Hsieh, F ve Kruskal-Wallis Testlerinin Monte Carlo Simülasyon Tekniği Kullanılarak I. Tip Hata Olasılıkları Bakımından Değerlendirilmesi

Yıl 2024, Cilt: 6 Sayı: 2, 132 - 137

Malik Ergin , Özgür Koşkan

https://doi.org/10.55979/tjse.1539525

Öz

Bu çalışmada, iki parametreli üstel dağılımdan farklı parametrelerle ve χ2(2) dağılımından üretilen örnekler kullanılarak Hsieh, F ve Kruskal-Wallis testleri, I.tip hata olasılıkları açısından karşılaştırılmıştır. Çalışmada incelenen testler arasında, Hsieh testinin I.tip hata olasılıklarının, Klasik F ve Kruskal-Wallis testlerine göre daha yüksek olduğu bulunmuş ve bu durum, I.tip hatayı %5 seviyesinde tutamadığını göstermektedir. Bu durum özellikle küçük örnek genişliklerinde ve varyansların homojenliği varsayımının sağlanmadığı durumlarda daha belirgin hale gelmektedir. Ayrıca, Levene testi tarafından göz ardı edilen heterojen varyans oranlarında bile, Hsieh testinin I.tip hata oranı %13.3'e ulaşmıştır. Sonuç olarak, Hsieh testindeki yüksek I.tip hata olasılığı, özellikle küçük örnek genişliklerinde ve grup varyanslarının homojen olmadığı durumlarda kullanımını sınırlamaktadır.

Anahtar Kelimeler

Hsieh testi, Varyans analizi, Kruskal-Wallis testi, I.tip hata olasılığı

Evaluating The Type I Error Rate Performances of Hsieh, F, and Kruskal-Wallis Tests Using Monte Carlo Simulation Technique

Öz

In this study, the Hsieh, Classical F, and Kruskal-Wallis tests were compared in terms of Type I error probabilities using samples generated from a two-parameter exponential distribution with various parameters and a χ2(2) distribution. Among the tests examined in the study, the Hsieh test was found to have higher Type I error probabilities compared to the Classical F and Kruskal-Wallis tests, indicating that it could not maintain the Type I error at the 5.0% level. The effect of this finding is more pronounced in small sample sizes and when the assumption of homogeneity of variance is not met. In addition, even in heterogeneous variance ratios, that Levene's test neglects, the Type I error rate of the Hsieh test reached 13.3%. In conclusion, the high probability of Type I error in the Hsieh test, especially in small sample sizes and when group variances are not homogeneous, restricts its usage.

Anahtar Kelimeler

Hsieh test, Analysis of variance, Kruskal-Wallis test, Type I error rate

Kaynakça

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