{"id":1304,"date":"2023-07-26T22:57:59","date_gmt":"2023-07-26T22:57:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/satterthwaite-yaklasimi\/"},"modified":"2023-07-26T22:57:59","modified_gmt":"2023-07-26T22:57:59","slug":"satterthwaite-yaklasimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/satterthwaite-yaklasimi\/","title":{"rendered":"Satterthwaite yakla\u015f\u0131m\u0131: tan\u0131m ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Satterthwaite yakla\u015f\u0131m\u0131,<\/strong> iki \u00f6rnekli bir t testinde &#8220;etkili serbestlik derecelerini&#8221; bulmak i\u00e7in kullan\u0131lan bir form\u00fcld\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">En s\u0131k, <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener\">\u00f6rneklerin<\/a> al\u0131nd\u0131\u011f\u0131 pop\u00fclasyonlar\u0131n e\u015fit varyanslara sahip oldu\u011funu varsaymadan, iki ba\u011f\u0131ms\u0131z \u00f6rne\u011fin ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131ran <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch t-testinde<\/a> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Satterthwaite yakla\u015f\u0131m\u0131n\u0131n form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">Degrees of freedom:<\/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>\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup> , s <sub>2<\/sub> <sup>2<\/sup> :<\/strong> S\u0131ras\u0131yla birinci ve ikinci \u00f6rneklerin \u00f6rnek varyans\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>n1<\/sub> , <sub>n2<\/sub> :<\/strong> S\u0131ras\u0131yla birinci ve ikinci \u00f6rneklerin \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, etkin serbestlik derecesini hesaplamak i\u00e7in Satterthwaite yakla\u015f\u0131m\u0131n\u0131n nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Satterthwaite yakla\u015f\u0131m\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130ki farkl\u0131 bitki t\u00fcr\u00fcn\u00fcn ortalama boyunun e\u015fit olup olmad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. B\u00f6ylece her t\u00fcrden iki basit rastgele \u00f6rnek toplayaca\u011f\u0131z ve her \u00f6rnekteki bitkilerin y\u00fcksekli\u011fini \u00f6l\u00e7ece\u011fiz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki de\u011ferler her numunenin y\u00fcksekli\u011fini (in\u00e7 cinsinden) g\u00f6sterir:<\/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;\">Ortalamalar, varyanslar ve \u00f6rneklem b\u00fcy\u00fckl\u00fckleri \u015fu \u015fekilde ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x1<\/span> <sub>=<\/sub><\/strong> 19,27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x2<\/span> <sub>=<\/sub><\/strong> 23,69<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> = 20,42<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s <sub>2<\/sub> <sup>2<\/sup><\/strong> = 83,23<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n1<\/strong> <sub><strong>=<\/strong><\/sub> 11<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n2<\/strong> = <sub><strong>13<\/strong><\/sub><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Daha sonra, etkin serbestlik derecelerini bulmak i\u00e7in varyanslar\u0131n ve \u00f6rnek boyutlar\u0131n\u0131n de\u011ferlerini Satterthwaite yakla\u015f\u0131m form\u00fcl\u00fcne ekleyebiliriz:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #000000;\">df = (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)]} \n\ndf = (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<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Etkin serbestlik derecesi <strong>18.137<\/strong> olarak ortaya \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Genellikle bu de\u011feri en yak\u0131n tam say\u0131ya yuvarlar\u0131z, dolay\u0131s\u0131yla Welch t testimizde kullanaca\u011f\u0131m\u0131z serbestlik derecesi <strong>18<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Son olarak, 18 serbestlik derecesi i\u00e7in alfa = 0,05 olan iki kuyruklu 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> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra test istatisti\u011fimizi \u015fu \u015fekilde hesaplar\u0131z:<\/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;\">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.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\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>Uygulamada Satterthwaite yakla\u015f\u0131m\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Uygulamada, Satterthwaite yakla\u015f\u0131m\u0131n\u0131 manuel olarak hesaplaman\u0131z nadiren gerekecektir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine R, Python, Excel, SAS ve Stata gibi yayg\u0131n istatistiksel yaz\u0131l\u0131mlar, sizin i\u00e7in etkin serbestlik derecelerini otomatik olarak hesaplamak \u00fczere Satterthwaite yakla\u015f\u0131m\u0131n\u0131 kullanabilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">Hipotez Testine Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/iki-orneginizi-test-edin\/\" target=\"_blank\" rel=\"noopener\">\u0130ki \u00f6rnekli t testine giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/welchs-t-testi\/\" target=\"_blank\" rel=\"noopener\">Welch t-testine giri\u015f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Satterthwaite yakla\u015f\u0131m\u0131, iki \u00f6rnekli bir t testinde &#8220;etkili serbestlik derecelerini&#8221; bulmak i\u00e7in kullan\u0131lan bir form\u00fcld\u00fcr. En s\u0131k, \u00f6rneklerin al\u0131nd\u0131\u011f\u0131 pop\u00fclasyonlar\u0131n e\u015fit varyanslara sahip oldu\u011funu varsaymadan, iki ba\u011f\u0131ms\u0131z \u00f6rne\u011fin ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131ran Welch t-testinde kullan\u0131l\u0131r. Satterthwaite yakla\u015f\u0131m\u0131n\u0131n form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir: Degrees of freedom: (s 1 2 \/n 1 + s 2 2 \/n 2 ) 2 \/ [&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-1304","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>Satterthwaite yakla\u015f\u0131m\u0131: tan\u0131m ve \u00f6rnek<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, bir form\u00fcl ve \u00f6rnek de dahil olmak \u00fczere Satterthwaite yakla\u015f\u0131m\u0131n\u0131n bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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