{"id":483,"date":"2023-07-29T18:29:23","date_gmt":"2023-07-29T18:29:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/"},"modified":"2023-07-29T18:29:23","modified_gmt":"2023-07-29T18:29:23","slug":"post-hoc-anova-testleri","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/","title":{"rendered":"Anova ile post-hoc testini kullanma k\u0131lavuzu"},"content":{"rendered":"

<\/p>\n

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ANOVA,<\/strong> \u00fc\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 kullan\u0131lan istatistiksel bir testtir.<\/span><\/p>\n

ANOVA’da kullan\u0131lan varsay\u0131mlar a\u015fa\u011f\u0131daki gibidir:<\/span><\/p>\n

S\u0131f\u0131r hipotezi (H 0<\/sub> ): \u00b5 1<\/sub> = \u00b5 2<\/sub> = \u00b5 3<\/sub> = \u2026 = \u00b5 k<\/sub> (ortalamalar her grup i\u00e7in e\u015fittir)<\/span><\/p>\n

Alternatif hipotez: (Ha): Ara\u00e7lardan en az biri di\u011ferlerinden farkl\u0131d\u0131r<\/span><\/p>\n

ANOVA’n\u0131n p de\u011feri anlaml\u0131l\u0131k seviyesinin alt\u0131ndaysa s\u0131f\u0131r hipotezini reddedebilir ve grup ortalamalar\u0131ndan en az birinin di\u011ferlerinden farkl\u0131 oldu\u011funu s\u00f6ylemek i\u00e7in yeterli kan\u0131t\u0131m\u0131z oldu\u011fu sonucuna varabiliriz.<\/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, bir yandan aileyi kontrol ederken bir yandan da birden fazla grubun ortalamalar\u0131 aras\u0131ndaki fark\u0131 ke\u015ffetmemize olanak tan\u0131yan post hoc testi<\/strong> (\u00e7oklu kar\u015f\u0131la\u015ft\u0131rma testi olarak da bilinir) yapmam\u0131z gerekir. . makul hata oran\u0131.<\/span><\/p>\n

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Teknik Not:<\/strong> Yaln\u0131zca ANOVA p de\u011feri istatistiksel olarak anlaml\u0131 oldu\u011funda post hoc testi yapmam\u0131z gerekti\u011fini unutmamak \u00f6nemlidir. P de\u011ferinin istatistiksel olarak anlaml\u0131 olmamas\u0131 t\u00fcm gruplar\u0131n ortalamalar\u0131n\u0131n birbirinden farkl\u0131 olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir. Bu nedenle hangi gruplar\u0131n birbirinden farkl\u0131 oldu\u011funu belirlemek i\u00e7in post hoc test yap\u0131lmas\u0131na gerek yoktur.<\/span><\/p>\n<\/blockquote>\n

Aile hata oran\u0131<\/span><\/strong><\/h2>\n

Daha \u00f6nce de belirtildi\u011fi gibi post hoc testler, birden fazla grubun ortalamalar\u0131 aras\u0131ndaki fark\u0131 test etmemize ve ayr\u0131ca aile ba\u015f\u0131na hata oran\u0131n\u0131<\/strong> kontrol etmemize olanak tan\u0131r.<\/span><\/p>\n

Hipotez testinde her zaman anlaml\u0131l\u0131k seviyemiz (alfa) taraf\u0131ndan tan\u0131mlanan ve bize ger\u00e7ekten do\u011fru olan bir s\u0131f\u0131r hipotezini reddetme olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yleyen bir Tip I hata oran\u0131 vard\u0131r. Yani ger\u00e7ekte durum b\u00f6yle de\u011filken gruplar aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark oldu\u011funu iddia etti\u011fimizde “yanl\u0131\u015f pozitif” elde etme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n

Hipotez testi yapt\u0131\u011f\u0131m\u0131zda Tip I hata oran\u0131 genellikle 0,01, 0,05 veya 0,10 olarak se\u00e7ilen anlaml\u0131l\u0131k d\u00fczeyine e\u015fittir. Ancak birden fazla hipotez testini ayn\u0131 anda \u00e7al\u0131\u015ft\u0131rd\u0131\u011f\u0131m\u0131zda yanl\u0131\u015f pozitif sonu\u00e7 alma olas\u0131l\u0131\u011f\u0131 artar.<\/span><\/p>\n

\u00d6rne\u011fin 20 kenarl\u0131 bir zar\u0131 att\u0131\u011f\u0131m\u0131z\u0131 d\u00fc\u015f\u00fcn\u00fcn. Zar\u0131n \u201c1\u201d gelme olas\u0131l\u0131\u011f\u0131 sadece %5’tir. Ancak iki zar\u0131 ayn\u0131 anda atarsan\u0131z, zarlardan birinin \u201c1\u201d rakam\u0131na gelme olas\u0131l\u0131\u011f\u0131 %9,75’e \u00e7\u0131kar. Ayn\u0131 anda be\u015f zar atarsak olas\u0131l\u0131k %22,6’ya \u00e7\u0131kar.<\/span><\/p>\n

Ne kadar \u00e7ok zar atarsak, zarlardan birinin \u201c1\u201d rakam\u0131na gelme olas\u0131l\u0131\u011f\u0131 o kadar y\u00fcksek olur. Benzer \u015fekilde, 0,05 anlaml\u0131l\u0131k d\u00fczeyini kullanarak birden fazla hipotez testini ayn\u0131 anda \u00e7al\u0131\u015ft\u0131r\u0131rsak, yanl\u0131\u015f pozitif alma olas\u0131l\u0131\u011f\u0131m\u0131z yaln\u0131zca 0,05’in \u00fczerine \u00e7\u0131kar.<\/span><\/p>\n

ANOVA’da \u00e7oklu kar\u015f\u0131la\u015ft\u0131rmalar<\/strong><\/span><\/h2>\n

ANOVA yapt\u0131\u011f\u0131m\u0131zda genellikle \u00fc\u00e7 veya daha fazla grubu kar\u015f\u0131la\u015ft\u0131r\u0131r\u0131z. Dolay\u0131s\u0131yla, grup ortalamalar\u0131 aras\u0131ndaki fark\u0131 ara\u015ft\u0131rmak i\u00e7in bir post hoc testi uygulad\u0131\u011f\u0131m\u0131zda, \u00e7oklu ikili<\/strong> kar\u015f\u0131la\u015ft\u0131rmalar\u0131 ara\u015ft\u0131rmak istiyoruz.<\/span><\/p>\n

\u00d6rne\u011fin, diyelim ki d\u00f6rt grubumuz var: A, B, C ve D. Bu, post hoc testle incelemek istedi\u011fimiz toplam alt\u0131 ikili kar\u015f\u0131la\u015ft\u0131rman\u0131n oldu\u011fu anlam\u0131na gelir:<\/span><\/p>\n

A \u2013 B (A grubu ortalamas\u0131 ile B grubu ortalamas\u0131 aras\u0131ndaki fark)<\/span>
AC<\/span>
DUYURU<\/span>
M.\u00d6.<\/span>
\u00e7izgi roman<\/span>
CD<\/span><\/p>\n

D\u00f6rtten fazla grubumuz varsa yapmak isteyece\u011fimiz ikili kar\u015f\u0131la\u015ft\u0131rmalar\u0131n say\u0131s\u0131 daha da artacakt\u0131r. A\u015fa\u011f\u0131daki tabloda her grup say\u0131s\u0131yla ili\u015fkili ikili kar\u015f\u0131la\u015ft\u0131rmalar\u0131n say\u0131s\u0131 ve aile ba\u015f\u0131na hata oran\u0131 g\u00f6sterilmektedir:<\/span><\/p>\n

Grup say\u0131s\u0131 (ve dolay\u0131s\u0131yla ikili kar\u015f\u0131la\u015ft\u0131rma say\u0131s\u0131) artt\u0131k\u00e7a aile ba\u015f\u0131na hata oran\u0131n\u0131n h\u0131zla artt\u0131\u011f\u0131na dikkat edin. Asl\u0131nda alt\u0131 gruba ula\u015ft\u0131\u011f\u0131m\u0131zda yanl\u0131\u015f pozitif sonu\u00e7 alma \u015fans\u0131m\u0131z asl\u0131nda %50’nin \u00fczerindedir!<\/span><\/p>\n

Bu, aile baz\u0131nda hata oran\u0131m\u0131z\u0131n bu kadar y\u00fcksek oldu\u011funu bilerek bu kadar \u00e7ok ikili kar\u015f\u0131la\u015ft\u0131rma yapmak zorunda kalsayd\u0131k, sonu\u00e7lar\u0131m\u0131z hakk\u0131nda ciddi \u015f\u00fcphelerimiz olaca\u011f\u0131 anlam\u0131na gelir.<\/span><\/p>\n

Neyse ki post-hoc testler, ailelere g\u00f6re hata oran\u0131n\u0131 kontrol ederken gruplar aras\u0131nda birden fazla kar\u015f\u0131la\u015ft\u0131rma yapmam\u0131za olanak tan\u0131yor.<\/span><\/p>\n

\u00d6rnek: Post-hoc testlerle tek y\u00f6nl\u00fc ANOVA<\/strong><\/span><\/h2>\n

A\u015fa\u011f\u0131daki \u00f6rnek, post hoc testlerle tek y\u00f6nl\u00fc ANOVA’n\u0131n<\/a> nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6stermektedir.<\/span><\/p>\n

Not:<\/strong> Bu \u00f6rnekte R programlama dili kullan\u0131lmaktad\u0131r ancak test sonu\u00e7lar\u0131n\u0131 veya \u00f6nemli \u00e7\u0131kar\u0131mlar\u0131 anlamak i\u00e7in R bilmenize gerek yoktur.<\/em><\/span><\/p>\n

\u0130lk olarak, grup ba\u015f\u0131na 20 g\u00f6zlem i\u00e7eren d\u00f6rt grup (A, B, C, D) i\u00e7eren bir veri seti olu\u015fturaca\u011f\u0131z:<\/span><\/p>\n

 #make this example reproducible\nset.seed(1)<\/span>\n\n#load tidyr<\/em> library to convert data from wide to long format<\/span>\nlibrary(tidyr)\n\n#create wide dataset\n<\/span>data <- data.frame(A = runif(20, 2, 5),\n                   B = runif(20, 3, 5),\n                   C = runif(20, 3, 6),\n                   D = runif(20, 4, 6))\n\n#convert to long dataset for ANOVA\n<\/span>data_long <- gather(data, key = \"group\", value = \"amount\", A, B, C, D)\n\n#view first six lines of dataset\n<\/span>head(data_long)\n\n# group amount\n#1 To 2.796526\n#2 A 3.116372\n#3 A 3.718560\n#4 A 4.724623\n#5 A 2.605046\n#6 A 4.695169\n<\/strong><\/pre>\n
 Daha sonra veri k\u00fcmesine tek y\u00f6nl\u00fc bir ANOVA yapaca\u011f\u0131z:<\/span><\/p>\n
 #fit anova model\n<\/span>anova_model <- aov(amount ~ group, data = data_long)\n\n#view summary of anova model\n<\/span>summary(anova_model)\n\n# Df Sum Sq Mean Sq F value Pr(>F)    \n#group 3 25.37 8.458 17.66 8.53e-09 ***\n#Residuals 76 36.39 0.479            \n<\/strong><\/pre>\n
 ANOVA tablosu sonucunda F istatisti\u011finin 17,66 oldu\u011funu ve buna kar\u015f\u0131l\u0131k gelen p de\u011ferinin son derece k\u00fc\u00e7\u00fck oldu\u011funu g\u00f6r\u00fcyoruz.<\/span><\/p>\n
 Bu, t\u00fcm grup ortalamalar\u0131n\u0131n e\u015fit oldu\u011funu \u00f6ne s\u00fcren s\u0131f\u0131r hipotezini reddetmek i\u00e7in yeterli kan\u0131t\u0131m\u0131z oldu\u011fu anlam\u0131na gelir. Daha sonra hangi grup ortalamalar\u0131n\u0131n birbirinden farkl\u0131 oldu\u011funu belirlemek i\u00e7in post hoc testi kullanabiliriz.<\/span><\/p>\n
 A\u015fa\u011f\u0131daki post hoc testlerin \u00f6rneklerini inceleyece\u011fiz:<\/span><\/p>\n
 Tukey testi<\/strong> \u2013 olas\u0131 t\u00fcm ikili kar\u015f\u0131la\u015ft\u0131rmalar\u0131 yapmak istedi\u011finizde kullan\u0131\u015fl\u0131d\u0131r<\/span><\/p>\n
 Holm’un y\u00f6ntemi<\/strong> – Tukey testinden biraz daha konservatif bir test<\/span><\/p>\n
 Dunnett d\u00fczeltmesi<\/strong><\/a> \u2013 her grubun ortalamas\u0131n\u0131 bir kontrol ortalamas\u0131yla kar\u015f\u0131la\u015ft\u0131rmak istedi\u011finizde ve tedavi ortalamalar\u0131n\u0131 birbiriyle kar\u015f\u0131la\u015ft\u0131rmak istemedi\u011finizde kullan\u0131\u015fl\u0131d\u0131r.<\/span><\/p>\n
 Tukey testi<\/strong><\/span><\/h2>\n
 Yerle\u015fik R i\u015flevi TukeyHSD()’yi<\/strong> kullanarak \u00e7oklu kar\u015f\u0131la\u015ft\u0131rmalar i\u00e7in Tukey testini a\u015fa\u011f\u0131daki gibi ger\u00e7ekle\u015ftirebiliriz:<\/span><\/p>\n
 #perform Tukey's Test for multiple comparisons\n<\/span>TukeyHSD(anova_model, conf.level=.95) \n\n#Tukey multiple comparisons of means\n# 95% family-wise confidence level\n#\n#Fit: aov(formula = amount ~ group, data = data_long)\n#\n#$group\n# diff lwr upr p adj\n#BA 0.2822630 -0.292540425 0.8570664 0.5721402\n#CA 0.8561388 0.281335427 1.4309423 0.0011117\n#DA 1.4676027 0.892799258 2.0424061 0.0000000\n#CB 0.5738759 -0.000927561 1.1486793 0.0505270\n#DB 1.1853397 0.610536271 1.7601431 0.0000041\n#DC 0.6114638 0.036660419 1.1862672 0.0326371\n<\/strong><\/pre>\n
 G\u00fcven d\u00fczeyimizin %95 oldu\u011funu belirtti\u011fimizi unutmay\u0131n, bu da aile ba\u015f\u0131na hata oran\u0131m\u0131z\u0131n 0,05 olmas\u0131n\u0131 istedi\u011fimiz anlam\u0131na gelir. R bize her bir ikili fark\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in iki \u00f6l\u00e7\u00fcm verir:<\/span><\/p>\n
    \n
  •  Ortalama fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131 ( lwr<\/em> ve upr<\/em> de\u011ferleriyle verilir)<\/span><\/li>\n
  •  Ortalama farka g\u00f6re ayarlanan p de\u011feri<\/span><\/li>\n<\/ul>\n
     G\u00fcven aral\u0131\u011f\u0131 ve p de\u011feri ayn\u0131 sonuca varacakt\u0131r.<\/span><\/p>\n
     \u00d6rne\u011fin C grubu ile A grubu aras\u0131ndaki ortalama fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 (0,2813, 1,4309) olup, bu aral\u0131k s\u0131f\u0131r i\u00e7ermedi\u011finden bu iki grubun ortalamalar\u0131 aras\u0131ndaki fark\u0131n istatistiksel olarak anlaml\u0131 oldu\u011funu biliyoruz. \u00d6zellikle g\u00fcven aral\u0131\u011f\u0131n\u0131n alt s\u0131n\u0131r\u0131 s\u0131f\u0131rdan b\u00fcy\u00fck oldu\u011fundan fark\u0131n pozitif oldu\u011funu biliyoruz.<\/span><\/p>\n
     Benzer \u015fekilde Grup C ile Grup A aras\u0131ndaki ortalama fark\u0131n p de\u011feri 0,0011 olup bizim anlaml\u0131l\u0131k d\u00fczeyimiz olan 0,05’ten d\u00fc\u015f\u00fckt\u00fcr, bu da iki grubun ortalamalar\u0131 aras\u0131ndaki fark\u0131n istatistiksel olarak anlaml\u0131 oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n
     Ayr\u0131ca Tukey testinden elde edilen %95 g\u00fcven aral\u0131klar\u0131n\u0131 R’dekiplot ()<\/strong> fonksiyonunu kullanarak g\u00f6rselle\u015ftirebiliriz:<\/span><\/p>\n
     plot(TukeyHSD(anova_model, conf.level=.95))\n<\/strong><\/pre>\n
     Aral\u0131k s\u0131f\u0131r i\u00e7eriyorsa, grup ortalamalar\u0131 aras\u0131ndaki fark\u0131n istatistiksel olarak anlaml\u0131 olmad\u0131\u011f\u0131n\u0131 biliyoruz. Yukar\u0131daki \u00f6rnekte BA ve CB’ye ili\u015fkin farklar istatistiksel olarak anlaml\u0131 de\u011fildir ancak di\u011fer d\u00f6rt ikili kar\u015f\u0131la\u015ft\u0131rmaya ili\u015fkin farklar istatistiksel olarak anlaml\u0131d\u0131r.<\/span><\/p>\n
     Holm’un y\u00f6ntemi<\/strong><\/span><\/h2>\n
     Ger\u00e7ekle\u015ftirebilece\u011fimiz bir di\u011fer post hoc test ise Holm’un y\u00f6ntemidir. Bu testin genellikle Tukey testinden daha konservatif oldu\u011fu d\u00fc\u015f\u00fcn\u00fclmektedir.<\/span><\/p>\n
     \u00c7oklu ikili kar\u015f\u0131la\u015ft\u0131rmalarda Holm y\u00f6ntemini \u00e7al\u0131\u015ft\u0131rmak i\u00e7in R’de a\u015fa\u011f\u0131daki kodu kullanabiliriz:<\/span><\/p>\n
     #perform holm's method for multiple comparisons<\/span>\npairwise.t.test(data_long$amount, data_long$group, p.adjust=\"holm\") \n# Pairwise comparisons using t tests with pooled SD \n#\n#data: data_long$amount and data_long$group \n#\n#ABC\n#B 0.20099 - -      \n#C 0.00079 0.02108 -      \n#D 1.9e-08 3.4e-06 0.01974\n#\n#P value adjustment method: holm<\/strong><\/pre>\n
     Bu test, her ikili kar\u015f\u0131la\u015ft\u0131rma i\u00e7in bir p de\u011ferleri tablosu sa\u011flar. \u00d6rne\u011fin A grubu ile B grubunun ortalamas\u0131 aras\u0131ndaki fark\u0131n p de\u011feri 0,20099’dur.<\/span><\/p>\n
     Bu testteki p de\u011ferlerini Tukey testindeki p de\u011ferleriyle kar\u015f\u0131la\u015ft\u0131r\u0131rsan\u0131z, C ve D gruplar\u0131 aras\u0131ndaki fark d\u0131\u015f\u0131nda ikili kar\u015f\u0131la\u015ft\u0131rmalar\u0131n her birinin ayn\u0131 sonuca vard\u0131\u011f\u0131n\u0131 fark edeceksiniz. Bu fark\u0131n de\u011feri Tukey testinde 0,0505 iken Holm y\u00f6nteminde 0,02108 idi.<\/span><\/p>\n
     B\u00f6ylece Tukey testini kullanarak C grubu ile D grubu aras\u0131ndaki fark\u0131n 0,05 anlaml\u0131l\u0131k d\u00fczeyinde istatistiksel olarak anlaml\u0131 olmad\u0131\u011f\u0131, Holm y\u00f6ntemini kullanarak ise C grubu ile D grubu aras\u0131ndaki fark\u0131n istatistiksel olarak anlaml\u0131 oldu\u011fu<\/em> sonucuna vard\u0131k.<\/span><\/p>\n
     Genel olarak Holm y\u00f6ntemiyle \u00fcretilen p de\u011ferleri, Tukey testiyle \u00fcretilenlerden daha d\u00fc\u015f\u00fck olma e\u011filimindedir.<\/span><\/p>\n
     Dunnett’in d\u00fczeltmesi<\/strong><\/span><\/h2>\n
     \u00c7oklu kar\u015f\u0131la\u015ft\u0131rmalar i\u00e7in kullanabilece\u011fimiz bir di\u011fer y\u00f6ntem ise Dunett d\u00fczeltmesidir. Her grubun ortalamas\u0131n\u0131 bir kontrol ortalamas\u0131yla kar\u015f\u0131la\u015ft\u0131rmak istedi\u011fimizde ve tedavi ortalamalar\u0131n\u0131 birbiriyle kar\u015f\u0131la\u015ft\u0131rmak istemedi\u011fimizde bu yakla\u015f\u0131m\u0131 kullan\u0131r\u0131z.<\/span><\/p>\n
     \u00d6rne\u011fin a\u015fa\u011f\u0131daki kodu kullanarak B, C ve D’nin grup ortalamalar\u0131n\u0131 A grubunun ortalamalar\u0131yla kar\u015f\u0131la\u015ft\u0131r\u0131yoruz. Bu nedenle A grubunu kontrol grubu olarak kullan\u0131yoruz ve B, C gruplar\u0131 aras\u0131ndaki farklarla ilgilenmiyoruz. . ve D.<\/span><\/p>\n
     #load multcomp library necessary for using Dunnett's Correction<\/span>\nlibrary(multicomp)\n\n#convert group variable to factor \n<\/span>data_long$group <- as.factor(data_long$group)\n\n#fit anova model\n<\/span>anova_model <- aov(amount ~ group, data = data_long)\n\n#performcomparisons\n<\/span>dunnet_comparison <- glht(anova_model, linfct = mcp(group = \"Dunnett\"))\n\n#view summary of comparisons\n<\/span>summary(dunnet_comparison)\n\n#Multiple Comparisons of Means: Dunnett Contrasts\n#\n#Fit: aov(formula = amount ~ group, data = data_long)\n#\n#Linear Assumptions:\n#Estimate Std. Error t value Pr(>|t|)    \n#B - A == 0 0.2823 0.2188 1.290 0.432445    \n#C - A == 0 0.8561 0.2188 3.912 0.000545 ***\n#D - A == 0 1.4676 0.2188 6.707 < 1e-04 ***<\/strong><\/pre>\n
     \u00c7\u0131kt\u0131daki p de\u011ferlerinden a\u015fa\u011f\u0131dakileri g\u00f6rebiliriz:<\/span><\/p>\n
      \n
    •  B grubu ortalamas\u0131 ile A grubu ortalamas\u0131 aras\u0131ndaki fark istatistiksel olarak 0,05 anlaml\u0131l\u0131k d\u00fczeyinde anlaml\u0131 de\u011fildir<\/em> . Bu testin p de\u011feri 0,4324’t\u00fcr<\/strong> .<\/span><\/li>\n
    •  C Grubu ile A Grubu ortalamalar\u0131 aras\u0131ndaki fark istatistiksel olarak 0,05 anlaml\u0131l\u0131k d\u00fczeyinde anlaml\u0131d\u0131r<\/em> . Bu testin p de\u011feri 0,0005’tir<\/strong> .<\/span><\/li>\n
    •  D Grubu ile A Grubu ortalamalar\u0131 aras\u0131ndaki fark istatistiksel olarak 0,05 anlaml\u0131l\u0131k d\u00fczeyinde anlaml\u0131d\u0131r<\/em> . Bu testin p de\u011feri 0,00004’t\u00fcr<\/strong> .<\/span><\/li>\n<\/ul>\n
       Daha \u00f6nce belirtildi\u011fi gibi, bu yakla\u015f\u0131m A Grubunu “kontrol” grubu olarak ele al\u0131r ve di\u011fer t\u00fcm gruplar\u0131n ortalamas\u0131n\u0131 A Grubunun ortalamas\u0131yla kar\u015f\u0131la\u015ft\u0131r\u0131r. B, C ve D gruplar\u0131 aras\u0131ndaki farklar i\u00e7in hi\u00e7bir test yap\u0131lmad\u0131\u011f\u0131n\u0131 unutmay\u0131n \u00e7\u00fcnk\u00fc yapma. Bu gruplar aras\u0131ndaki farklarla ilgilenmiyorum.<\/span><\/p>\n
       Post-hoc testler ve istatistiksel g\u00fc\u00e7 \u00fczerine bir not<\/span><\/strong><\/h2>\n
       Post hoc testler, aile baz\u0131nda hata oran\u0131n\u0131 kontrol etme konusunda m\u00fckemmel bir i\u015f \u00e7\u0131kar\u0131r, ancak bunun kar\u015f\u0131l\u0131\u011f\u0131, kar\u015f\u0131la\u015ft\u0131rmalar\u0131n istatistiksel g\u00fcc\u00fcn\u00fc azaltmalar\u0131d\u0131r. Asl\u0131nda aile baz\u0131nda hata oran\u0131n\u0131 azaltman\u0131n tek yolu, t\u00fcm bireysel kar\u015f\u0131la\u015ft\u0131rmalar i\u00e7in daha d\u00fc\u015f\u00fck bir anlaml\u0131l\u0131k d\u00fczeyi kullanmakt\u0131r.<\/span><\/p>\n
       \u00d6rne\u011fin, alt\u0131 ikili kar\u015f\u0131la\u015ft\u0131rma i\u00e7in Tukey testini kulland\u0131\u011f\u0131m\u0131zda ve aile baz\u0131nda hata oran\u0131n\u0131 0,05 olarak korumak istedi\u011fimizde, her bir anlaml\u0131l\u0131k d\u00fczeyi i\u00e7in yakla\u015f\u0131k 0,011’lik bir anlaml\u0131l\u0131k d\u00fczeyi kullanmal\u0131y\u0131z. Ne kadar \u00e7ok ikili kar\u015f\u0131la\u015ft\u0131rma yaparsak, her bir anlaml\u0131l\u0131k d\u00fczeyi i\u00e7in kullanmam\u0131z gereken anlaml\u0131l\u0131k d\u00fczeyi o kadar d\u00fc\u015f\u00fck olur.<\/span><\/p>\n
       Sorun, daha d\u00fc\u015f\u00fck anlaml\u0131l\u0131k d\u00fczeylerinin daha d\u00fc\u015f\u00fck istatistiksel g\u00fcce kar\u015f\u0131l\u0131k gelmesidir. Bu, pop\u00fclasyonda grup ortalamalar\u0131 aras\u0131nda bir fark ger\u00e7ekten varsa, daha az g\u00fc\u00e7l\u00fc bir \u00e7al\u0131\u015fman\u0131n bunu tespit etme olas\u0131l\u0131\u011f\u0131n\u0131n daha d\u00fc\u015f\u00fck oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n
       Bu de\u011fi\u015f toku\u015fun etkilerini azaltman\u0131n bir yolu, yapt\u0131\u011f\u0131m\u0131z ikili kar\u015f\u0131la\u015ft\u0131rmalar\u0131n say\u0131s\u0131n\u0131 azaltmakt\u0131r. \u00d6rne\u011fin \u00f6nceki \u00f6rneklerde d\u00f6rt farkl\u0131 grup i\u00e7in alt\u0131 ikili kar\u015f\u0131la\u015ft\u0131rma yapt\u0131k. Ancak \u00e7al\u0131\u015fman\u0131z\u0131n ihtiya\u00e7lar\u0131na ba\u011fl\u0131 olarak yaln\u0131zca birka\u00e7 kar\u015f\u0131la\u015ft\u0131rma yapmak isteyebilirsiniz.<\/span><\/p>\n
       Daha az kar\u015f\u0131la\u015ft\u0131rma yaparak istatistiksel g\u00fcc\u00fc o kadar azaltman\u0131za gerek kalmaz.<\/span><\/p>\n
       ANOVA’y\u0131 ger\u00e7ekle\u015ftirmeden \u00f6nce<\/em> tam olarak hangi gruplarda kar\u015f\u0131la\u015ft\u0131rma yapmak istedi\u011finizi ve bu kar\u015f\u0131la\u015ft\u0131rmalar\u0131 yapmak i\u00e7in hangi post hoc testi kullanaca\u011f\u0131n\u0131z\u0131 belirlemeniz gerekti\u011fini unutmaman\u0131z \u00f6nemlidir. Aksi takdirde, hangi post hoc testin istatistiksel olarak anlaml\u0131 sonu\u00e7lar \u00fcretti\u011fini g\u00f6rmek \u00e7al\u0131\u015fman\u0131n b\u00fct\u00fcnl\u00fc\u011f\u00fcn\u00fc azalt\u0131r.<\/span><\/p>\n
       \u00c7\u00f6z\u00fcm<\/strong><\/span><\/h2>\n
       Bu yaz\u0131da a\u015fa\u011f\u0131dakileri \u00f6\u011frendik:<\/span><\/p>\n
        \n
      •  ANOVA, \u00fc\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 kullan\u0131l\u0131r.<\/span><\/li>\n
      •  Bir ANOVA anlaml\u0131l\u0131k seviyemizin alt\u0131nda bir p de\u011feri \u00fcretirse, hangi grup ortalamalar\u0131n\u0131n birbirinden farkl\u0131 oldu\u011funu bulmak i\u00e7in post hoc testleri kullanabiliriz.<\/span><\/li>\n
      •  Post-hoc testler, birka\u00e7 ikili kar\u015f\u0131la\u015ft\u0131rma yaparken aile ba\u015f\u0131na hata oran\u0131n\u0131 kontrol etmemize olanak tan\u0131r.<\/span><\/li>\n
      •  Aile baz\u0131nda hata oran\u0131n\u0131 kontrol etmenin kar\u015f\u0131l\u0131\u011f\u0131 daha az istatistiksel g\u00fc\u00e7t\u00fcr. Daha az ikili kar\u015f\u0131la\u015ft\u0131rma yaparak daha d\u00fc\u015f\u00fck istatistiksel g\u00fcc\u00fcn etkilerini azaltabiliriz.<\/span><\/li>\n
      •  \u00d6ncelikle hangi gruplar \u00fczerinde ikili kar\u015f\u0131la\u015ft\u0131rma yapmak istedi\u011finizi ve bunu yapmak i\u00e7in hangi post hoc testi kullanaca\u011f\u0131n\u0131z\u0131 belirlemelisiniz.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
        ANOVA, \u00fc\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 kullan\u0131lan istatistiksel bir testtir. ANOVA’da kullan\u0131lan varsay\u0131mlar a\u015fa\u011f\u0131daki gibidir: S\u0131f\u0131r hipotezi (H 0 ): \u00b5 1 = \u00b5 2 = \u00b5 3 = \u2026 = \u00b5 k (ortalamalar her grup i\u00e7in e\u015fittir) Alternatif hipotez: (Ha): Ara\u00e7lardan en […]<\/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-483","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\nANOVA ile Post Hoc Testini Kullanma K\u0131lavuzu - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, grup ortalamalar\u0131 aras\u0131ndaki farklar\u0131 test etmek i\u00e7in ANOVA ile post-hoc testin nas\u0131l kullan\u0131laca\u011f\u0131 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\/post-hoc-anova-testleri\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"ANOVA ile Post Hoc Testini Kullanma K\u0131lavuzu - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde, grup ortalamalar\u0131 aras\u0131ndaki farklar\u0131 test etmek i\u00e7in ANOVA ile post-hoc testin nas\u0131l kullan\u0131laca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T18:29:23+00:00\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/\",\"url\":\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/\",\"name\":\"ANOVA ile Post Hoc Testini Kullanma K\u0131lavuzu - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T18:29:23+00:00\",\"dateModified\":\"2023-07-29T18:29:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde, grup ortalamalar\u0131 aras\u0131ndaki farklar\u0131 test etmek i\u00e7in ANOVA ile post-hoc testin nas\u0131l kullan\u0131laca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/post-hoc-anova-testleri\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Anova ile post-hoc testini kullanma k\u0131lavuzu\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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