{"id":3997,"date":"2026-10-14T22:19:32","date_gmt":"2026-10-14T21:19:32","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/"},"modified":"2026-10-14T22:19:32","modified_gmt":"2026-10-14T21:19:32","slug":"kruskal-wallis-testi-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/","title":{"rendered":"Kruskal\u2013Wallis Testi Hesaplama Arac\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">\u00dc\u00e7 veya daha fazla grubu s\u0131ralara g\u00f6re kar\u015f\u0131la\u015ft\u0131r\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"3997\" data-favorite-title=\"Kruskal\u2013Wallis Testi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/\" data-favorite-excerpt=\"\u00dc\u00e7 ya da d\u00f6rt gruba ait g\u00f6zlemleri girin; bu ara\u00e7 Kruskal\u2013Wallis testini uygular: t\u00fcm de\u011ferleri birlikte s\u0131ralar, e\u015fitlik d\u00fczeltilmi\u015f H istatisti\u011fini, serbestlik derecesini, p de\u011ferini ve se\u00e7ti\u011finiz anlaml\u0131l\u0131k d\u00fczeyine g\u00f6re karar\u0131 hesaplar.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-wpcalc-bell-curve\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-3997\" data-post=\"3997\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">1. grubun g\u00f6zlemleri<\/label><textarea id=\"field-1\" name=\"1_grubun_gzlemleri\">7; 8; 9; 9; 10<\/textarea><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">2. grubun g\u00f6zlemleri<\/label><textarea id=\"field-2\" name=\"2_grubun_gzlemleri\">5; 6; 6; 7; 8<\/textarea><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">3. grubun g\u00f6zlemleri<\/label><textarea id=\"field-3\" name=\"3_grubun_gzlemleri\">3; 4; 4; 5; 6; 7<\/textarea><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">4. grubun g\u00f6zlemleri (iste\u011fe ba\u011fl\u0131)<\/label><textarea id=\"field-4\" name=\"4_grubun_gzlemleri_istee_bal\"><\/textarea><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Anlaml\u0131l\u0131k d\u00fczeyi<\/label><div class=\"term\">\u03b1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"anlamllk_dzeyi\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.05\" min=\"0.0001\" max=\"0.5\" value=\"0.05\"\/><small id=\"calc-info-5\">I. tip hata oran\u0131 olan \u03b1, p de\u011ferinin istatistiksel olarak anlaml\u0131 say\u0131ld\u0131\u011f\u0131 e\u015fiktir. Yayg\u0131n kullan\u0131lan de\u011fer 0,05&#039;tir.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"3997\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Kruskal\u2013Wallis Testi Sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>H istatisti\u011fi (ba\u011f d\u00fczeltmesi uygulanm\u0131\u015f)<\/span><span class=\"result-term\">H\u2032<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Ba\u011f d\u00fczeltmesi \u00f6ncesi H<\/span><span class=\"result-term\">H<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Serbestlik derecesi<\/span><span class=\"result-term\">\u03bd<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>p de\u011feri (ki-kare yakla\u015f\u0131m\u0131)<\/span><span class=\"result-term\">p<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>\u03b1 anlaml\u0131l\u0131k d\u00fczeyindeki karar<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-6\"><span class=\"field-title\"><span>Grup s\u0131ralar\u0131 ve medyanlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-7\"><span class=\"field-title\"><span>Testin \u00e7al\u0131\u015fma prensibi ve yorumu<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"3997\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Kruskal\u2013Wallis Test Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ H = \\frac{12}{N(N+1)} \\sum_{j=1}^{k} \\frac{R_j^2}{n_j} - 3(N+1) \\\\ H' = \\frac{H}{C}, \\quad C = 1 - \\frac{\\sum \\left(t^3 - t\\right)}{N^3 - N} \\\\ p = P\\!\\left(\\chi^2_{k-1} \\ge H'\\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 grup say\u0131s\u0131<\/li>\n<li>\\(n_j\\) \u2014 \\(j\\). gruptaki g\u00f6zlem say\u0131s\u0131<\/li>\n<li>\\(N\\) \u2014 t\u00fcm gruplardaki toplam g\u00f6zlem say\u0131s\u0131, \\(N = \\sum n_j\\)<\/li>\n<li>\\(R_j\\) \u2014 \\(j\\). grubun s\u0131ra toplam\u0131; t\u00fcm \\(N\\) g\u00f6zlem en k\u00fc\u00e7\u00fckten (1) en b\u00fcy\u00fc\u011fe (\\(N\\)) do\u011fru birlikte s\u0131ralan\u0131r ve e\u015fit de\u011ferler, kendi s\u0131ralar\u0131n\u0131n ortalamas\u0131n\u0131 al\u0131r<\/li>\n<li>\\(t\\) \u2014 e\u015fit de\u011ferlerin olu\u015fturdu\u011fu her bir k\u00fcmenin b\u00fcy\u00fckl\u00fc\u011f\u00fc (\\(C\\) d\u00fczeltme \u00e7arpan\u0131nda kullan\u0131l\u0131r)<\/li>\n<li>\\(\\chi^2_{k-1}\\) \u2014 \\(k-1\\) serbestlik dereceli ki-kare da\u011f\u0131l\u0131m\u0131<\/li>\n<\/ul>\n<p>\\(H\\) istatisti\u011fi, her grubun ortalama s\u0131ras\u0131n\u0131 genel ortalama s\u0131ra olan \\((N+1)\/2\\) de\u011feriyle kar\u015f\u0131la\u015ft\u0131r\u0131r. T\u00fcm gruplar ayn\u0131 da\u011f\u0131l\u0131mdan geliyorsa her grubun ortalama s\u0131ras\u0131 birbirine yak\u0131n olur ve \\(H\\) k\u00fc\u00e7\u00fck \u00e7\u0131kar; bir grupta daha b\u00fcy\u00fck (ya da daha k\u00fc\u00e7\u00fck) de\u011ferler birikiyorsa, o grubun ortalama s\u0131ras\u0131 genel ortalamadan uzakla\u015f\u0131r ve \\(H\\) b\u00fcy\u00fcr. S\u0131f\u0131r hipotez alt\u0131nda \\(H'\\), \\(k-1\\) serbestlik dereceli bir ki-kare da\u011f\u0131l\u0131m\u0131n\u0131 yakla\u015f\u0131k olarak izler; p de\u011feri de buradan gelir.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Kruskal\u2013Wallis Testi \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> bir ara\u015ft\u0131rmac\u0131 \u00fc\u00e7 tedavi alt\u0131ndaki hasta memnuniyet puanlar\u0131n\u0131 (0\u201310) kar\u015f\u0131la\u015ft\u0131r\u0131yor. 1. grup: 7; 8; 9; 9; 10. 2. grup: 5; 6; 6; 7; 8. 3. grup: 3; 4; 4; 5; 6; 7. Burada \\(k = 3\\), \\(N = 16\\).<\/p>\n<p>16 g\u00f6zlemin hepsi birlikte s\u0131raland\u0131\u011f\u0131nda (e\u015fit de\u011ferler ortalama s\u0131ra al\u0131r) s\u0131ra toplamlar\u0131 \\(R_1 = 67.5\\), \\(R_2 = 41\\), \\(R_3 = 27.5\\) olur.<\/p>\n<p>\\[ H = \\frac{12}{16 \\cdot 17}\\left(\\frac{67.5^2}{5} + \\frac{41^2}{5} + \\frac{27.5^2}{6}\\right) - 3 \\cdot 17 = \\frac{12}{272} \\cdot 1373.4917 - 51 = 9.5952 \\]<\/p>\n<p>Verilerde e\u015fit de\u011ferler var (b\u00fcy\u00fckl\u00fckleri 2, 2, 3, 3, 2, 2 olan alt\u0131 e\u015fitlik grubu); bu y\u00fczden \\(\\sum(t^3 - t) = 72\\) ve \\(N^3 - N = 4080\\) olur:<\/p>\n<p>\\[ C = 1 - \\frac{72}{4080} = 0.9824, \\quad H' = \\frac{9.5952}{0.9824} = 9.7674 \\]<\/p>\n<p>\\(\\nu = k - 1 = 2\\) serbestlik derecesiyle ki-kare yakla\u015f\u0131m\u0131 \\(p = 0.0076\\) de\u011ferini verir.<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(H' = 9.7674\\), \\(p = 0.0076 \\le \\alpha = 0.05\\) oldu\u011fundan s\u0131f\u0131r hipotez reddedilir \u2014 en az bir tedavi farkl\u0131 puanlar e\u011filimindedir. 1. grup en y\u00fcksek ortalama s\u0131raya sahiptir (13,5; genel ortalama 8,5), yani genel olarak daha b\u00fcy\u00fck de\u011ferler i\u00e7erir.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplama arac\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>\u0130lk grubunuzun g\u00f6zlemlerini <strong>1. grup g\u00f6zlemleri<\/strong> alan\u0131na girin. Say\u0131lar\u0131 bo\u015fluk, sat\u0131r sonu ya da noktal\u0131 virg\u00fclle ay\u0131rabilirsiniz; ondal\u0131kl\u0131 virg\u00fcl (\u00f6r. 7,5) kabul edilir.<\/li>\n<li><strong>2. grup g\u00f6zlemleri<\/strong> ve <strong>3. grup g\u00f6zlemleri<\/strong> alanlar\u0131n\u0131 ayn\u0131 bi\u00e7imde doldurun. T\u00fcm gruplar ayn\u0131 de\u011fi\u015fkeni ayn\u0131 \u00f6l\u00e7ek \u00fczerinde \u00f6l\u00e7melidir.<\/li>\n<li>D\u00f6rd\u00fcnc\u00fc bir grubunuz varsa <strong>4. grup g\u00f6zlemleri (iste\u011fe ba\u011fl\u0131)<\/strong> alan\u0131na girin; yaln\u0131zca \u00fc\u00e7 grubu kar\u015f\u0131la\u015ft\u0131r\u0131yorsan\u0131z bo\u015f b\u0131rak\u0131n. Bo\u015f b\u0131rakt\u0131\u011f\u0131n\u0131z gruplar hesaplamaya dahil edilmez.<\/li>\n<li><strong>Anlaml\u0131l\u0131k d\u00fczeyini<\/strong> belirleyin (varsay\u0131lan 0,05) \u2014 p de\u011ferinin bu e\u015fi\u011fin alt\u0131na d\u00fc\u015fmesi istatistiksel olarak anlaml\u0131 say\u0131l\u0131r.<\/li>\n<li><strong>Hesapla<\/strong> d\u00fc\u011fmesine bas\u0131n. E\u015fitlik d\u00fczeltilmi\u015f \\(H'\\) istatisti\u011fini, d\u00fczeltilmemi\u015f \\(H\\) de\u011ferini, serbestlik derecesini, p de\u011ferini, se\u00e7ti\u011finiz \\(\\alpha\\) d\u00fczeyine g\u00f6re karar\u0131 ve her grubun g\u00f6zlem say\u0131s\u0131, s\u0131ra toplam\u0131, ortalama s\u0131ras\u0131 ile ortanca de\u011ferini g\u00f6steren bir tabloyu al\u0131rs\u0131n\u0131z.<\/li>\n<\/ol>\n<h2>Kruskal\u2013Wallis testi nedir?<\/h2>\n<p>Kruskal\u2013Wallis testi, \u00fc\u00e7 ya da daha fazla ba\u011f\u0131ms\u0131z grubu kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131lan parametrik olmayan bir y\u00f6ntemdir. Tek y\u00f6nl\u00fc varyans analizinin (ANOVA) t testini genelle\u015ftirmesi gibi, bu test de Mann\u2013Whitney U testinin (iki grup durumu) geni\u015fletilmi\u015f h\u00e2lidir. Grup ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak yerine t\u00fcm g\u00f6zlemleri birle\u015ftirir, her de\u011feri s\u0131ras\u0131yla de\u011fi\u015ftirir ve s\u0131ralar\u0131n gruplar aras\u0131nda dengeli da\u011f\u0131l\u0131p da\u011f\u0131lmad\u0131\u011f\u0131n\u0131 sorgular. Bir grup sistematik olarak en b\u00fcy\u00fck de\u011ferleri i\u00e7eriyorsa, ortalama s\u0131ras\u0131 \\((N+1)\/2\\) genel ortalama s\u0131ran\u0131n olduk\u00e7a \u00fcst\u00fcnde yer al\u0131r ve \\(H\\) istatisti\u011fi b\u00fcy\u00fcr.<\/p>\n<p>Test s\u0131ralar \u00fczerinde \u00e7al\u0131\u015ft\u0131\u011f\u0131 i\u00e7in, temel al\u0131nan da\u011f\u0131l\u0131mlar\u0131n bi\u00e7imi hakk\u0131nda hi\u00e7bir varsay\u0131m yapmaz. Normallik gerektirmez, \u00e7arp\u0131k verilere dayan\u0131r ve u\u00e7 de\u011ferlere kar\u015f\u0131 dayan\u0131kl\u0131d\u0131r \u2014 tek bir a\u015f\u0131r\u0131 de\u011fer bir ortalamay\u0131 bozabilir, ancak bir s\u0131ray\u0131 yaln\u0131zca sabit miktarda kayd\u0131r\u0131r. Bu y\u00f6n\u00fcyle, ANOVA varsay\u0131mlar\u0131 (yakla\u015f\u0131k normal art\u0131klar, benzer varyanslar) \u015f\u00fcpheli oldu\u011funda ya da veriler s\u0131ral\u0131 puanlar, dereceler veya keyf\u00ee bir \u00f6l\u00e7ekteki puanlar oldu\u011funda <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/anova-hesaplama\/\">tek y\u00f6nl\u00fc ANOVA<\/a> yerine standart se\u00e7enektir. S\u0131ra temelli kar\u015f\u0131la\u015ft\u0131rma mant\u0131\u011f\u0131, <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/spearman-sira-korelasyon-hesaplama\/\">Spearman s\u0131ra korelasyonu<\/a> ile ayn\u0131d\u0131r.<\/p>\n<p>S\u0131f\u0131r hipotez, t\u00fcm gruplar\u0131n ayn\u0131 da\u011f\u0131l\u0131mdan geldi\u011fini, yani hi\u00e7bir grubun di\u011ferlerinden daha b\u00fcy\u00fck ya da k\u00fc\u00e7\u00fck de\u011ferler \u00fcretme e\u011filiminde olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. K\u00fc\u00e7\u00fck bir p de\u011feri (\\(\\alpha\\) d\u00fczeyine e\u015fit ya da alt\u0131nda), g\u00f6zlenen s\u0131ra farklar\u0131n\u0131n rastgele \u00f6rnekleme alt\u0131nda beklenme olas\u0131l\u0131\u011f\u0131n\u0131n d\u00fc\u015f\u00fck oldu\u011fu anlam\u0131na gelir; bu durumda s\u0131f\u0131r hipotezi reddeder ve en az bir grubun farkl\u0131 oldu\u011fu sonucuna var\u0131rs\u0131n\u0131z. Testin neyi <em>s\u00f6ylemedi\u011fine<\/em> dikkat edin: hangi gruplar\u0131n hangilerinden farkl\u0131 oldu\u011funu. Bunun i\u00e7in Dunn testi gibi bir post-hoc i\u015flem ya da Bonferroni d\u00fczeltmesiyle e\u015fi\u011fi \\(\\alpha \/ (k(k-1)\/2)\\) olarak ayarlanm\u0131\u015f ikili Mann\u2013Whitney U testleri uygulan\u0131r. Sonucu nas\u0131l yorumlayaca\u011f\u0131n\u0131zdan emin de\u011filseniz, <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/p-degeri-hesaplayici\/\">p de\u011feri hesaplama arac\u0131<\/a> anlaml\u0131l\u0131k testinin mant\u0131\u011f\u0131n\u0131 daha ayr\u0131nt\u0131l\u0131 a\u00e7\u0131klar.<\/p>\n<p>Ortanca yorumu dikkat ister. Kat\u0131 bi\u00e7imde s\u00f6ylemek gerekirse Kruskal\u2013Wallis testi b\u00fct\u00fcn da\u011f\u0131l\u0131mlar\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131r (bir grubun de\u011ferleri di\u011ferininkine bask\u0131n olma e\u011filiminde mi). Ortanca kar\u015f\u0131la\u015ft\u0131rmas\u0131 olarak okunabilmesi, grup da\u011f\u0131l\u0131mlar\u0131n\u0131n bi\u00e7im ve yay\u0131l\u0131m\u0131n\u0131n kabaca benzer olmas\u0131na ba\u011fl\u0131d\u0131r. Ara\u00e7, her grubun ortancas\u0131n\u0131 ve ortalama s\u0131ras\u0131n\u0131 raporlayarak farklar\u0131n nereden kaynakland\u0131\u011f\u0131n\u0131 g\u00f6rmenizi sa\u011flar; ancak bi\u00e7imsel sonu\u00e7 her zaman da\u011f\u0131l\u0131mlar hakk\u0131ndad\u0131r, tek bir \u00f6zet istatistik hakk\u0131nda de\u011fil.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve pratik \u00f6neriler<\/h2>\n<ul>\n<li><strong>Ba\u011f\u0131ms\u0131z \u00f6rneklem.<\/strong> Gruplar birbiriyle ili\u015fkisiz olmal\u0131d\u0131r (her grupta farkl\u0131 bireyler). E\u015fle\u015ftirilmi\u015f ya da tekrarl\u0131 \u00f6l\u00e7\u00fcm tasar\u0131mlar\u0131nda Kruskal\u2013Wallis testi uygun de\u011fildir \u2014 bu durumlarda genellikle Friedman testi kullan\u0131l\u0131r.<\/li>\n<li><strong>Gruplar i\u00e7inde ba\u011f\u0131ms\u0131z g\u00f6zlemler.<\/strong> Her de\u011fer farkl\u0131 bir bireyden ya da deney biriminden gelmelidir; ayn\u0131 birimin tekrarlanan \u00f6l\u00e7\u00fcmleri etkin \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc \u015fi\u015firir.<\/li>\n<li><strong>S\u0131ral\u0131 ya da s\u00fcrekli veri.<\/strong> De\u011ferler en az\u0131ndan s\u0131ralanabilir olmal\u0131d\u0131r. Nominal kategoriler (renkler, kan gruplar\u0131) bu \u015fekilde test edilemez \u2014 kategorik veriler i\u00e7in bunun yerine <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/ki-kare-testi-hesaplama\/\">ki-kare testi<\/a> kullan\u0131n.<\/li>\n<li><strong>Ki-kare yakla\u015f\u0131m\u0131.<\/strong> p de\u011feri, \\(H'\\) istatisti\u011finin \\(\\chi^2_{k-1}\\) da\u011f\u0131l\u0131m\u0131yla yakla\u015f\u0131klanmas\u0131ndan gelir. Bu yakla\u015f\u0131m, her grupta en az 5 g\u00f6zlem oldu\u011funda en iyi \u00e7al\u0131\u015f\u0131r. Daha k\u00fc\u00e7\u00fck gruplarda p de\u011ferine ihtiyatla yakla\u015f\u0131n; tam (exact) ya da perm\u00fctasyona dayal\u0131 bir y\u00f6ntem tercih edilir.<\/li>\n<li><strong>E\u015fit de\u011ferler do\u011fru i\u015flenir.<\/strong> E\u015fit de\u011ferler ortalama s\u0131ra al\u0131r ve istatistik \\(C\\) d\u00fczeltme \u00e7arpan\u0131yla ayarlan\u0131r; dolay\u0131s\u0131yla \u00f6l\u00e7ek puanlar\u0131nda s\u0131k g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi orta say\u0131da e\u015fitlik sorun yaratmaz. Ara\u00e7 hem \\(H\\) hem de d\u00fczeltilmi\u015f \\(H'\\) de\u011ferini g\u00f6sterir ki d\u00fczeltmenin b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc g\u00f6rebilesiniz.<\/li>\n<li><strong>Benzer da\u011f\u0131l\u0131mlar yorumu kolayla\u015ft\u0131r\u0131r.<\/strong> Gruplar\u0131n bi\u00e7imleri ya da varyanslar\u0131 belirgin bi\u00e7imde farkl\u0131ysa, anlaml\u0131 bir \\(H'\\) t\u00fcm da\u011f\u0131l\u0131mdaki fark\u0131 yans\u0131t\u0131r; yaln\u0131zca konum fark\u0131 oldu\u011funu s\u00f6ylemeyebilir.<\/li>\n<li><strong>Grup b\u00fcy\u00fckl\u00fcklerinin e\u015fit olmas\u0131 gerekmez.<\/strong> Form\u00fcl e\u015fit olmayan \\(n_j\\) de\u011ferlerini hesaba katar; yaln\u0131zca \u00e7ok k\u00fc\u00e7\u00fck gruplar ki-kare yakla\u015f\u0131m\u0131n\u0131 zay\u0131flat\u0131r.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u00dc\u00e7 ya da d\u00f6rt gruba ait g\u00f6zlemleri girin; bu ara\u00e7 Kruskal\u2013Wallis testini uygular: t\u00fcm de\u011ferleri birlikte s\u0131ralar, e\u015fitlik d\u00fczeltilmi\u015f H istatisti\u011fini, serbestlik derecesini, p de\u011ferini ve se\u00e7ti\u011finiz anlaml\u0131l\u0131k d\u00fczeyine g\u00f6re karar\u0131 hesaplar.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[12],"tags":[46],"class_list":["post-3997","post","type-post","status-publish","format-standard","hentry","category-istatistik","tag-hipotez-testi"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/3997","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=3997"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/3997\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=3997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=3997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=3997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}