{"id":1241,"date":"2023-07-27T04:19:56","date_gmt":"2023-07-27T04:19:56","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-bonferroni-duzeltmesi\/"},"modified":"2023-07-27T04:19:56","modified_gmt":"2023-07-27T04:19:56","slug":"rde-bonferroni-duzeltmesi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-bonferroni-duzeltmesi\/","title":{"rendered":"R'de bonferroni d\u00fczeltmesi nas\u0131l yap\u0131l\u0131r"},"content":{"rendered":"

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\u00dc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in tek y\u00f6nl\u00fc ANOVA<\/a> kullan\u0131l\u0131r.<\/span><\/p>\n

ANOVA tablosunun genel p de\u011feri belirli bir anlaml\u0131l\u0131k d\u00fczeyinin alt\u0131ndaysa, grup ortalamalar\u0131ndan en az birinin di\u011ferlerinden farkl\u0131 oldu\u011funu s\u00f6ylemek i\u00e7in yeterli kan\u0131t\u0131m\u0131z var demektir.<\/span><\/p>\n

Ancak bu bize hangi<\/em> gruplar\u0131n birbirinden farkl\u0131 oldu\u011funu s\u00f6ylemez. Bu bize basit\u00e7e t\u00fcm grup ortalamalar\u0131n\u0131n e\u015fit olmad\u0131\u011f\u0131n\u0131 s\u00f6yler.<\/span><\/p>\n

Hangi gruplar\u0131n birbirinden farkl\u0131 oldu\u011funu tam olarak bilmek i\u00e7in,<\/span> aile baz\u0131nda hata oran\u0131n\u0131<\/a> kontrol ederken her grup aras\u0131nda ikili t-testleri yapmam\u0131z gerekir.<\/span><\/p>\n

Bunu ba\u015farman\u0131n en yayg\u0131n yollar\u0131ndan biri, ikili t testlerinin her biri i\u00e7in p de\u011ferlerini hesaplarken Bonferroni d\u00fczeltmesini<\/strong> kullanmakt\u0131r.<\/span><\/p>\n

Bu e\u011fitimde R’de Bonferroni d\u00fczeltmesinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n

\u00d6rnek: R’de Bonferroni d\u00fczeltmesi<\/strong><\/span><\/h3>\n

Bir \u00f6\u011fretmenin \u00fc\u00e7 farkl\u0131 \u00e7al\u0131\u015fma tekni\u011finin \u00f6\u011frenciler aras\u0131nda farkl\u0131 test puanlar\u0131na yol a\u00e7\u0131p a\u00e7mad\u0131\u011f\u0131n\u0131 bilmek istedi\u011fini varsayal\u0131m.<\/span><\/p>\n

Bunu test etmek i\u00e7in her \u00e7al\u0131\u015fma tekni\u011fini kullanmak \u00fczere 10 \u00f6\u011frenciyi rastgele g\u00f6revlendiriyor.<\/span> Bir hafta kendilerine verilen \u00e7al\u0131\u015fma tekni\u011fini kulland\u0131ktan sonra her \u00f6\u011frenci ayn\u0131 s\u0131nava girer.<\/span><\/p>\n

Tek y\u00f6nl\u00fc bir ANOVA’y\u0131 s\u0131\u011fd\u0131rmak i\u00e7in R’de a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanabiliriz ve her grubun s\u0131nav sonu\u00e7lar\u0131 aras\u0131ndaki ikili farklar\u0131 hesaplamak i\u00e7in Bonferroni d\u00fczeltmesini kullanabiliriz.<\/span><\/p>\n

Ad\u0131m 1: Veri k\u00fcmesini olu\u015fturun.<\/span><\/strong><\/p>\n

A\u015fa\u011f\u0131daki kod, 30 \u00f6\u011frencinin tamam\u0131n\u0131n s\u0131nav sonu\u00e7lar\u0131n\u0131 i\u00e7eren bir veri k\u00fcmesinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n

 #create data frame<\/span>\ndata <- data.frame(technique = rep<\/span> (c(\"tech1\", \"tech2\", \"tech3\"), each<\/span> = 10<\/span> ),\n                   score = c(76, 77, 77, 81, 82, 82, 83, 84, 85, 89,\n                             81, 82, 83, 83, 83, 84, 87, 90, 92, 93,\n                             77, 78, 79, 88, 89, 90, 91, 95, 95, 98))\n\n#view first six rows of data frame<\/span>\nhead(data)\n\n  technical score\n1 tech1 76\n2 tech1 77\n3 tech1 77\n4 tech1 81\n5 tech1 82\n6 tech1 82\n<\/strong><\/pre>\n
 Ad\u0131m 2: Her grubun s\u0131nav sonu\u00e7lar\u0131n\u0131 g\u00f6r\u00fcnt\u00fcleyin.<\/span><\/strong><\/p>\n
 A\u015fa\u011f\u0131daki kod, her grup i\u00e7in s\u0131nav sonu\u00e7lar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek amac\u0131yla kutu grafiklerinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n
 boxplot(score ~ technique,\n        data = data,\n        main = \"Exam Scores by Studying Technique\",\n        xlab = \"Studying Technique\",\n        ylab = \"Exam Scores\",\n        col = \"steelblue\",\n        border = \"black\")\n<\/strong><\/pre>\n
\"R'de<\/p>\n
 Ad\u0131m 3: Tek y\u00f6nl\u00fc ANOVA ger\u00e7ekle\u015ftirin.<\/span><\/strong><\/p>\n
 A\u015fa\u011f\u0131daki kod, her gruptaki ortalama s\u0131nav puanlar\u0131 aras\u0131ndaki farklar\u0131 test etmek i\u00e7in tek y\u00f6nl\u00fc ANOVA’n\u0131n nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir:<\/span><\/p>\n
 #fit the one-way ANOVA model<\/span>\nmodel <- aov(score ~ technique, data = data)\n\n#view model output\n<\/span>summary(model)\n\n            Df Sum Sq Mean Sq F value Pr(>F)  \ntechnical 2 211.5 105.73 3.415 0.0476 *\nResiduals 27 836.0 30.96                 \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/strong><\/pre>\n
 Genel p de\u011feri ( 0,0476<\/strong> ) 0,05’ten k\u00fc\u00e7\u00fck oldu\u011fundan bu durum her grubun ayn\u0131 ortalama s\u0131nav puan\u0131na sahip olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n
 Daha sonra, her grubun s\u0131nav sonu\u00e7lar\u0131 aras\u0131ndaki ikili farklar\u0131 hesaplamak i\u00e7in p de\u011ferleri i\u00e7in Bonferroni d\u00fczeltmesini kullanarak ikili t testleri ger\u00e7ekle\u015ftirece\u011fiz.<\/span><\/p>\n
 Ad\u0131m 4: \u0130kili t-testlerini ger\u00e7ekle\u015ftirin.<\/strong><\/span><\/p>\n
 R’de Bonferroni d\u00fczeltmesi ile ikili t testleri ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki s\u00f6zdizimini kullanan \u00e7ift y\u00f6nl\u00fc.t.test()<\/a> i\u015flevini kullanabiliriz:<\/span><\/p>\n
 pairwise.t.test(x, g, p.adjust.method=\u201dbonferroni\u201d)<\/strong><\/span><\/p>\n
 Alt\u0131n:<\/span><\/p>\n