{"id":2503,"date":"2023-07-22T00:00:38","date_gmt":"2023-07-22T00:00:38","guid":{"rendered":"https:\/\/statorials.org\/tr\/gruplar-arasindaki-varyasyonun-novasinda\/"},"modified":"2023-07-22T00:00:38","modified_gmt":"2023-07-22T00:00:38","slug":"gruplar-arasindaki-varyasyonun-novasinda","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/gruplar-arasindaki-varyasyonun-novasinda\/","title":{"rendered":"Anova&#39;da grup i\u00e7i veya gruplar aras\u0131 varyasyon"},"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> \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tek y\u00f6nl\u00fc ANOVA 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<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> T\u00fcm grup ortalamalar\u0131 e\u015fittir.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> En az bir grubun ortalamas\u0131 di\u011ferlerinden farkl\u0131.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Tek y\u00f6nl\u00fc ANOVA&#8217;y\u0131 her ger\u00e7ekle\u015ftirdi\u011finizde a\u015fa\u011f\u0131daki gibi bir \u00f6zet tablo elde edersiniz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22312 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variation1.png\" alt=\"\" width=\"572\" height=\"138\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">ANOVA&#8217;n\u0131n \u00f6l\u00e7t\u00fc\u011f\u00fc iki farkl\u0131 varyasyon kayna\u011f\u0131n\u0131n oldu\u011funu g\u00f6rebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Gruplar aras\u0131 varyasyon<\/strong> : Her grubun ortalamas\u0131 ile genel ortalama aras\u0131ndaki toplam varyasyon.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup i\u00e7i varyasyon<\/strong> : her gruptaki bireysel de\u011ferlerin toplam de\u011fi\u015fimi ve grup ortalamalar\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Gruplar aras\u0131ndaki varyasyon, grup i\u00e7indeki varyasyona g\u00f6re y\u00fcksekse, ANOVA&#8217;n\u0131n F istatisti\u011fi daha y\u00fcksek olacak ve kar\u015f\u0131l\u0131k gelen p-de\u011feri daha d\u00fc\u015f\u00fck olacak, bu da s\u0131f\u0131r hipotezinin reddedilme olas\u0131l\u0131\u011f\u0131n\u0131 art\u0131racakt\u0131r. grup ortalamalar\u0131 e\u015fittir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek, pratikte tek y\u00f6nl\u00fc ANOVA i\u00e7in gruplar aras\u0131 varyasyonun ve grup i\u00e7i varyasyonun nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: ANOVA&#8217;da grup i\u00e7i ve gruplar aras\u0131 varyasyonun hesaplanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00dc\u00e7 farkl\u0131 \u00e7al\u0131\u015fma y\u00f6nteminin farkl\u0131 ortalama s\u0131nav puanlar\u0131na yol a\u00e7\u0131p a\u00e7mad\u0131\u011f\u0131n\u0131 belirlemek istedi\u011fimizi varsayal\u0131m. Bunu test etmek i\u00e7in 30 \u00f6\u011frenciyi i\u015fe al\u0131yoruz ve her birine farkl\u0131 bir \u00e7al\u0131\u015fma y\u00f6ntemi kullanmalar\u0131 i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/rastgele-secim-ve-rastgele-atama\/\" target=\"_blank\" rel=\"noopener\">rastgele 10 \u00f6\u011frenci atad\u0131k<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her gruptaki \u00f6\u011frencilerin s\u0131nav sonu\u00e7lar\u0131 a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22314 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variation2.png\" alt=\"\" width=\"213\" height=\"261\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Gruplar aras\u0131ndaki de\u011fi\u015fimi<\/strong> hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Gruplar aras\u0131 de\u011fi\u015fim<\/strong> = \u03a3n <sub>j<\/sub> (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 <sub>j<\/sub><\/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 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;\">Bu de\u011feri hesaplamak i\u00e7in \u00f6ncelikle her grubun ortalamas\u0131n\u0131 ve genel ortalamay\u0131 hesaplayaca\u011f\u0131z:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22315 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variation3.png\" alt=\"\" width=\"313\" height=\"313\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra gruplar aras\u0131 de\u011fi\u015fimi \u015fu \u015fekilde hesapl\u0131yoruz: 10(80,5-83,1) <sup>2<\/sup> + 10(82,1-83,1) <sup>2<\/sup> + 10(86,7-83,1) <sup>2<\/sup> = <strong>207,2<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra <strong>grup i\u00e7i de\u011fi\u015fimi<\/strong> hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup i\u00e7i varyasyon<\/strong> : \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 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 grup i\u00e7indeki varyasyonu \u015fu \u015fekilde hesapl\u0131yoruz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 1:<\/strong> (75-80,5) <sup>2<\/sup> + (77-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (78-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (78-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (79-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (83-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (86-80,5) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-80,5) <sup>2<\/sup> = <strong>136,5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 2:<\/strong> (78-82,1) <sup>2<\/sup> + (78-82,1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (79-82,1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-82.1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (81-82.1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (82-82,1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (83-82.1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (85-82,1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (86-82,1) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (88-82,1) <sup>2<\/sup> = <strong>104,9<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup 3:<\/strong> (82-86,7) <sup>2<\/sup> + (82-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (84-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (86-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (86-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (87-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (89-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (90-86,7) <sup>2<\/sup> + <strong>&nbsp;<\/strong> (94-86,7) <sup>2<\/sup> = <strong>122,1<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Grup i\u00e7i varyasyon:<\/strong> 136,5 + 104,9 + 122,1 = <strong>363,5<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu veri k\u00fcmesini kullanarak tek y\u00f6nl\u00fc ANOVA ger\u00e7ekle\u015ftirmek i\u00e7in istatistiksel yaz\u0131l\u0131m kullan\u0131rsak a\u015fa\u011f\u0131daki ANOVA tablosunu elde ederiz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-22317 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/variation4.png\" alt=\"\" width=\"571\" height=\"131\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Gruplar aras\u0131 ve grup i\u00e7i varyasyon de\u011ferlerinin manuel olarak hesaplad\u0131\u011f\u0131m\u0131z de\u011ferlerle e\u015fle\u015fti\u011fini unutmay\u0131n.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tablodaki genel F istatisti\u011fi, gruplar aras\u0131ndaki varyasyon ile grup i\u00e7indeki varyasyon aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">F istatisti\u011fi ne kadar b\u00fcy\u00fck olursa, gruplar aras\u0131ndaki varyasyonun, gruplar i\u00e7indeki varyasyona g\u00f6re o kadar b\u00fcy\u00fck oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani, F istatisti\u011fi ne kadar b\u00fcy\u00fckse, grup ortalamalar\u0131 aras\u0131nda bir fark oldu\u011fu o kadar a\u00e7\u0131kt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte 7,6952 F istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011ferinin <strong>0,0023<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu de\u011fer \u03b1 = 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fu i\u00e7in ANOVA&#8217;n\u0131n s\u0131f\u0131r hipotezini reddediyoruz ve \u00fc\u00e7 \u00e7al\u0131\u015fma tekni\u011finin s\u0131navda ayn\u0131 puana yol a\u00e7mad\u0131\u011f\u0131 sonucuna var\u0131yoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler ANOVA modelleri hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/tek-yonlu-anova\/\" target=\"_blank\" rel=\"noopener\">Tek Y\u00f6nl\u00fc ANOVA&#8217;ya Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/anova-f-degeri-p-degeri\/\" target=\"_blank\" rel=\"noopener\">ANOVA&#8217;da F de\u011feri ve P de\u011feri nas\u0131l yorumlan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/anova-sonuclari-nasil-raporlanir\/\" target=\"_blank\" rel=\"noopener\">Tam K\u0131lavuz: ANOVA Sonu\u00e7lar\u0131 Nas\u0131l Raporlan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tek y\u00f6nl\u00fc ANOVA, \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131n\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r. Tek y\u00f6nl\u00fc ANOVA a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezleri kullan\u0131r: H 0 : T\u00fcm grup ortalamalar\u0131 e\u015fittir. H A : En az bir grubun ortalamas\u0131 di\u011ferlerinden farkl\u0131. Tek y\u00f6nl\u00fc ANOVA&#8217;y\u0131 her ger\u00e7ekle\u015ftirdi\u011finizde a\u015fa\u011f\u0131daki gibi bir \u00f6zet tablo elde edersiniz: ANOVA&#8217;n\u0131n [&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-2503","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>ANOVA&#039;da grup i\u00e7i veya gruplar aras\u0131 varyasyon - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, tan\u0131mlar ve bir \u00f6rnek de dahil olmak \u00fczere ANOVA modellerindeki grup i\u00e7i ve gruplar aras\u0131 farkl\u0131l\u0131klar 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\/gruplar-arasindaki-varyasyonun-novasinda\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ANOVA&#039;da grup i\u00e7i veya gruplar aras\u0131 varyasyon - 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