{"id":528,"date":"2023-07-29T14:56:51","date_gmt":"2023-07-29T14:56:51","guid":{"rendered":"https:\/\/statorials.org\/tr\/welchs-t-testi\/"},"modified":"2023-07-29T14:56:51","modified_gmt":"2023-07-29T14:56:51","slug":"welchs-t-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/welchs-t-testi\/","title":{"rendered":"Welch&#39;in t testi: ne zaman kullan\u0131lmal\u0131 + \u00f6rnekler"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130ki ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak istedi\u011fimizde iki farkl\u0131 test aras\u0131nda se\u00e7im yapabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6\u011frenci t testi:<\/strong> Bu test, iki veri grubunun normal bir da\u011f\u0131l\u0131m izleyen pop\u00fclasyonlardan \u00f6rneklendi\u011fini ve iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsayar.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Welch&#8217;in t testi:<\/strong> Bu test, her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini varsayar, <em>ancak bu iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsaymaz<\/em> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6\u011frenci t testi ile Welch t testi aras\u0131ndaki fark<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">\u00d6\u011frenci t testi ile Welch t testinin ger\u00e7ekle\u015ftirilme bi\u00e7iminde iki fark vard\u0131r:<\/span><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><strong>Test istatisti\u011fi<\/strong><\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><strong>\u00d6zg\u00fcrl\u00fck derecesi<\/strong><\/span><\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6\u011frencinin t testi:<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Test istatisti\u011fi:<\/strong> ( <span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> ) \/ s <sub>p<\/sub> (\u221a <span style=\"border-top: 1px solid black;\">1\/n <sub>1<\/sub> + 1\/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">burada <span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> ve <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> \u00f6rnek ortalamalar\u0131d\u0131r, n <sub>1<\/sub> ve n <sub>2<\/sub> s\u0131ras\u0131yla \u00f6rnek 1 ve \u00f6rnek 2 i\u00e7in \u00f6rnek boyutlar\u0131d\u0131r ve burada <sub>sp<\/sub> a\u015fa\u011f\u0131daki gibi hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>p<\/sub><\/span> = <span style=\"color: #000000;\">\u221a <span style=\"border-top: 1px solid black;\">(n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">burada s <sub>1<\/sub> <sup>2<\/sup> ve s <sub>2<\/sub> <sup>2<\/sup> \u00f6rnek varyanslard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Serbestlik derecesi:<\/strong> n <sub>1<\/sub> + n <sub>2<\/sub> \u2013 2<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Welch&#8217;in T testi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Test istatisti\u011fi:<\/strong> ( <span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Serbestlik dereceleri:<\/strong><\/span> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ { [ (s <sub>1<\/sub> <sup>2<\/sup> \/ n <sub>1<\/sub> ) <sup>2<\/sup> \/ (n <sub>1<\/sub> \u2013 1) ] + [ (s <sub>2<\/sub> <sup>2<\/sup> \/ n <sub>2<\/sub> ) <sup>2<\/sup> \/ (n <sub>2<\/sub> \u2013 1) ] }<\/span><\/p>\n<p> <span style=\"color: #000000;\">Welch t-testi i\u00e7in serbestlik derecelerini hesaplamaya y\u00f6nelik form\u00fcl, iki standart sapma aras\u0131ndaki fark\u0131 hesaba katar. \u0130ki <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener\">numunenin<\/a> standart sapmalar\u0131 ayn\u0131ysa Welch t testinin serbestlik derecesi, \u00d6\u011frenci t testinin serbestlik derecesiyle tamamen ayn\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tipik olarak, iki numunenin standart sapmalar\u0131 ayn\u0131 de\u011fildir ve bu nedenle Welch t-testinin serbestlik dereceleri, \u00d6\u011frenci t-testinin serbestlik derecelerinden daha k\u00fc\u00e7\u00fck olma e\u011filimindedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Welch t-testindeki serbestlik derecelerinin genellikle tam say\u0131 olmad\u0131\u011f\u0131na dikkat etmek de \u00f6nemlidir. Manuel olarak test yap\u0131yorsan\u0131z en d\u00fc\u015f\u00fck tam say\u0131ya yuvarlamak en iyisidir. E\u011fer <em>R<\/em> gibi istatistiksel bir yaz\u0131l\u0131m kullan\u0131rsan\u0131z, yaz\u0131l\u0131m serbestlik derecesinin ondal\u0131k de\u011ferini sa\u011flayabilecektir.<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Welch t-testini ne zaman kullanmal\u0131s\u0131n\u0131z?<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Baz\u0131 insanlar <a href=\"https:\/\/daniellakens.blogspot.com\/2015\/01\/always-use-welchs-t-test-instead-of.html\" target=\"_blank\" rel=\"noopener noreferrer\">, Welch&#8217;in t testinin iki ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in varsay\u0131lan se\u00e7im olmas\u0131 gerekti\u011fini,<\/a> \u00e7\u00fcnk\u00fc \u00f6rneklem b\u00fcy\u00fckl\u00fckleri ve varyanslar gruplar aras\u0131nda e\u015fit olmad\u0131\u011f\u0131nda \u00d6\u011frenci t testinden daha iyi performans g\u00f6sterdi\u011fini ve \u00f6rneklem b\u00fcy\u00fckl\u00fckleri e\u015fit olmad\u0131\u011f\u0131nda ayn\u0131 sonu\u00e7lar\u0131 verdi\u011fini ileri s\u00fcrmektedir. farkl\u0131d\u0131r. farklar e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygulamada, iki grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rd\u0131\u011f\u0131n\u0131zda her grubun standart sapmalar\u0131n\u0131n ayn\u0131 olmas\u0131 pek olas\u0131 de\u011fildir. Dolay\u0131s\u0131yla her zaman Welch t-testini kullanmak iyi bir fikirdir, b\u00f6ylece varyanslar\u0131n e\u015fitli\u011fi hakk\u0131nda varsay\u0131mlarda bulunman\u0131za gerek kalmaz.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Welch t-testini kullanma \u00f6rnekleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Daha sonra, pop\u00fclasyon ortalamalar\u0131n\u0131n 0,05 anlaml\u0131l\u0131k seviyesinde \u00f6nemli \u00f6l\u00e7\u00fcde farkl\u0131l\u0131k g\u00f6sterip g\u00f6stermedi\u011fini belirlemek i\u00e7in a\u015fa\u011f\u0131daki iki \u00f6rnek \u00fczerinde Welch t-testi uygulayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong> 14, 15, 15, 15, 16, 18, 22, 23, 24, 25, 25<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong> 10, 12, 14, 15, 18, 22, 24, 27, 31, 33, 34, 34, 34<\/span><\/p>\n<p> <span style=\"color: #000000;\">Testin \u00fc\u00e7 farkl\u0131 \u015fekilde nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">El ile<\/span><\/li>\n<li> <span style=\"color: #000000;\">Microsoft Excel&#8217;i kullan\u0131n<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> istatistiksel programlama dilini kullan\u0131n<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Welch&#8217;in T testi elle<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Welch t-testini elle ger\u00e7ekle\u015ftirmek i\u00e7in \u00f6ncelikle \u00f6rnek ortalamas\u0131n\u0131, \u00f6rnek varyanslar\u0131n\u0131 ve \u00f6rnek boyutlar\u0131n\u0131 bulmam\u0131z gerekir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x1<\/span> <sub>\u2013<\/sub><\/strong> 19,27<br \/><\/span> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x2<\/span> <sub>\u2013<\/sub><\/strong> 23,69<br \/> <strong><sub>12<\/sub> <sup>\u2013<\/sup><\/strong> 20:42<br \/><\/span> <span style=\"color: #000000;\"><strong>madde <sub>2<\/sub> <sup>2<\/sup><\/strong> \u2013 83.23<br \/> <strong>#<\/strong> <sub><strong>1<\/strong><\/sub> \u2013 11 <strong><br \/>#<\/strong> <sub><strong>2<\/strong><\/sub> \u2013 13<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra test istatisti\u011fini bulmak i\u00e7in bu say\u0131lar\u0131 girebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Test istatisti\u011fi:<\/strong> ( <span style=\"border-top: 1px solid black;\">x <sub>1<\/sub><\/span> \u2013 <span style=\"border-top: 1px solid black;\">x <sub>2<\/sub><\/span> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi: (19,27 \u2013 23,69) \/ (\u221a <span style=\"border-top: 1px solid black;\">20,42\/11 + 83,23\/13<\/span> ) = -4,42 \/ 2,873 = <strong>-1,538<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Serbestlik dereceleri:<\/strong> (s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ { [ (s <sub>1<\/sub> <sup>2<\/sup> \/ n <sub>1<\/sub> ) <sup>2<\/sup> \/ (n <sub>1<\/sub> \u2013 1) ] + [ (s <sub>2<\/sub> <sup>2<\/sup> \/ n <sub>2<\/sub> ) <sup>2<\/sup> \/ (n <sub>2<\/sub> \u2013 1) ] }<\/span><\/p>\n<p> <span style=\"color: #000000;\">Serbestlik derecesi: (20,42\/11 + 83,23\/13) <sup>2<\/sup> \/ { [ (20,42\/11) <sup>2<\/sup> \/ (11 \u2013 1) ] + [ (83,23\/13) <sup>2<\/sup> \/ (13 \u2013 1) ] } = 18,137. Bu sonucu en yak\u0131n tam say\u0131 olan <strong>18&#8217;e<\/strong> yuvarlar\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, 18 serbestlik derecesi i\u00e7in alfa = 0,05 olan iki tarafl\u0131 bir teste kar\u015f\u0131l\u0131k gelen t da\u011f\u0131l\u0131m tablosunda kritik <em>t<\/em> de\u011ferini bulaca\u011f\u0131z:<\/span> <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png\" alt=\"Da\u011f\u0131t\u0131m tablosu T\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Kritik de\u011fer t <strong>2,101&#8217;dir<\/strong> . Test istatisti\u011fimizin mutlak de\u011feri (1,538), kritik t de\u011ferinden b\u00fcy\u00fck olmad\u0131\u011f\u0131ndan testin s\u0131f\u0131r hipotezini reddedemiyoruz. \u0130ki pop\u00fclasyonun ortalamalar\u0131n\u0131n \u00f6nemli \u00f6l\u00e7\u00fcde farkl\u0131 oldu\u011funu s\u00f6ylemek i\u00e7in yeterli kan\u0131t yok.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Welch&#8217;in Excel ile T testi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Welch&#8217;in t-testini Excel&#8217;de ger\u00e7ekle\u015ftirmek i\u00e7in \u00f6ncelikle \u00fccretsiz Analysis ToolPak yaz\u0131l\u0131m\u0131n\u0131 indirmemiz gerekiyor. Hen\u00fcz Excel&#8217;de indirmediyseniz, <a href=\"https:\/\/statorials.org\/tr\/analiz-arac-paketini-excele-nasil-yukleyebilirim\/\" target=\"_blank\" rel=\"noopener noreferrer\">nas\u0131l indirece\u011finize dair h\u0131zl\u0131 bir e\u011fitim<\/a> yazd\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Analiz Ara\u00e7 Paketi&#8217;ni indirdikten sonra iki \u00f6rne\u011fimiz \u00fczerinde Welch&#8217;in t-testini ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 takip edebilirsiniz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Verileri girin.<\/strong> \u0130ki \u00f6rnek i\u00e7in veri de\u011ferlerini A ve B s\u00fctunlar\u0131na ve her s\u00fctunun ilk h\u00fccresine <em>\u00d6rnek 1<\/em> ve <em>\u00d6rnek 2<\/em> ba\u015fl\u0131klar\u0131n\u0131 girin.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Analiz Ara\u00e7 Paketi&#8217;ni kullanarak Welch t-testini ger\u00e7ekle\u015ftirin.<\/strong> \u00dcst \u015feritteki <strong>Veri<\/strong> sekmesine gidin. Daha sonra, <strong>Analiz<\/strong> grubu alt\u0131nda Analiz Ara\u00e7 Paketi simgesine t\u0131klay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">G\u00f6r\u00fcnt\u00fclenen ileti\u015fim kutusunda <strong>t-testi: e\u015fit olmayan varyanslar\u0131 varsayan iki \u00f6rnek se\u00e7ene\u011fine<\/strong> t\u0131klay\u0131n ve ard\u0131ndan Tamam&#8217;a t\u0131klay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak a\u015fa\u011f\u0131daki de\u011ferleri doldurun ve Tamam&#8217;a t\u0131klay\u0131n:<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki sonu\u00e7 g\u00f6r\u00fcnmelidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu testin sonu\u00e7lar\u0131n\u0131n manuel olarak elde etti\u011fimiz sonu\u00e7lara kar\u015f\u0131l\u0131k geldi\u011fini unutmay\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Test istatisti\u011fi <strong>-1,5379&#8217;dur<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u0130ki tarafl\u0131 kritik de\u011fer <strong>2,1009&#8217;dur<\/strong> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">Test istatisti\u011finin mutlak de\u011feri, iki kuyruklu kritik de\u011ferden b\u00fcy\u00fck olmad\u0131\u011f\u0131ndan, iki pop\u00fclasyonun ortalamalar\u0131 istatistiksel olarak farkl\u0131 de\u011fildir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ayr\u0131ca, testin iki kuyruklu p de\u011feri 0,14&#8217;t\u00fcr; bu 0,05&#8217;ten b\u00fcy\u00fckt\u00fcr ve iki pop\u00fclasyonun ortalamalar\u0131n\u0131n istatistiksel olarak farkl\u0131 olmad\u0131\u011f\u0131n\u0131 do\u011frular.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Welch&#8217;in R kullanarak t testi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, <em>R<\/em> istatistiksel programlama dilini kullanarak iki \u00f6rne\u011fimiz i\u00e7in Welch t testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6stermektedir:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create two vectors to hold sample data values\n<\/span>sample1 &lt;- c(14, 15, 15, 15, 16, 18, 22, 23, 24, 25, 25)\nsample2 &lt;- c(10, 12, 14, 15, 18, 22, 24, 27, 31, 33, 34, 34, 34)\n\n<span style=\"color: #008080;\">#conduct Welch's test\n<\/span><span style=\"color: #800080;\">t.test(<\/span> sample1, sample2)\n\n# Welch Two Sample t-test\n#\n#data: sample1 and sample2\n#t = -1.5379, df = 18.137, p-value = 0.1413\n#alternative hypothesis: true difference in means is not equal to 0\n#95 percent confidence interval:\n#-10.453875 1.614714\n#sample estimates:\n#mean of x mean of y \n#19.27273 23.69231 \n#<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>t.test()<\/strong> i\u015flevi a\u015fa\u011f\u0131daki ilgili \u00e7\u0131kt\u0131y\u0131 g\u00f6r\u00fcnt\u00fcler:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>t:<\/strong> test istatisti\u011fi = <strong>-1,5379<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>df<\/strong> : serbestlik derecesi = <strong>18.137<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p de\u011feri:<\/strong> iki kuyruklu testin p de\u011feri = <strong>0,1413<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>%95 g\u00fcven aral\u0131\u011f\u0131<\/strong> : pop\u00fclasyon ortalamalar\u0131ndaki ger\u00e7ek fark i\u00e7in %95<a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">g\u00fcven aral\u0131\u011f\u0131<\/a> = <strong>(-10,45, 1,61)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu testin sonu\u00e7lar\u0131, manuel olarak ve Excel kullan\u0131larak elde edilenlere kar\u015f\u0131l\u0131k gelir: bu iki pop\u00fclasyon i\u00e7in ortalamalar aras\u0131ndaki fark, alfa = 0,05 d\u00fczeyinde istatistiksel olarak anlaml\u0131 de\u011fildir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130ki ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak istedi\u011fimizde iki farkl\u0131 test aras\u0131nda se\u00e7im yapabiliriz: \u00d6\u011frenci t testi: Bu test, iki veri grubunun normal bir da\u011f\u0131l\u0131m izleyen pop\u00fclasyonlardan \u00f6rneklendi\u011fini ve iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsayar. Welch&#8217;in t testi: Bu test, her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini varsayar, ancak bu iki pop\u00fclasyonun ayn\u0131 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-528","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Welch&#039;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials<\/title>\n<meta name=\"description\" content=\"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Welch&#039;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials\" \/>\n<meta property=\"og:description\" content=\"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T14:56:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\",\"url\":\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\",\"name\":\"Welch&#39;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T14:56:51+00:00\",\"dateModified\":\"2023-07-29T14:56:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/welchs-t-testi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/welchs-t-testi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Welch&#39;in t testi: ne zaman kullan\u0131lmal\u0131 + \u00f6rnekler\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. Daha fazlas\u0131n\u0131 bil\",\"sameAs\":[\"https:\/\/statorials.org\/tr\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Welch&#39;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials","description":"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/tr\/welchs-t-testi\/","og_locale":"tr_TR","og_type":"article","og_title":"Welch&#39;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials","og_description":"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.","og_url":"https:\/\/statorials.org\/tr\/welchs-t-testi\/","og_site_name":"Statorials","article_published_time":"2023-07-29T14:56:51+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png"}],"author":"Dr.benjamin anderson","twitter_card":"summary_large_image","twitter_misc":{"Yazan:":"Dr.benjamin anderson","Tahmini okuma s\u00fcresi":"5 dakika"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/tr\/welchs-t-testi\/","url":"https:\/\/statorials.org\/tr\/welchs-t-testi\/","name":"Welch&#39;in t-testi: Ne zaman kullan\u0131lmal\u0131 + \u00d6rnekler - Statorials","isPartOf":{"@id":"https:\/\/statorials.org\/tr\/#website"},"datePublished":"2023-07-29T14:56:51+00:00","dateModified":"2023-07-29T14:56:51+00:00","author":{"@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48"},"description":"Welch t testinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 ve ne zaman kullan\u0131laca\u011f\u0131n\u0131 birka\u00e7 \u00f6rnekle birlikte a\u00e7\u0131klayan basit bir k\u0131lavuz.","breadcrumb":{"@id":"https:\/\/statorials.org\/tr\/welchs-t-testi\/#breadcrumb"},"inLanguage":"tr","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/tr\/welchs-t-testi\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/tr\/welchs-t-testi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Ev","item":"https:\/\/statorials.org\/tr\/"},{"@type":"ListItem","position":2,"name":"Welch&#39;in t testi: ne zaman kullan\u0131lmal\u0131 + \u00f6rnekler"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/tr\/#website","url":"https:\/\/statorials.org\/tr\/","name":"Statorials","description":"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/tr\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"tr"},{"@type":"Person","@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48","name":"Dr.benjamin anderson","image":{"@type":"ImageObject","inLanguage":"tr","@id":"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg","caption":"Dr.benjamin anderson"},"description":"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=528"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/528\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}