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class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-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="Edukiak" 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="Eduki taularen ikusgarritasuna aldatu" > <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 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class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Wikipedia, Entziklopedia askea</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><p><b>Korrelazio koefiziente tetrakorikoa</b>, bi <a href="/w/index.php?title=Aldagai_dikotomiko&action=edit&redlink=1" class="new" title="Aldagai dikotomiko (sortu gabe)">aldagai dikotomikoen</a> arteko <a href="/wiki/Korrelazio" title="Korrelazio">korrelazioa</a> neurtzeko <a href="/wiki/Koefiziente_(estatistika)" title="Koefiziente (estatistika)">koefizientea</a> da, bi aldagai dikotomikoak era ezkutu edo sorrean <a href="/wiki/Banaketa_normal" title="Banaketa normal">banaketa normalaren</a> araberakoak direla pentsatzen delarik. <a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a> estatistikariak asmatu zuen <a href="/wiki/1901" title="1901">1901</a>. urtean. Korrelazio tetrakorikoa korrelazio polikorikoaren kasu berezia da, non bi aldagaiak <a href="/w/index.php?title=Eskala_(estatistika)&action=edit&redlink=1" class="new" title="Eskala (estatistika) (sortu gabe)">ordinalak</a> diren. <a href="/wiki/Psikometria" title="Psikometria">Psikometrian</a> erabili ohi da, aldagaiak era kuantitatiboan neurtzeko zailtasuna dela eta, askotan elementuak edo banakoak bi sailetan banatzen direlako (adibidez, azterketa bat gainditu edo ez gainditu, test edo estimulu baten aurrean erantzuna positiboa edo negatiboa izan den). Ez da erabili behar aldagaiak berez dikotomikoak direnean (adibidez, sexua). </p><p>Bi aldagai dikotomikoen arteko korrelazioa edo <a href="/wiki/Asoziazio_(estatistika)" title="Asoziazio (estatistika)">asoziazioa</a> aztertzeko beste teknika batzuk badaude, <a href="/wiki/Phi_(estatistika)" title="Phi (estatistika)">phi</a> koefizientea esaterako, baina hauek korrelazioa sistematikoki gutxietsi egiten dutela frogatu izan da. Korrelazio koefiziente tetrakorikoa korrelazio maila zehatzagoa ematen saiatzen da, aldagai dikotomikoen ezkutuan banaketa normalaren araberakoak diren bi <a href="/wiki/Aldagai_kuantitatibo" title="Aldagai kuantitatibo">aldagai kuantitatibo</a> daudela pentsatuz betiere. </p> <div class="mw-heading mw-heading2"><h2 id="Kalkulua">Kalkulua</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korrelazio_koefiziente_tetrakoriko&veaction=edit&section=1" title="Aldatu atal hau: «Kalkulua»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korrelazio_koefiziente_tetrakoriko&action=edit&section=1" title="Edit section's source code: Kalkulua"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kalkulurako 2x2 <a href="/wiki/Kontingentzia_taula" title="Kontingentzia taula">kontingentzia taula</a> batetik abiatzen da: </p> <center> <table border="1" cellspacing="0px" cellpadding="5px" style="border-collapse:collapse;"> <tbody><tr> <td bgcolor="#CCCCCC" width="10px"> </td> <td bgcolor="#CCCCCC" width="10px"><b>0</b> </td> <td bgcolor="#CCCCCC" width="10px"><b>1</b> </td></tr> <tr> <td bgcolor="#CCCCCC"><b>0</b> </td> <td bgcolor="#EEEEEE" align="center">a </td> <td bgcolor="#EEEEEE" align="center">b </td></tr> <tr> <td bgcolor="#CCCCCC"><b>1</b> </td> <td bgcolor="#EEEEEE" align="center">c </td> <td bgcolor="#EEEEEE" align="center">d </td></tr></tbody></table></center> <p>Korrelazio koefiziente tetrakorikoa zehatz kalkulatzea ez da erraza, ez eta erosoa ere. Hau dela eta, korrelazio koefiziente tetrakorikorako hurbilketak proposatu dira. Horietako bat hau da: </p> <dl><dd><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 r_{\text{tet}}=\cos {\Bigg (}{\frac {\pi }{1+{\sqrt {\frac {ad}{bc}}}}}{\Bigg )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>tet</mtext> </mrow> </msub> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>a</mi> <mi>d</mi> </mrow> <mrow> <mi>b</mi> <mi>c</mi> </mrow> </mfrac> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{tet}}=\cos {\Bigg (}{\frac {\pi }{1+{\sqrt {\frac {ad}{bc}}}}}{\Bigg )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc93bbebafa8d3a968bfe4a997331fa6aa262555" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:23.296ex; height:9.009ex;" alt="{\displaystyle r_{\text{tet}}=\cos {\Bigg (}{\frac {\pi }{1+{\sqrt {\frac {ad}{bc}}}}}{\Bigg )}}"></span></dd></dl></dd></dl> <p><a href="/wiki/Korrelazio-koefiziente" title="Korrelazio-koefiziente">Pearsonen korrelazio koefiziente lineala</a> bezala interpretatzen da (izan ere, korrelazio tetrakorikoa Pearsonen koefizientearen zenbatespen bat besterik ez baita): negatiboa denean korrelazioa negatiboa izango da (hau da, aldagai batean 0 izateak beste aldagaian 1 izateko joera dakar eta alderantziz) eta positiboa denean, korrelazio positiboa izango da (hau da, aldagai batean 0 izateak beste aldagaian ere 0 izateko joera dakar, eta berdin 1 kategoriarekin). Sendotasunari buruz, eskuarki balio absolutuan 0.7tik gorako balioek korrelazio sendoa erakusten du, <a href="/wiki/Inferentzia_estatistiko" title="Inferentzia estatistiko">inferentzia</a> azterketa gorabehera. </p> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Korrelazio_koefiziente_tetrakoriko&veaction=edit&section=2" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Korrelazio_koefiziente_tetrakoriko&action=edit&section=2" title="Edit section's source code: Kanpo estekak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="clear:both;"></div><style data-mw-deduplicate="TemplateStyles:r7786466">.mw-parser-output .mw-authority-control{margin-top:1.5em}.mw-parser-output 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