypoteesin käsitteen. Sen ei tarvitse olla nollahypoteesin looginen <a href="/wiki/Negaatio" class="mw-redirect" title="Negaatio">negaatio</a>, mutta se ennustaa kokeen tuloksen, jos vaihtoehtohypoteesi on paikkansapitävä. </p><p>On tärkeää ymmärtää, että nollahypoteesia ei voida koskaan todistaa. Kokeellisen datan perusteella nollahypoteesi voidaan vain falsifioida tai jättää falsifioimatta. Jos esimerkiksi kahden ryhmän (esimerkiksi hoitoa saaneiden ja hoitamattomien) vertailu ei paljasta tilastollisesti merkitsevää eroa ryhmien välillä, eroa saattaa silti todellisuudessa olla. Tällaisessa tilanteessa voidaan ainoastaan sanoa, ettei aineisto tarjoa evidenssiä nollahypoteesin hylkäämiselle.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Nollahypoteesin_käyttö"><span id="Nollahypoteesin_k.C3.A4ytt.C3.B6"></span>Nollahypoteesin käyttö</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nollahypoteesi&veaction=edit&section=1" title="Muokkaa osiota Nollahypoteesin käyttö" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nollahypoteesi&action=edit&section=1" title="Muokkaa osion lähdekoodia: Nollahypoteesin käyttö"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Tilastollisen_hypoteesin_testaus" title="Tilastollisen hypoteesin testaus">Tilastollinen testaus</a> etenee seuraavasti: </p> <ol><li>Valitaan testattavalle suureelle <i>x</i> nollahypoteesi ja vaihtoehtoinen hypoteesi, esimerkiksi <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}:x=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> <mo>:</mo> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}:x=0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/825a2954b659c7296fbc185daecbcd6a7d605b0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.9ex; height:2.509ex;" alt="{\displaystyle H_{0}:x=0\,}" /></span> ja <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}:x\neq 0}"> <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> <mo>:</mo> <mi>x</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{1}:x\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf85ff86f83cd2ff1232c1cd47c2e97f796dffa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.513ex; height:2.676ex;" alt="{\displaystyle H_{1}:x\neq 0}" /></span></li> <li>Valitaan testin <a href="/w/index.php?title=Riskitaso&action=edit&redlink=1" class="new" title="Riskitaso (sivua ei ole)">riskitaso</a>, esimerkiksi 5 % tai 1 %</li> <li>Lasketaan testisuure tutkittavasta aineistosta, esimerkiksi <a href="/wiki/T-testi" class="mw-redirect" title="T-testi">t-testi</a></li> <li>Verrataan testisuuretta sen jakaumaan olettaen, että nollahypoteesi on tosi. Yleisimpien testisuureiden kriittiset arvot ovat taulukoituna oppi- ja taulukkokirjoissa.</li> <li>Hylätään nollahypoteesi, jos testisuure ylittää kriittisen arvon valitulla riskitasolla. Esimerkiksi kaksisuuntaisen suuren otoksen t-testin kriittinen arvo 5 % riskitasolla on noin 1,96. Muutoin nollahypoteesi jää voimaan.</li></ol> <p>Nollahypoteesin hylkäämiseen voi liittyä kahdenlaisia virheitä: </p> <ul><li><i>Tyypin I virhe</i> syntyy, kun nollahypoteesi on oikein, mutta tilastollinen testi hylkää sen</li> <li><i>Tyypin II virhe</i> syntyy, kun nollahypoteesi on virheellinen, mutta tilastollinen testi hyväksyy sen</li></ul> <p><a href="/wiki/Tilastollinen_testi" class="mw-redirect" title="Tilastollinen testi">Tilastollista testiä</a> suunniteltaessa tyypin I virheen todennäköisyys kiinnitetään (eli valitaan <a href="/w/index.php?title=Riskitaso&action=edit&redlink=1" class="new" title="Riskitaso (sivua ei ole)">riskitaso</a>) ja tyypin II virhe pyritään minimoimaan. </p> <div class="mw-heading mw-heading2"><h2 id="Ongelmia">Ongelmia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nollahypoteesi&veaction=edit&section=2" title="Muokkaa osiota Ongelmia" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nollahypoteesi&action=edit&section=2" title="Muokkaa osion lähdekoodia: Ongelmia"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tutkijoilla on usein taipumus jättää <a href="/wiki/Tiedejulkaisu" title="Tiedejulkaisu">julkaisematta</a> tutkimuksia, joissa nollahypoteesi jää voimaan. Yleensä tämä tilanne syntyy, kun lopputulos ei eroa jo aikaisemmin otaksutusta. </p> <div class="mw-heading mw-heading2"><h2 id="Lähteet"><span id="L.C3.A4hteet"></span>Lähteet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Nollahypoteesi&veaction=edit&section=3" title="Muokkaa osiota Lähteet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Nollahypoteesi&action=edit&section=3" title="Muokkaa osion lähdekoodia: Lähteet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r23091323">.mw-parser-output div.viitteet-malline ol.references{list-style-type:inherit}.mw-parser-output .viitteet-sarakkeet li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output ol.references>li:target{background-color:var(--background-color-interactive,#DEF)}.mw-parser-output sup.reference:target{background-color:var(--background-color-interactive,#DEF)}.mw-parser-output span[rel="mw:referencedBy"]{counter-reset:mw-ref-linkback 0}.mw-parser-output span[rel="mw:referencedBy"]>a::before{font-style:italic;content:counter(mw-ref-linkback,lower-alpha)}body.action-info .mw-parser-output :target{background-color:var(--background-color-interactive,#DEF)}</style><div id="viitteet-malline" class="viitteet-malline" style="list-style-type:decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="verkkoviite" title="Verkkoviite"><a rel="nofollow" class="external text" href="http://www.businessdictionary.com/definition/null-hypothesis.html">null hypothesis definition</a> Businessdictionary.com. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100704125422/http://www.businessdictionary.com/definition/null-hypothesis.html">Arkistoitu</a> 4.7.2010. Viitattu 29.7.2010.</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="verkkoviite" title="Verkkoviite"><a rel="nofollow" class="external text" href="http://www.nlm.nih.gov/nichsr/hta101/ta101014.html">HTA 101: Glossary</a> 8.9.2009. Nlm.nih.gov. Viitattu 29.7.2010.</span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="verkkoviite" title="Verkkoviite"><a rel="nofollow" class="external text" href="http://statistics.berkeley.edu/~stark/SticiGui/Text/gloss.htm#null_hypothesis">Glossary</a> 25.7.2010. Statistics.berkeley.edu. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130308045920/http://statistics.berkeley.edu/~stark/SticiGui/Text/gloss.htm#null_hypothesis">Arkistoitu</a> 8.3.2013. Viitattu 29.7.2010.</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">OED quote: <b>1935</b> R. A. Fisher, <i>Design Experience</i> ii. 19, "We may speak of this hypothesis as the ‘null hypothesis’, and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><span class="verkkoviite" title="Verkkoviite"><a rel="nofollow" class="external text" href="http://stattrek.com/Lesson5/HypothesisTesting.aspx">Can We Accept the Null Hypothesis?</a> <i>stattrek.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110522033717/http://stattrek.com/Lesson5/HypothesisTesting.aspx">Arkistoitu</a> 22.5.2011. 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