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

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.