Murat ERİŞOĞLU, Ülkü ERİŞOĞLU, Ahmet PEKGÖR, Aydın KARAKOCA

R ile Normallik Testlerinin Deneysel 1. Tip Hata Oranı ve Güç Karşılaştırması

Normallik istatistiksel testlerde ana varsayımlardan biridir. Normallik testlerinin çokluğu, araştırmacılar için uygun normallik testini seçme konusunda başka bir problem ortaya çıkarmaktadır. İstatistiksel analizlerde sıklıkla kullanılan ücretsiz bir yazılım olan R’da 4 farklı pakette 18 normallik testi bulunmaktadır. Bu çalışmada, normallik testlerinin performansını ampirik 1. tip hata oranı ve güç açısından Monte Carlo simülasyonu ile karşılaştırılmıştır. Çalışma sonucunda verinin dağılımı (simetrik veya asimetrik) ne olursa olsun Shapiro-Francia testi, ayrıca Frosini B testi de deneysel tip 1 hata oranı açısından diğer normallik testlerinden daha iyi performans göstermiştir.Ayrıca yaygın olarak kullanılan Kolmogorov-Smirnov testi ampirik tip 1 hata oranı ve testin gücü açısından diğer normallik testlerinden daha kötü performans göstermiştir.

Empirical Type 1 Error Rate and Power Comparisons of Normality Tests with R

Normality is one of the main presuppositions instatistical tests. The multiplicity of the normality tests bring out anotherproblem of choosing the appropriate test for researchers. The free software Rwhich has a great popularity in the statistical analysis has 18 normality testsin 4 different packages. In this study we compared performance of thesenormality tests in terms of empirical type 1 error rate and power by MonteCarlo simulation. As a result, regardless of the distribution of data (symetricor asymmetric) the Shapiro-Francia test, also the Frosini B test performedbetter than the other normality tests in terms of experimental type 1 errorrate. However the widely used Kolmogorov-Smirnov test showed worse performancethan other normality tests in terms of empirical type 1 error rate and power.

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