{"id":1483,"date":"2023-07-26T05:23:04","date_gmt":"2023-07-26T05:23:04","guid":{"rendered":"https:\/\/statorials.org\/tr\/bartlett-testi\/"},"modified":"2023-07-26T05:23:04","modified_gmt":"2023-07-26T05:23:04","slug":"bartlett-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/bartlett-testi\/","title":{"rendered":"Bartlett&#39;in varyanslar\u0131n homojenli\u011fi testi (tan\u0131m ve \u00f6rnek)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Bartlett testi,<\/strong> birden fazla grup aras\u0131ndaki varyanslar\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan istatistiksel bir testtir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir\u00e7ok istatistiksel test ( <a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-anova\/\" target=\"_blank\" rel=\"noopener\">tek y\u00f6nl\u00fc ANOVA<\/a> gibi), \u00f6rnekler aras\u0131ndaki varyanslar\u0131n e\u015fit oldu\u011funu varsayar. Bartlett testi bu hipotezi do\u011frulamak i\u00e7in kullan\u0131labilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki ad\u0131mlarda Bartlett testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> Bu testi, g\u00f6zlemlenen korelasyon matrisini birim matrisle kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131lan <a href=\"https:\/\/statorials.org\/tr\/bartletts-kureselit-testi\/\" target=\"_blank\" rel=\"noopener\">Bartlett k\u00fcresellik testiyle<\/a> kar\u0131\u015ft\u0131rmay\u0131n.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bartlett Testini Ger\u00e7ekle\u015ftirme Ad\u0131mlar\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bartlett testi a\u015fa\u011f\u0131daki bo\u015f ve alternatif <a href=\"https:\/\/statorials.org\/tr\/hipotez-testi-1\/\" target=\"_blank\" rel=\"noopener\">hipotezleri<\/a> kullan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> Her grup aras\u0131ndaki varyans e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> En az bir grubun varyans\u0131 di\u011ferlerine e\u015fit de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fi \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">B = (nk)lns <sup>2<\/sup> \u2013 \u03a3(n <sub>j<\/sub> -1)lns <sub>j<\/sub> <sup>2<\/sup> \/ c<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">n: t\u00fcm gruplardaki toplam g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">k: Toplam grup say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">ln: Bu \u201cdo\u011fal log\u201d anlam\u0131na gelir<\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sup>2<\/sup> : Birle\u015ftirilmi\u015f varyans<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>j<\/sub> : j grubundaki g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">s <sub>j<\/sub> <sup>2<\/sup> : j grubunun varyans\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ve \u015fu \u015fekilde <em>hesaplan\u0131r<\/em> :<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">c = 1 + (1\/3(k-1))*(\u03a3(1\/(n <sub>j<\/sub> -1)) \u2013 (1\/(nk))<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu test istatisti\u011fi k-1 serbestlik derecesine sahip bir Ki-kare da\u011f\u0131l\u0131m\u0131n\u0131 takip eder. Yani B~ <sup>X2<\/sup> (k-1).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Test istatisti\u011fine kar\u015f\u0131l\u0131k gelen <a href=\"https:\/\/statorials.org\/tr\/p-degerleri-istatistiksel-anlamlilik\/\" target=\"_blank\" rel=\"noopener\">p de\u011feri<\/a> belirli bir anlaml\u0131l\u0131k d\u00fczeyinin alt\u0131ndaysa (\u03b1 = 0,05 gibi), o zaman s\u0131f\u0131r hipotezini reddedebilir ve t\u00fcm gruplar\u0131n ayn\u0131 varyansa sahip olmad\u0131\u011f\u0131 sonucuna varabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Bartlett testi<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir profes\u00f6r\u00fcn, \u00fc\u00e7 farkl\u0131 \u00e7al\u0131\u015fma tekni\u011finin s\u0131navlarda farkl\u0131 ortalama notlara yol a\u00e7\u0131p a\u00e7mad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir hafta boyunca her tekni\u011fi kullanmalar\u0131 i\u00e7in rastgele 10 \u00f6\u011frenciye g\u00f6rev veriyor ve ard\u0131ndan her \u00f6\u011frenciye e\u015fit zorlukta bir s\u0131nav veriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">30 \u00f6\u011frencinin s\u0131nav sonu\u00e7lar\u0131 a\u015fa\u011f\u0131da sunulmu\u015ftur:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8258\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aller-simple2.png\" alt=\"Bartlett testi i\u00e7in \u00f6rnek veri k\u00fcmesi\" width=\"245\" height=\"254\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Profes\u00f6r, \u00fc\u00e7 tekni\u011fin s\u0131navda farkl\u0131 ortalama puanlara yol a\u00e7\u0131p a\u00e7mad\u0131\u011f\u0131n\u0131 g\u00f6rmek i\u00e7in tek y\u00f6nl\u00fc bir ANOVA uygulamak istiyor, ancak \u00f6nce \u00fc\u00e7 grubun e\u015fit varyansa sahip oldu\u011funu do\u011frulamak i\u00e7in Bartlett testini yapmas\u0131 gerekiyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bartlett testini elle yapmak s\u0131k\u0131c\u0131 oldu\u011fundan <a href=\"https:\/\/statorials.org\/tr\/bartletts-testi-hesaplayici\/\" target=\"_blank\" rel=\"noopener\">Bartlett test hesaplay\u0131c\u0131s\u0131na<\/a> a\u015fa\u011f\u0131daki veri de\u011ferlerini girece\u011fiz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14687 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/bartlett1.png\" alt=\"Bartlett'in e\u015fit varyanslar i\u00e7in testi\" width=\"399\" height=\"560\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Test a\u015fa\u011f\u0131daki sonu\u00e7lar\u0131 d\u00f6nd\u00fcr\u00fcr:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Test istatisti\u011fi <em>B<\/em> : <strong>3.30244<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">P de\u011feri: <strong>0,19182<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">P de\u011feri 0,05&#8217;ten az olmad\u0131\u011f\u0131ndan profes\u00f6r s\u0131f\u0131r hipotezini reddetme konusunda ba\u015far\u0131s\u0131z olacakt\u0131r. Ba\u015fka bir deyi\u015fle, \u00fc\u00e7 grubun farkl\u0131 bo\u015fluklara sahip oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131 yok.<\/span><\/p>\n<p> <span style=\"color: #000000;\">B\u00f6ylece tek y\u00f6nl\u00fc ANOVA&#8217;y\u0131 ger\u00e7ekle\u015ftirmeye devam edebilir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rde-bartletts-testi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de Bartlett Testi Nas\u0131l Yap\u0131l\u0131r (Ad\u0131m Ad\u0131m)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/bartletts-piton-testi\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Bartlett Testi Nas\u0131l Yap\u0131l\u0131r (Ad\u0131m Ad\u0131m)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bartlett testi, birden fazla grup aras\u0131ndaki varyanslar\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan istatistiksel bir testtir. Bir\u00e7ok istatistiksel test ( tek y\u00f6nl\u00fc ANOVA gibi), \u00f6rnekler aras\u0131ndaki varyanslar\u0131n e\u015fit oldu\u011funu varsayar. Bartlett testi bu hipotezi do\u011frulamak i\u00e7in kullan\u0131labilir. A\u015fa\u011f\u0131daki ad\u0131mlarda Bartlett testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r. Not: Bu testi, g\u00f6zlemlenen korelasyon matrisini birim matrisle kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131lan [&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-1483","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>Varyanslar\u0131n homojenli\u011fi i\u00e7in Bartlett testi (tan\u0131m ve \u00f6rnek)<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, resmi bir tan\u0131m ve \u00f6rnek de dahil olmak \u00fczere, varyanslar\u0131n homojenli\u011fi i\u00e7in Bartlett testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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