{"id":773,"date":"2023-07-28T19:45:12","date_gmt":"2023-07-28T19:45:12","guid":{"rendered":"https:\/\/statorials.org\/tr\/tek-yonlu-anova-a-la-main\/"},"modified":"2023-07-28T19:45:12","modified_gmt":"2023-07-28T19:45:12","slug":"tek-yonlu-anova-a-la-main","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/tek-yonlu-anova-a-la-main\/","title":{"rendered":"Tek y\u00f6nl\u00fc anova manuel olarak nas\u0131l ger\u00e7ekle\u015ftirilir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-anova\/\" target=\"_blank\" rel=\"noopener\">Tek y\u00f6nl\u00fc ANOVA<\/a> (&#8220;varyans analizi&#8221;), kar\u015f\u0131l\u0131k gelen pop\u00fclasyonun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde tek y\u00f6nl\u00fc ANOVA&#8217;n\u0131n manuel olarak nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u00d6rnek: Manuel tek y\u00f6nl\u00fc ANOVA<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u00dc\u00e7 farkl\u0131 s\u0131nava haz\u0131rl\u0131k program\u0131n\u0131n belirli bir s\u0131navda farkl\u0131 ortalama puanlara yol a\u00e7\u0131p a\u00e7mad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in 30 \u00f6\u011frenciyi bir \u00e7al\u0131\u015fmaya kat\u0131yoruz ve onlar\u0131 \u00fc\u00e7 gruba ay\u0131r\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her gruptaki \u00f6\u011frenciler, bir s\u0131nava haz\u0131rlanmak i\u00e7in sonraki \u00fc\u00e7 hafta boyunca \u00fc\u00e7 s\u0131nav haz\u0131rl\u0131k program\u0131ndan birini kullanmak \u00fczere rastgele atan\u0131r. \u00dc\u00e7 haftan\u0131n sonunda t\u00fcm \u00f6\u011frenciler ayn\u0131 s\u0131nava girerler.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her gruba ait s\u0131nav sonu\u00e7lar\u0131 a\u015fa\u011f\u0131da g\u00f6sterilmektedir:<\/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\" sizes=\"auto, \" srcset=\"\" alt=\"Tek y\u00f6nl\u00fc ANOVA verilerine \u00f6rnek\" width=\"237\" height=\"246\"><\/p>\n<p> <span style=\"color: #000000;\">Ortalama s\u0131nav puan\u0131n\u0131n \u00fc\u00e7 grup aras\u0131nda farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek amac\u0131yla tek y\u00f6nl\u00fc ANOVA&#8217;y\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: Grup ortalamas\u0131n\u0131 ve genel ortalamay\u0131 hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130lk olarak, \u00fc\u00e7 grubun ortalamas\u0131n\u0131 ve genel ortalamay\u0131 hesaplayaca\u011f\u0131z:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8434 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/anovamain1-1.png\" alt=\"\" width=\"300\" height=\"257\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: SSR&#8217;yi hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak kareler toplam\u0131 regresyonunu (SSR) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">n\u03a3(X <sub>j<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> ..) <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : j grubunun \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\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>X <sub>j<\/sub><\/strong> : j grubunun ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> ..<\/strong> : genel ortalama<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fimizde SSR = 10(83,4-85,8) <sup>2<\/sup> + 10(89,3-85,8) <sup>2<\/sup> + 10(84,7-85,8) <sup>2<\/sup> = <strong>192,2<\/strong> oldu\u011funu hesapl\u0131yoruz.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: SES&#8217;i hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak karesel hatan\u0131n toplam\u0131n\u0131 (SSE) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3(X <sub>ij<\/sub> \u2013 <span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/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>X <sub>ij<\/sub><\/strong> : j grubunun <sup>i&#8217;inci<\/sup> g\u00f6zlemi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">X<\/span> <sub>j<\/sub><\/strong> : j grubunun ortalamas\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fimizde SSE&#8217;yi \u015fu \u015fekilde hesapl\u0131yoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 1:<\/strong> (85-83,4) <sup>2<\/sup> + (86-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (75-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (78-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (98-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (79-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (71-83,4) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (80-83,4) <sup>2<\/sup> = <strong>640,4<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 2:<\/strong> (91-89,3) <sup>2<\/sup> + (92-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (93-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (84-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (95-89,3) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (96-89,3) <sup>2<\/sup> = <strong>208,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 3:<\/strong> (79-84,7) <sup>2<\/sup> + (78-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (92-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (83-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-84,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-84,7) <sup>2<\/sup> = <strong>252,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ESS:<\/strong> 640,4 + 208,1 + 252,1 = <strong>1.100,6<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: SST&#8217;yi hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak toplam kareler toplam\u0131n\u0131 (SST) hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fimizde SST = 192,2 + 1100,6 = <strong>1292,8<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: ANOVA tablosunu doldurun.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131k SSR, SSE ve SST&#8217;ye sahip oldu\u011fumuza g\u00f6re 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;\"> <strong><span style=\"color: #000000;\">Kareler toplam\u0131 (SS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">df<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Ortalama kareler (MS)<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">F<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Tedavi<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">192.2<\/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;\">96.1<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.358<\/span><\/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;\">1100.6<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">40.8<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td> <span style=\"color: #000000;\"><strong>Toplam<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1292.8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">29<\/span><\/td>\n<td><\/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>tedavi sd:<\/strong> k-1 = 3-1 = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>hata df:<\/strong> nk = 30-3 = 27<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>toplam sd:<\/strong> n-1 = 30-1 = 29<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>SEP tedavisi:<\/strong> SST tedavisi \/ df = 192,2 \/ 2 = 96,1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MS hatas\u0131:<\/strong> SSE hatas\u0131 \/ df = 1100,6 \/ 27 = 40,8<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F:<\/strong> MS i\u015fleme \/ MS hatas\u0131 = 96,1 \/ 40,8 = 2,358<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><em><strong>Not:<\/strong> n = toplam g\u00f6zlem say\u0131s\u0131, k = grup say\u0131s\u0131<\/em><\/span><\/p>\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 ANOVA&#8217;n\u0131n F testi istatisti\u011fi <strong>2,358&#8217;dir<\/strong> . 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\">F da\u011f\u0131l\u0131m tablosunda<\/a> bulunan kritik F de\u011feriyle a\u015fa\u011f\u0131daki de\u011ferlerle 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 i\u015flemi = 2<\/span><\/li>\n<li> <span style=\"color: #000000;\">DF2 (paydan\u0131n serbestlik derecesi) = hata df = 27<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">F&#8217;nin kritik de\u011ferinin <strong>3,3541<\/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 k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddedemiyoruz. Bu, \u00fc\u00e7 grubun ortalama s\u0131nav puanlar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark oldu\u011funu s\u00f6yleyecek yeterli kan\u0131ta sahip olmad\u0131\u011f\u0131m\u0131z anlam\u0131na geliyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Bonus Kayna\u011f\u0131:<\/strong> Be\u015f \u00f6rne\u011fe kadar otomatik olarak tek y\u00f6nl\u00fc ANOVA ger\u00e7ekle\u015ftirmek i\u00e7in bu <a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-danova-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">tek y\u00f6nl\u00fc ANOVA hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tek y\u00f6nl\u00fc ANOVA (&#8220;varyans analizi&#8221;), kar\u015f\u0131l\u0131k gelen pop\u00fclasyonun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131 kar\u015f\u0131la\u015ft\u0131r\u0131r. Bu e\u011fitimde tek y\u00f6nl\u00fc ANOVA&#8217;n\u0131n manuel olarak nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r. \u00d6rnek: Manuel tek y\u00f6nl\u00fc ANOVA \u00dc\u00e7 farkl\u0131 s\u0131nava haz\u0131rl\u0131k program\u0131n\u0131n belirli bir s\u0131navda farkl\u0131 ortalama puanlara yol a\u00e7\u0131p [&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-773","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>Elle Tek Y\u00f6nl\u00fc ANOVA Nas\u0131l Yap\u0131l\u0131r?<\/title>\n<meta name=\"description\" content=\"Tek y\u00f6nl\u00fc ANOVA&#039;n\u0131n manuel olarak nas\u0131l 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