{"id":3771,"date":"2023-07-15T15:42:15","date_gmt":"2023-07-15T15:42:15","guid":{"rendered":"https:\/\/statorials.org\/tr\/t-testi-icin-serbestlik-derecelerini-hesaplayin\/"},"modified":"2023-07-15T15:42:15","modified_gmt":"2023-07-15T15:42:15","slug":"t-testi-icin-serbestlik-derecelerini-hesaplayin","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/t-testi-icin-serbestlik-derecelerini-hesaplayin\/","title":{"rendered":"Herhangi bir t testi i\u00e7in serbestlik derecesi nas\u0131l hesaplan\u0131r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde yayg\u0131n olarak kullan\u0131lan \u00fc\u00e7 t testi vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ornek-t-testi\/\" target=\"_blank\" rel=\"noopener\">Tek \u00f6rnek t testi<\/a> : Pop\u00fclasyon ortalamas\u0131n\u0131 belirli bir de\u011ferle kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">\u0130ki \u00f6rnekli t testi<\/a> : iki pop\u00fclasyon ortalamas\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi\/\" target=\"_blank\" rel=\"noopener\">E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi<\/a> : Bir \u00f6rnekteki her g\u00f6zlem di\u011fer \u00f6rnekteki bir g\u00f6zlemle ili\u015fkilendirilebildi\u011finde iki pop\u00fclasyonun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her t-testini \u00e7al\u0131\u015ft\u0131r\u0131rken bir test istatisti\u011fi ve buna kar\u015f\u0131l\u0131k gelen <strong>serbestlik derecesini<\/strong> hesaplaman\u0131z gerekecektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her bir test t\u00fcr\u00fc i\u00e7in serbestlik derecesinin nas\u0131l hesaplanaca\u011f\u0131 a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Tek \u00f6rnekli t testi: df = n-1<\/strong> burada <em>n<\/em> , toplam g\u00f6zlem say\u0131s\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0130ki \u00f6rnekli t testi: df = n <sub>1<\/sub> + n <sub>2<\/sub> \u2013 2<\/strong> burada <em>n <sub>1<\/sub><\/em> , <em>n <sub>2<\/sub><\/em> her \u00f6rne\u011fin toplam g\u00f6zlemleridir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi: n-1<\/strong> burada <em>n<\/em> , toplam \u00e7ift say\u0131s\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, pratikte her bir t-testi t\u00fcr\u00fc i\u00e7in serbestlik derecesinin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Tek \u00f6rnekli t testi i\u00e7in serbestlik dereceleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pound olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131<\/span> <span style=\"color: #000000;\">varsayal\u0131m<\/span> :<\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki hipotezlerle tek \u00f6rnekli bir t testi ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">H <sub>0<\/sub> : \u03bc = 310 (N\u00fcfus ortalamas\u0131 310 kitaba e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\">H <sub>A<\/sub> : \u03bc \u2260 310 (n\u00fcfus ortalamas\u0131 310 pound&#8217;a e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130lk olarak test istatisti\u011fini hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">t = ( <span style=\"text-decoration: overline;\">x<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"text-decoration: overline;\">\u221an<\/span> ) = (300-310) \/ (18,5\/ <span style=\"text-decoration: overline;\">\u221a40<\/span> ) = -3,4187<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra <strong>serbestlik derecelerini hesaplayaca\u011f\u0131z:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">df = n -1 = 40 \u2013 1 = 39<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, p de\u011ferinin <strong>0,00149<\/strong> oldu\u011funu bulmak i\u00e7in test istatistiklerini ve serbestlik derecelerini <a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P de\u011feri T puan\u0131 hesaplay\u0131c\u0131s\u0131na<\/a> ba\u011flayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri bizim anlaml\u0131l\u0131k seviyemiz olan \u03b1 = 0,05&#8217;in alt\u0131nda oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Bu kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pounda e\u015fit olmad\u0131\u011f\u0131n\u0131 s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z var.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: \u0130ki \u00f6rnekli bir t testi i\u00e7in serbestlik dereceleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Diyelim ki iki farkl\u0131 kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 bilmek istiyoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her pop\u00fclasyondan a\u015fa\u011f\u0131daki bilgilerle birlikte rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n <sub>1<\/sub> = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s <sub>1<\/sub> = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n <sub>2<\/sub> = 38<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> = 305<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s <sub>2<\/sub> = 16,7<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki varsay\u0131mlarla iki \u00f6rnekli bir t testi ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">H <sub>0<\/sub> : \u03bc <sub>1<\/sub> = \u03bc <sub>2<\/sub> (iki pop\u00fclasyon ortalamas\u0131 e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\">H <sub>A<\/sub> : \u03bc <sub>1<\/sub> \u2260 \u03bc <sub>2<\/sub> (iki pop\u00fclasyon ortalamas\u0131 e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130lk olarak, birle\u015ftirilmi\u015f standart sapma s <sub>p&#8217;yi<\/sub> hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>p<\/sub> = \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) = \u221a (<\/span> <span style=\"border-top: 1px solid black;\">40-1)18,5 <sup>2<\/sup> + (38-1) 16,7 <sup>2<\/sup> \/ (40+38-2)<\/span> = 17,647<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra <em>t<\/em> -test istatisti\u011fini hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">t = ( <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> ) = (300-305) \/ 17,647(\u221a <span style=\"border-top: 1px solid black;\">1\/40 + 1\/38<\/span> ) = -1,2508<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra <strong>serbestlik derecelerini hesaplayaca\u011f\u0131z:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">df = n <sub>1<\/sub> + n <sub>2<\/sub> \u2013 2 = 40 + 38 \u2013 2 = 76<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, p de\u011ferinin <strong>0,21484<\/strong> oldu\u011funu bulmak i\u00e7in test istatistiklerini ve serbestlik derecelerini <a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P de\u011feri T puan\u0131 hesaplay\u0131c\u0131s\u0131na<\/a> ba\u011flayaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri bizim anlaml\u0131l\u0131k d\u00fczeyimiz olan \u03b1 = 0,05&#8217;ten d\u00fc\u015f\u00fck olmad\u0131\u011f\u0131 i\u00e7in s\u0131f\u0131r hipotezini reddedemiyoruz. Bu iki pop\u00fclasyon aras\u0131ndaki kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n farkl\u0131 oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z yok.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 3: E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi i\u00e7in serbestlik dereceleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Belirli bir antrenman program\u0131n\u0131n kolej basketbol oyuncular\u0131n\u0131n maksimum dikey s\u0131\u00e7ramas\u0131n\u0131 (in\u00e7 cinsinden) art\u0131rma kapasitesine sahip olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu test etmek i\u00e7in, 20 \u00fcniversite basketbol oyuncusundan olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit rastgele bir \u00f6rneklemi<\/a> i\u015fe alabilir ve onlar\u0131n maksimum dikey s\u0131\u00e7ramalar\u0131n\u0131n her birini \u00f6l\u00e7ebiliriz. Daha sonra her oyuncunun bir ay boyunca antrenman program\u0131n\u0131 kullanmas\u0131n\u0131 sa\u011flayabiliriz ve ay sonunda maksimum dikey s\u0131\u00e7ramalar\u0131n\u0131 tekrar \u00f6l\u00e7ebiliriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7956 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/jumelet1.png\" alt=\"\u00d6rnek E\u015fle\u015ftirilmi\u015f T Testi Veri K\u00fcmesi\" width=\"348\" height=\"443\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Antrenman program\u0131n\u0131n ger\u00e7ekten maksimum dikey s\u0131\u00e7rama \u00fczerinde etkisinin olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in e\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi ger\u00e7ekle\u015ftirece\u011fiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6ncelikle farklar i\u00e7in a\u015fa\u011f\u0131daki \u00f6zet verileri hesaplayaca\u011f\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x<\/span> <sub>diff<\/sub> : farklar\u0131n \u00f6rnek ortalamas\u0131 = -0,95<\/span><\/li>\n<li> <span style=\"color: #000000;\">s: farklar\u0131n \u00f6rnek standart sapmas\u0131 = 1,317<\/span><\/li>\n<li> <span style=\"color: #000000;\">n: \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc (yani \u00e7ift say\u0131s\u0131) = 20<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki varsay\u0131mlarla e\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">H <sub>0<\/sub> : \u03bc <sub>1<\/sub> = \u03bc <sub>2<\/sub> (iki pop\u00fclasyon ortalamas\u0131 e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\">H <sub>A<\/sub> : \u03bc <sub>1<\/sub> \u2260 \u03bc <sub>2<\/sub> (iki pop\u00fclasyon ortalamas\u0131 e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha sonra test istatisti\u011fini hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">t = <span style=\"text-decoration: overline;\">x<\/span> <sub>fark<\/sub> \/ (s <sub>fark<\/sub> \/\u221an) = -0,95 \/ (1,317\/\u221a20) = -3,226<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra <strong>serbestlik derecelerini hesaplayaca\u011f\u0131z<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">sd = n \u2013 1 = 20 \u2013 1 = 19<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P De\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re T puan\u0131na<\/a> g\u00f6re, t = -3,226 ve serbestlik derecesi = n-1 = 20-1 = 19 ile ili\u015fkili p de\u011feri <strong>0,00445&#8217;tir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri bizim anlaml\u0131l\u0131k seviyemiz olan \u03b1 = 0,05&#8217;in alt\u0131nda oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Oyuncular\u0131n ortalama maksimum dikey s\u0131\u00e7ramas\u0131n\u0131n antrenman program\u0131na kat\u0131lmadan \u00f6nce ve sonra farkl\u0131 oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z var.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Sa\u011flad\u0131\u011f\u0131n\u0131z verilere g\u00f6re t testlerini otomatik olarak ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki hesap makineleri kullan\u0131labilir:<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/tr\/ornek-bir-t-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">Bir t-testi hesap makinesi \u00f6rne\u011fi<\/a><br \/> <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><br \/> <a href=\"https:\/\/statorials.org\/tr\/eslestirilmis-ornekler-t-testi-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">E\u015fle\u015ftirilmi\u015f \u00d6rnekler t-Testi Hesaplay\u0131c\u0131<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde yayg\u0131n olarak kullan\u0131lan \u00fc\u00e7 t testi vard\u0131r: Tek \u00f6rnek t testi : Pop\u00fclasyon ortalamas\u0131n\u0131 belirli bir de\u011ferle kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r. \u0130ki \u00f6rnekli t testi : iki pop\u00fclasyon ortalamas\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r. E\u015fle\u015ftirilmi\u015f \u00f6rnekler t-testi : Bir \u00f6rnekteki her g\u00f6zlem di\u011fer \u00f6rnekteki bir g\u00f6zlemle ili\u015fkilendirilebildi\u011finde iki pop\u00fclasyonun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131l\u0131r. Her t-testini \u00e7al\u0131\u015ft\u0131r\u0131rken bir [&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-3771","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>Herhangi Bir T Testi \u0130\u00e7in Serbestlik Derecesi Nas\u0131l Hesaplan\u0131r - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde istatistikteki herhangi bir t testi i\u00e7in serbestlik derecesinin nas\u0131l hesaplanaca\u011f\u0131 \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/t-testi-icin-serbestlik-derecelerini-hesaplayin\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Herhangi Bir T Testi \u0130\u00e7in Serbestlik Derecesi Nas\u0131l Hesaplan\u0131r - 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