{"id":4085,"date":"2026-10-15T07:39:05","date_gmt":"2026-10-15T06:39:05","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/istatistik\/friedman-testi-hesaplayicisi\/"},"modified":"2026-10-15T07:39:05","modified_gmt":"2026-10-15T06:39:05","slug":"friedman-testi-hesaplayicisi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/istatistik\/friedman-testi-hesaplayicisi\/","title":{"rendered":"Friedman testi hesaplay\u0131c\u0131s\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 ili\u015fkili ko\u015fulu s\u0131ralamalar\u0131na 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=\"4085\" data-favorite-title=\"Friedman testi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/istatistik\/friedman-testi-hesaplayicisi\/\" data-favorite-excerpt=\"Her kat\u0131l\u0131mc\u0131 i\u00e7in t\u00fcm ko\u015fullardaki de\u011ferleri bir sat\u0131ra girin. Friedman testi hesaplay\u0131c\u0131s\u0131, e\u015fit de\u011ferlere g\u00f6re d\u00fczeltilmi\u015f ki-kare istatisti\u011fini, serbestlik derecesini, p-de\u011ferini, Kendall&#039;\u0131n W katsay\u0131s\u0131n\u0131 ve se\u00e7ti\u011finiz anlaml\u0131l\u0131k d\u00fczeyine g\u00f6re karar\u0131 hesaplas\u0131n.\" 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\/friedman-testi-hesaplayicisi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4085\" data-post=\"4085\"><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\">\u00d6l\u00e7\u00fcmler (her sat\u0131ra bir denek)<\/label><textarea id=\"field-1\" name=\"lmler_her_satra_bir_denek\">7 6 5\n5 4 6\n8 7 6\n4 5 3\n6 6 4\n7 5 6\n5 3 4\n9 8 7<\/textarea><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Anlaml\u0131l\u0131k d\u00fczeyi<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"anlamllk_dzeyi\"><option value=\"0.10\">0.10<\/option><option value=\"0.05\" selected>0.05<\/option><option value=\"0.025\">0.025<\/option><option value=\"0.01\">0.01<\/option><option value=\"0.001\">0.001<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4085\">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> Friedman testi sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Friedman test istatisti\u011fi (\u03c7\u00b2, e\u015fit s\u0131ralar i\u00e7in d\u00fczeltilmi\u015f)<\/span><span class=\"result-term\">\u03c7\u00b2\u1d3f<\/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>Serbestlik derecesi<\/span><span class=\"result-term\">sd<\/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>p de\u011feri (\u03c7\u00b2 yakla\u015f\u0131m\u0131)<\/span><span class=\"result-term\">p<\/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>Kendall&#039;\u0131n W katsay\u0131s\u0131 (etki b\u00fcy\u00fckl\u00fc\u011f\u00fc)<\/span><span class=\"result-term\">W<\/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 d\u00fczeyinde 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>Ko\u015fullara g\u00f6re s\u0131ra toplamlar\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>Friedman testi nas\u0131l \u00e7al\u0131\u015f\u0131r?<\/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=\"4085\" 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>Friedman testi<\/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\\[ \\chi_F^2 = \\frac{12}{n\\,k\\,(k+1)} \\sum_{j=1}^{k} R_j^2 \\; - \\; 3n(k+1) \\qquad\\text{(e\u015fit de\u011ferlere g\u00f6re d\u00fczeltilmi\u015f: } \\chi^2 = \\chi_F^2 \/ C\\text{)} \\\\ C = 1 - \\frac{\\sum\\left(t^3 - t\\right)}{n\\left(k^3 - k\\right)} \\\\ W = \\frac{\\chi^2}{n(k-1)} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(n\\) \u2014 kat\u0131l\u0131mc\u0131 (blok) say\u0131s\u0131<\/li>\n<li>\\(k\\) \u2014 ili\u015fkili ko\u015ful say\u0131s\u0131 (\\(k \\ge 3\\))<\/li>\n<li>\\(R_j\\) \u2014 \\(j\\) ko\u015fulunun s\u0131ra toplam\u0131; her kat\u0131l\u0131mc\u0131n\u0131n de\u011ferleri, en k\u00fc\u00e7\u00fc\u011fe 1 ve en b\u00fcy\u00fc\u011fe \\(k\\) verilerek s\u0131ralan\u0131r, e\u015fit de\u011ferlere ise ortalama s\u0131ra verilir<\/li>\n<li>\\(t\\) \u2014 bir kat\u0131l\u0131mc\u0131n\u0131n e\u015fit de\u011ferlerinden olu\u015fan her grubun b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/li>\n<li>\\(W\\) \u2014 etki b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc g\u00f6steren Kendall uyum katsay\u0131s\u0131<\/li>\n<\/ul>\n<p>\u0130statistik, g\u00f6zlenen s\u0131ra toplamlar\u0131n\u0131 t\u00fcm ko\u015fullar e\u015fit oldu\u011funda beklenen \\(nk(k+1)\/4\\cdot 2\\) de\u011feriyle kar\u015f\u0131la\u015ft\u0131r\u0131r; sapma b\u00fcy\u00fcd\u00fck\u00e7e \\(\\chi^2\\) de b\u00fcy\u00fcr. E\u015fit de\u011ferler varsa d\u00fczeltme, istatisti\u011fin de\u011ferini art\u0131r\u0131r. p-de\u011feri ise \\(k-1\\) serbestlik dereceli \\(\\chi^2\\) da\u011f\u0131l\u0131m\u0131ndan elde edilir.<\/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>Friedman testi \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> Sekiz kat\u0131l\u0131mc\u0131n\u0131n her biri \u00fc\u00e7 \u00fcr\u00fcn\u00fc bir \u00f6l\u00e7ek \u00fczerinde de\u011ferlendiriyor (hesaplay\u0131c\u0131daki varsay\u0131lan veriler). Her kat\u0131l\u0131mc\u0131n\u0131n \u00fc\u00e7 puan\u0131 kendi i\u00e7inde 1\u20133 aras\u0131nda s\u0131raland\u0131\u011f\u0131nda s\u0131ra toplamlar\u0131 \\(R_1 = 21.5\\), \\(R_2 = 14.5\\), \\(R_3 = 12\\) olur.<\/p>\n<p>\\[ \\chi_F^2 = \\frac{12}{8 \\cdot 3 \\cdot 4}\\left(21.5^2 + 14.5^2 + 12^2\\right) - 3 \\cdot 8 \\cdot 4 = 6.0625 \\]<\/p>\n<p>Bir kat\u0131l\u0131mc\u0131 iki \u00fcr\u00fcne ayn\u0131 puan\u0131 verdi\u011finden, \\(t=2\\) b\u00fcy\u00fckl\u00fc\u011f\u00fcndeki bir e\u015fit de\u011fer grubu d\u00fczeltme hesab\u0131na \\(t^3 - t = 6\\) katk\u0131da bulunur:<\/p>\n<p>\\[ C = 1 - \\frac{6}{8(27 - 4 + -3)} = 1 - \\frac{6}{192} = 0.96875, \\qquad \\chi^2 = \\frac{6.0625}{0.96875} = 6.2581 \\]<\/p>\n<p>\\(df = k - 1 = 2\\) oldu\u011funda \\(\\chi^2\\) yakla\u015f\u0131m\u0131 \\(p = 0.0438\\) sonucunu verir; Kendall'\u0131n W katsay\u0131s\u0131 ise \\(W = 6.2581 \/ (8 \\cdot 2) = 0.3911\\) olur.<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(\\chi^2 = 6.2581\\), \\(df = 2\\), \\(p = 0.0438\\). \\(\\alpha = 0.05\\) d\u00fczeyinde \\(H_0\\) reddedilir: \u00dc\u00e7 \u00fcr\u00fcn aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark vard\u0131r ve kat\u0131l\u0131mc\u0131lar aras\u0131nda orta d\u00fczeyde uyum g\u00f6r\u00fcl\u00fcr (\\(W \\approx 0.39\\)).<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>Verilerinizi <strong>\u00d6l\u00e7\u00fcmler (her sat\u0131ra bir kat\u0131l\u0131mc\u0131)<\/strong> alan\u0131na yap\u0131\u015ft\u0131r\u0131n veya yaz\u0131n. Her sat\u0131rda bir kat\u0131l\u0131mc\u0131n\u0131n, her ko\u015ful i\u00e7in birer tane olmak \u00fczere, bo\u015fluk ya da noktal\u0131 virg\u00fclle ayr\u0131lm\u0131\u015f de\u011ferleri bulunmal\u0131d\u0131r. \u00d6rne\u011fin <code>7 6 5<\/code> veya <code>7; 6; 5<\/code> yazabilirsiniz. B\u00fct\u00fcn sat\u0131rlarda ayn\u0131 say\u0131da ve en az \u00fc\u00e7 de\u011fer olmal\u0131d\u0131r.<\/li>\n<li>Say\u0131lar\u0131n\u0131zda ondal\u0131k ay\u0131r\u0131c\u0131 olarak virg\u00fcl kullan\u0131yorsan\u0131z (\u00f6rne\u011fin <code>7,5<\/code>), de\u011ferleri oldu\u011fu gibi girebilirsiniz; hesaplay\u0131c\u0131 bunlar\u0131 otomatik olarak d\u00f6n\u00fc\u015ft\u00fcr\u00fcr.<\/li>\n<li>Bir <strong>Anlaml\u0131l\u0131k d\u00fczeyi<\/strong> (0,10; 0,05; 0,025; 0,01 veya 0,001) se\u00e7in. Bu, s\u0131f\u0131r hipotezinin reddedilip reddedilmeyece\u011fini belirleyen \\(\\alpha\\) e\u015fi\u011fidir.<\/li>\n<li>Sonu\u00e7lar\u0131 inceleyin: e\u015fit de\u011ferlere g\u00f6re d\u00fczeltilmi\u015f Friedman istatisti\u011fi \\(\\chi^2\\), serbestlik derecesi, p-de\u011feri, Kendall'\u0131n \\(W\\) katsay\u0131s\u0131, \\(\\alpha\\) d\u00fczeyindeki karar, ko\u015fullara g\u00f6re s\u0131ra toplamlar\u0131 tablosu ve k\u0131sa bir a\u00e7\u0131klama g\u00f6sterilir.<\/li>\n<\/ol>\n<h2>Friedman testi nedir?<\/h2>\n<p>Friedman testi, tek y\u00f6nl\u00fc tekrarl\u0131 \u00f6l\u00e7\u00fcmler ANOVA's\u0131n\u0131n parametrik olmayan alternatifidir. \u00dc\u00e7 veya daha fazla <em>ili\u015fkili<\/em> ko\u015fulu kar\u015f\u0131la\u015ft\u0131r\u0131r. Genellikle ayn\u0131 kat\u0131l\u0131mc\u0131lar her ko\u015fulda \u00f6l\u00e7\u00fcl\u00fcr ya da her blo\u011fun b\u00fct\u00fcn uygulamalar\u0131 ald\u0131\u011f\u0131 rastgele blok d\u00fczeni kullan\u0131l\u0131r. Test, ko\u015fullar\u0131n konum bak\u0131m\u0131ndan farkl\u0131la\u015f\u0131p farkl\u0131la\u015fmad\u0131\u011f\u0131n\u0131, yani puanlar\u0131n baz\u0131 ko\u015fullarda sistematik olarak daha y\u00fcksek olma e\u011filimi g\u00f6sterip g\u00f6stermedi\u011fini inceler.<\/p>\n<p>Test yaln\u0131zca s\u0131ralara dayan\u0131r. Her kat\u0131l\u0131mc\u0131n\u0131n de\u011ferleri kendi i\u00e7inde s\u0131ralan\u0131r; b\u00f6ylece kat\u0131l\u0131mc\u0131lar aras\u0131ndaki farklar ortadan kalkar. Her \u015feye y\u00fcksek puan veren bir kat\u0131l\u0131mc\u0131 ile her \u015feye d\u00fc\u015f\u00fck puan veren bir kat\u0131l\u0131mc\u0131, ayn\u0131 s\u0131ralama d\u00fczenine sahipse sonuca ayn\u0131 \u015fekilde katk\u0131da bulunur. Ko\u015fullar birbirinden farkl\u0131 de\u011filse her ko\u015fulun s\u0131ralar\u0131 \\(1, \\dots, k\\) de\u011ferlerinin rastgele bir perm\u00fctasyonudur. Bu durumda her ko\u015ful i\u00e7in beklenen s\u0131ra toplam\u0131 \\(n \\cdot k(k+1)\/2\\) olur. Friedman istatisti\u011fi, g\u00f6zlenen s\u0131ra toplamlar\u0131n\u0131n bu beklentiden ne kadar sapt\u0131\u011f\u0131n\u0131 \u00f6l\u00e7er: Bir ko\u015ful s\u00fcrekli en \u00fcst s\u0131rada yer al\u0131yorsa onun s\u0131ra toplam\u0131 b\u00fcy\u00fcr, ba\u015fka bir ko\u015fulunki k\u00fc\u00e7\u00fcl\u00fcr ve \\(\\chi^2\\) artar.<\/p>\n<p>p-de\u011feri, istatisti\u011fin \\(\\chi^2_{k-1}\\) da\u011f\u0131l\u0131m\u0131yla kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131yla bulunur. \\(p \\le \\alpha\\) ise s\u0131f\u0131r hipotezini reddeder ve en az bir ko\u015fulun di\u011ferlerinden daha y\u00fcksek ya da daha d\u00fc\u015f\u00fck s\u0131rada yer alma e\u011filiminde oldu\u011fu sonucuna var\u0131rs\u0131n\u0131z. Ancak test, bunun hangi ko\u015ful oldu\u011funu s\u00f6ylemez. Kendall'\u0131n \\(W = \\chi^2 \/ (n(k-1))\\) katsay\u0131s\u0131, kat\u0131l\u0131mc\u0131lar\u0131n ko\u015fullar\u0131 s\u0131ralama bi\u00e7imlerinin ne kadar tutarl\u0131 oldu\u011funu g\u00f6sterir: 0 uyum olmad\u0131\u011f\u0131n\u0131, 1 t\u00fcm kat\u0131l\u0131mc\u0131lar\u0131n ko\u015fullar\u0131 tam olarak ayn\u0131 s\u0131raya koydu\u011funu belirtir. 0,3\u20130,5 civar\u0131ndaki de\u011ferler genellikle orta d\u00fczeyde uyum olarak tan\u0131mlan\u0131r.<\/p>\n<p>Anlaml\u0131 bir sonu\u00e7 yaln\u0131zca ilk ad\u0131md\u0131r. <em>Hangi<\/em> ko\u015fullar\u0131n farkl\u0131 oldu\u011funu belirlemek i\u00e7in ikili kar\u015f\u0131la\u015ft\u0131rmalar yap\u0131n: ortalama s\u0131ralar i\u00e7in kritik fark\u0131 \\(q_\\alpha\\sqrt{k(k+1)\/(6n)}\\) olan Nemenyi testini veya Bonferroni d\u00fczeltmesi uygulanm\u0131\u015f bir anlaml\u0131l\u0131k d\u00fczeyiyle <a href=\"https:\/\/wpcalc.com\/en\/statistics\/wilcoxon-signed-rank-test-calculator\/\">Wilcoxon i\u015faretli s\u0131ralar testlerini<\/a> kullanabilirsiniz. Gruplar\u0131n\u0131z e\u015fle\u015ftirilmi\u015f de\u011fil de <em>ba\u011f\u0131ms\u0131zsa<\/em> Friedman testi uygun de\u011fildir; bunun yerine <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/kruskal-wallis-testi-hesaplama\/\">Kruskal\u2013Wallis testini<\/a> kullan\u0131n.<\/p>\n<h2>Varsay\u0131mlar ve uygulamaya y\u00f6nelik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>E\u015fle\u015ftirilmi\u015f veriler:<\/strong> Her kat\u0131l\u0131mc\u0131n\u0131n (blo\u011fun) her ko\u015ful i\u00e7in bir de\u011feri olmal\u0131d\u0131r. Eksik de\u011ferlerle i\u015flem yap\u0131lamaz; verileri girmeden \u00f6nce ilgili kat\u0131l\u0131mc\u0131y\u0131 \u00e7\u0131kar\u0131n veya eksik de\u011feri uygun bir y\u00f6ntemle tamamlay\u0131n.<\/li>\n<li><strong>Ba\u011f\u0131ms\u0131z kat\u0131l\u0131mc\u0131lar:<\/strong> Kat\u0131l\u0131mc\u0131lar veya bloklar birbirini etkilememelidir. Ayn\u0131 kat\u0131l\u0131mc\u0131dan al\u0131nan tekrarl\u0131 \u00f6l\u00e7\u00fcmler ise do\u011fal olarak ili\u015fkilidir; test zaten bu t\u00fcr veriler i\u00e7in tasarlanm\u0131\u015ft\u0131r.<\/li>\n<li><strong>En az s\u0131ral\u0131 \u00f6l\u00e7ek:<\/strong> De\u011ferlerin yaln\u0131zca her kat\u0131l\u0131mc\u0131 i\u00e7inde s\u0131ralanabilir olmas\u0131 yeterlidir. Dolay\u0131s\u0131yla Likert de\u011ferlendirmeleri, s\u0131ralar ve puanlar kullan\u0131labilir.<\/li>\n<li><strong>p-de\u011feri yakla\u015f\u0131k bir de\u011ferdir.<\/strong> Referans al\u0131nan \\(\\chi^2\\) da\u011f\u0131l\u0131m\u0131, \\(nk\\) b\u00fcy\u00fcd\u00fck\u00e7e daha do\u011fru sonu\u00e7 verir. K\u00fc\u00e7\u00fck \u00f6rneklemlerde ise test biraz fazla kolay anlaml\u0131 sonu\u00e7 verme e\u011filimindedir; p-de\u011ferleri olmas\u0131 gerekenden k\u00fc\u00e7\u00fck \u00e7\u0131kabilir. \u00d6rne\u011fin \\(k = 3\\) iken yakla\u015f\u0131k 13'ten az kat\u0131l\u0131mc\u0131 varsa, s\u0131n\u0131rda kalan bir karara g\u00fcvenmeden \u00f6nce istatisti\u011fi Friedman testinin kesin kritik de\u011ferleriyle kar\u015f\u0131la\u015ft\u0131r\u0131n.<\/li>\n<li><strong>E\u015fit de\u011ferler hesaba kat\u0131l\u0131r, ancak \u00e7ok say\u0131da e\u015fit de\u011fer testin g\u00fcc\u00fcn\u00fc azalt\u0131r.<\/strong> Hesaplay\u0131c\u0131 standart e\u015fitlik d\u00fczeltmesi \\(C\\)'yi uygular. B\u00fct\u00fcn kat\u0131l\u0131mc\u0131lar ko\u015fullar\u0131n t\u00fcm\u00fcne ayn\u0131 de\u011feri verirse istatistik, hesaplama gere\u011fi s\u0131f\u0131r olur ve bir fark saptanamaz.<\/li>\n<li><strong>W'yi p-de\u011feriyle birlikte yorumlay\u0131n.<\/strong> Kat\u0131l\u0131mc\u0131 say\u0131s\u0131 \u00e7ok oldu\u011funda s\u0131ra toplamlar\u0131ndaki \u00e7ok k\u00fc\u00e7\u00fck, uygulamada \u00f6nemsiz bir fark bile istatistiksel olarak anlaml\u0131 olabilir. Kendall'\u0131n \\(W\\) katsay\u0131s\u0131, sonucun arkas\u0131ndaki uyumun ger\u00e7ekten kayda de\u011fer olup olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir. De\u011ferlendiriciler aras\u0131ndaki s\u0131ralama uyumuna ba\u015fka bir a\u00e7\u0131dan bakmak i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/kendall-tau-hesaplayici\/\">Kendall'\u0131n tau hesaplay\u0131c\u0131s\u0131na<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/istatistik\/spearman-sira-korelasyon-hesaplama\/\">Spearman s\u0131ra korelasyonu hesaplay\u0131c\u0131s\u0131na<\/a> bak\u0131n.<\/li>\n<\/ul>\n<p>Etkinin y\u00f6n\u00fcn\u00fc s\u0131ra toplamlar\u0131 tablosundan g\u00f6rebilirsiniz: Ortalama s\u0131ras\u0131 en b\u00fcy\u00fck olan ko\u015ful genellikle en y\u00fcksek, en k\u00fc\u00e7\u00fck olan ko\u015ful ise en d\u00fc\u015f\u00fck puanlar\u0131 al\u0131r. Her ko\u015fulun ortalama s\u0131ras\u0131n\u0131 s\u0131f\u0131r hipotezi alt\u0131nda beklenen \\(k(k+1)\/2\\) de\u011feriyle kar\u015f\u0131la\u015ft\u0131rarak sonuca hangi ko\u015fullar\u0131n y\u00f6n verdi\u011fini g\u00f6rebilirsiniz.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Her kat\u0131l\u0131mc\u0131 i\u00e7in t\u00fcm ko\u015fullardaki de\u011ferleri bir sat\u0131ra girin. Friedman testi hesaplay\u0131c\u0131s\u0131, e\u015fit de\u011ferlere g\u00f6re d\u00fczeltilmi\u015f ki-kare istatisti\u011fini, serbestlik derecesini, p-de\u011ferini, Kendall'\u0131n W katsay\u0131s\u0131n\u0131 ve se\u00e7ti\u011finiz anlaml\u0131l\u0131k d\u00fczeyine g\u00f6re karar\u0131 hesaplas\u0131n.<\/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-4085","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\/4085","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=4085"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4085\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}