{"id":776,"date":"2023-07-28T19:28:17","date_gmt":"2023-07-28T19:28:17","guid":{"rendered":"https:\/\/statorials.org\/tr\/anova-elle-tekrarlanan-olcumler\/"},"modified":"2023-07-28T19:28:17","modified_gmt":"2023-07-28T19:28:17","slug":"anova-elle-tekrarlanan-olcumler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/anova-elle-tekrarlanan-olcumler\/","title":{"rendered":"Tekrarlanan \u00f6l\u00e7\u00fcmlerin manuel olarak ger\u00e7ekle\u015ftirilmesi anova"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/anova-tekrarlanan-olcumler\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA,<\/strong><\/a> her grupta ayn\u0131 deneklerin yer ald\u0131\u011f\u0131 \u00fc\u00e7 veya daha fazla grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde, tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcm ANOVA&#8217;s\u0131n\u0131n manuel olarak nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA&#8217;n\u0131n elle yap\u0131lmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ara\u015ft\u0131rmac\u0131lar \u00fc\u00e7 farkl\u0131 ilac\u0131n farkl\u0131 reaksiyon s\u00fcrelerine neden olup olmad\u0131\u011f\u0131n\u0131 bilmek istiyorlar. Bunu test etmek i\u00e7in be\u015f hastan\u0131n her ilaca tepki s\u00fcresini (saniye cinsinden) \u00f6l\u00e7\u00fcyorlar. Sonu\u00e7lar a\u015fa\u011f\u0131da g\u00f6sterilmektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8449 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/repanovahand1.png\" alt=\"\" width=\"315\" height=\"145\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Her hasta \u00fc\u00e7 ilac\u0131n her birinde \u00f6l\u00e7\u00fcld\u00fc\u011f\u00fcnden, ortalama reaksiyon s\u00fcresinin ila\u00e7lar aras\u0131nda farkl\u0131l\u0131k g\u00f6sterip g\u00f6stermedi\u011fini belirlemek i\u00e7in tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA&#8217;s\u0131n\u0131 kullanaca\u011f\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tekrarlanan \u00f6l\u00e7\u00fcmlerin ANOVA&#8217;s\u0131n\u0131 manuel olarak ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 izleyin:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: SST&#8217;yi hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130lk olarak, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak bulunabilecek toplam kareler toplam\u0131n\u0131 (SST) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = s <sup>2<\/sup> <sub>toplam<\/sub> (n <sub>toplam<\/sub> -1)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>s <sup>2<\/sup> <sub>toplam<\/sub><\/strong> : veri k\u00fcmesinin varyans\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n <sub>toplam<\/sub><\/strong> : veri k\u00fcmesindeki toplam g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte SST&#8217;yi \u015fu \u015fekilde hesapl\u0131yoruz: (64,2667)(15-1) = <strong>899,7<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: SSB&#8217;yi hesaplay\u0131n<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak bulunabilecek karelerin toplam\u0131n\u0131 (SSB) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSB = \u03a3n <sub>j<\/sub> ( <span style=\"text-decoration: overline;\">x<\/span> <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> <sub>toplam<\/sub> ) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n <sub>j<\/sub><\/strong> : <sup>j&#8217;inci<\/sup> gruptaki toplam g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> <sub>j<\/sub><\/strong> : <sup>j&#8217;inci<\/sup> grubun ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> <sub>toplam<\/sub><\/strong> : t\u00fcm verilerin ortalamas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte SSB&#8217;yi \u015fu \u015fekilde hesapl\u0131yoruz: (5)(26,4-22,533) <sup>2<\/sup> +(5)(25,6-22,533) <sup>2<\/sup> + (5)(15,6-22,533) <sup>2<\/sup> = <strong>362,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: SSS&#8217;yi hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak bulunabilecek konu kareler toplam\u0131n\u0131 (SSS) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSS =(\u03a3r <sup>2<\/sup> <sub>k<\/sub> \/c) \u2013 (N <sup>2<\/sup> \/rc)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : \u201ctoplam\u201d anlam\u0131na gelen Yunanca bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>r <sup>2<\/sup><\/strong> <sub>k<\/sub> : <sup>k&#8217;inci<\/sup> hastan\u0131n kare toplam\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> t\u00fcm verilerin genel toplam\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>r:<\/strong> toplam hasta say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>c:<\/strong> toplam grup say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte SSS&#8217;yi \u015fu \u015fekilde hesapl\u0131yoruz: ((74 <sup>2<\/sup> + 42 <sup>2<\/sup> + 62 <sup>2<\/sup> + 92 <sup>2<\/sup> + 68 <sup>2<\/sup> )\/3) \u2013 (338 <sup>2<\/sup> \/(5)(3)) = <strong>441,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: SES&#8217;i hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak bulunabilecek karesel hatan\u0131n (SSE) toplam\u0131n\u0131 hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSE = SST \u2013 SSB \u2013 SSS<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte SES&#8217;i \u015fu \u015fekilde hesapl\u0131yoruz: 899,7 \u2013 362,1 \u2013 441,1 = <strong>96,5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA tablosunu doldurun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131k SSB, SSS ve SSE&#8217;ye sahip oldu\u011fumuza g\u00f6re tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA tablosunu doldurabiliriz:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Kaynak<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Kareler toplam\u0131 (SS)<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>df<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Ortalama kareler (MS)<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>F<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Aras\u0131nda<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">362.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">181.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15.006<\/span><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Ders<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">441.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">4<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">110.3<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Hata<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">96.5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12.1<\/span><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Tablodaki farkl\u0131 say\u0131lar\u0131 \u015fu \u015fekilde hesaplad\u0131k:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>df aras\u0131nda:<\/strong> #gruplar \u2013 1 = 3 \u2013 1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>df konusu:<\/strong> #kat\u0131l\u0131mc\u0131lar \u2013 1 = 5 \u2013 1 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Hata df:<\/strong> * df konusu = 2*4 = 8 aras\u0131nda df<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS girer:<\/strong> SSB \/ df girer = 362,1 \/ 2 = 181,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS konusu:<\/strong> SSS konusu \/ df = 441,1 \/ 4 = 110,3<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS hatas\u0131:<\/strong> SSE hatas\u0131 \/ df = 96,5 \/ 8 = 12,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F:<\/strong> MS girer \/ MS hatas\u0131 = 181,1 \/ 12,1 = 15,006<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 6: Sonu\u00e7lar\u0131 yorumlay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcmler i\u00e7in ANOVA&#8217;n\u0131n F testi istatisti\u011fi <strong>15,006&#8217;d\u0131r<\/strong> .<\/span> Bunun istatistiksel olarak anlaml\u0131 bir sonu\u00e7 olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in bunu <a href=\"https:\/\/statorials.org\/tr\/f-dagitim-tablosu\/\" target=\"_blank\" rel=\"noopener noreferrer\">F da\u011f\u0131l\u0131m tablosunda<\/a> bulunan kritik F de\u011feriyle <span style=\"color: #000000;\">a\u015fa\u011f\u0131daki de\u011ferlerle<\/span> <span style=\"color: #000000;\">kar\u015f\u0131la\u015ft\u0131rmam\u0131z gerekir<\/span> :<\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u03b1 (anlaml\u0131l\u0131k d\u00fczeyi) = 0,05<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF1 (pay\u0131n serbestlik derecesi) = df = 2 aras\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF2 (paydan\u0131n serbestlik derecesi) = hata df = 8<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">F&#8217;nin kritik de\u011ferinin <strong>4,459<\/strong> oldu\u011funu bulduk.<\/span><\/p>\n<p> <span style=\"color: #000000;\">ANOVA tablosundaki F testi istatisti\u011fi, F da\u011f\u0131l\u0131m tablosundaki kritik F de\u011ferinden b\u00fcy\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Bu, ila\u00e7lar\u0131n ortalama yan\u0131t s\u00fcreleri aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark oldu\u011funu s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z oldu\u011fu anlam\u0131na geliyor.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA, her grupta ayn\u0131 deneklerin yer ald\u0131\u011f\u0131 \u00fc\u00e7 veya daha fazla grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r. Bu e\u011fitimde, tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcm ANOVA&#8217;s\u0131n\u0131n manuel olarak nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r. \u00d6rnek: Tek y\u00f6nl\u00fc tekrarlanan \u00f6l\u00e7\u00fcmler ANOVA&#8217;n\u0131n elle yap\u0131lmas\u0131 Ara\u015ft\u0131rmac\u0131lar \u00fc\u00e7 farkl\u0131 ilac\u0131n farkl\u0131 reaksiyon s\u00fcrelerine neden olup [&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-776","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>Tekrarlanan \u00d6l\u00e7\u00fcmlerin Manuel Olarak Ger\u00e7ekle\u015ftirilmesi ANOVA \u2013 Statorials<\/title>\n<meta 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