{"id":1610,"date":"2023-07-25T16:21:04","date_gmt":"2023-07-25T16:21:04","guid":{"rendered":"https:\/\/statorials.org\/tr\/esit-veya-esit-olmayan-varyansi-belirlemek\/"},"modified":"2023-07-25T16:21:04","modified_gmt":"2023-07-25T16:21:04","slug":"esit-veya-esit-olmayan-varyansi-belirlemek","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/esit-veya-esit-olmayan-varyansi-belirlemek\/","title":{"rendered":"T testlerinde e\u015fit veya e\u015fit olmayan varyans nas\u0131l belirlenir"},"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\u0131ndan se\u00e7im yapabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">\u00d6\u011frenci t testi:<\/a><\/strong> Her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini ve iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsayar.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch&#8217;in t testi:<\/a><\/strong> Her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini varsayar ancak <strong>bu iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsaymaz<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla, e\u011fer iki \u00f6rnek ayn\u0131 varyansa sahip de\u011filse Welch&#8217;in t-testini kullanmak daha iyidir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ancak iki \u00f6rne\u011fin ayn\u0131 varyansa sahip olup olmad\u0131\u011f\u0131n\u0131 nas\u0131l belirleyebiliriz?<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu yapman\u0131n iki yolu vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Temel varyans kural\u0131n\u0131 kullan\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Genel bir kural olarak, en b\u00fcy\u00fck varyans\u0131n en k\u00fc\u00e7\u00fck varyansa oran\u0131 4&#8217;ten k\u00fc\u00e7\u00fckse varyanslar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011funu varsayabilir ve \u00d6\u011frenci t testini kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, a\u015fa\u011f\u0131daki iki \u00f6rne\u011fimiz oldu\u011funu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15978 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/egalvar1.png\" alt=\"\" width=\"159\" height=\"325\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">1. numunenin varyans\u0131 24.86, 2. numunenin varyans\u0131 ise 15.76&#8217;d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">En b\u00fcy\u00fck \u00f6rnek varyans\u0131n\u0131n en k\u00fc\u00e7\u00fck \u00f6rnek varyans\u0131na oran\u0131 \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oran = 24,86 \/ 15,76 = 1,577<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu oran\u0131n 4&#8217;ten k\u00fc\u00e7\u00fck olmas\u0131 nedeniyle iki grup aras\u0131ndaki farklar\u0131n yakla\u015f\u0131k olarak e\u015fit oldu\u011fu varsay\u0131labilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece iki grubun ayn\u0131 ortalamaya sahip olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00d6\u011frenci t testi yapabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Bir F testi yap\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>F testi,<\/strong> a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullanan resmi bir istatistiksel testtir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">H <sub>0<\/sub> : \u00d6rneklemlerin varyanslar\u0131 e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">H <sub>A<\/sub> : \u00d6rneklemlerin varyanslar\u0131 e\u015fit de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Test istatisti\u011fi \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">F = sn <sub>1<\/sub> <sup>2<\/sup> \/ sn <sub>2<\/sub> <sup>2<\/sup><\/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;\">Test istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri belirli bir anlaml\u0131l\u0131k d\u00fczeyinin (0,05 gibi) alt\u0131ndaysa, \u00f6rneklerin e\u015fit varyansa sahip olmad\u0131\u011f\u0131n\u0131 s\u00f6ylemek i\u00e7in yeterli kan\u0131t\u0131m\u0131z vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tekrar a\u015fa\u011f\u0131daki iki \u00f6rne\u011fe sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15978 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/egalvar1.png\" alt=\"\" width=\"159\" height=\"325\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu iki \u00f6rnek \u00fczerinde F testi ger\u00e7ekle\u015ftirmek i\u00e7in F testi istatisti\u011fini a\u015fa\u011f\u0131daki \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">F = sn <sub>1<\/sub> <sup>2<\/sup> \/ sn <sub>2<\/sub> <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\">F = 24,86 \/ 15,76<\/span><\/li>\n<li> <span style=\"color: #000000;\">F = 1,577<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/f-dagitim-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">F Da\u011f\u0131l\u0131m\u0131 Hesaplay\u0131c\u0131s\u0131na<\/a> g\u00f6re, pay\u0131 df = n <sub>1<\/sub> -1 = 12 ve paydas\u0131 df = n <sub>2<\/sub> -1 = 12 olan 1,577&#8217;lik bir F de\u011feri, 0,22079&#8217;luk bir p de\u011ferine kar\u015f\u0131l\u0131k gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131ndan s\u0131f\u0131r hipotezini reddedemiyoruz. Ba\u015fka bir deyi\u015fle \u00f6rneklem varyanslar\u0131n\u0131n e\u015fit oldu\u011funu varsayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece iki grubun ayn\u0131 ortalamaya sahip olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00d6\u011frenci t testi yapabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00d6\u011frenci t-testini ger\u00e7ekle\u015ftirmeye karar verirseniz a\u015fa\u011f\u0131daki e\u011fitimleri referans olarak kullanabilirsiniz:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/tr\/iki-ornek-t-testi-excel\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de iki t testi \u00f6rne\u011fi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/iki-ornek-t-testi-ti-84-hesap-makinesi\/\" target=\"_blank\" rel=\"noopener\">TI-84 hesap makinesinde iki \u00f6rnekli t testi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/iki-ornek-t-testi-spss\/\" target=\"_blank\" rel=\"noopener\">SPSS&#8217;de iki \u00f6rnekli t testi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/iki-ornek-t-testi-python\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da iki t-testi \u00f6rne\u011fi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/ta-test-hesap-makinesi-iki-ornek\/\" target=\"_blank\" rel=\"noopener\">\u0130ki \u00f6rnekli t testi hesaplay\u0131c\u0131s\u0131<\/a><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Welch&#8217;in t-testini ger\u00e7ekle\u015ftirmeye karar verirseniz a\u015fa\u011f\u0131daki e\u011fitimleri referans olarak kullanabilirsiniz:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch&#8217;in Excel&#8217;deki T testi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/rde-welch-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch&#8217;in R&#8217;deki t testi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/welch-t-testi-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Welch&#8217;in T testi<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Welch&#8217;in t-testi hesaplay\u0131c\u0131s\u0131<\/a><\/li>\n<\/ul>\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\u0131ndan se\u00e7im yapabiliriz: \u00d6\u011frenci t testi: Her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini ve iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu varsayar. Welch&#8217;in t testi: Her iki veri grubunun da normal da\u011f\u0131l\u0131ma sahip pop\u00fclasyonlardan \u00f6rneklendi\u011fini varsayar ancak bu iki pop\u00fclasyonun ayn\u0131 varyansa sahip oldu\u011funu [&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-1610","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>T testlerinde e\u015fit veya e\u015fit olmayan varyans nas\u0131l belirlenir<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, t-testlerinde iki \u00f6rne\u011fin e\u015fit veya e\u015fit olmayan varyanslara sahip olup olmad\u0131\u011f\u0131n\u0131n nas\u0131l belirlenece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" 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