Robustness of S_1 Statistic with Hodges-Lehmann for Skewed Distributions

摘要

Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of nonnormal and heteroscedastic settings. When the assumptions are violated, researchers are looking for alternative such as Kruskal-Wallis under nonparametric or robust method. This study focused on flexible method, S_1 statistic for comparing groups using median as the location estimator. S_1 statistic was modified by substituting the median with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MAD_n to produce two different test statistics for comparing groups. Bootstrap method was used for testing the hypotheses since the sampling distributions of these modified S_1 statistics are unknown. The performance of the proposed statistic in terms of Type I error was measured and compared against the original S_1 statistic, ANOVA and Kruskal-Wallis. The propose procedures show improvement compared to the original statistic especially under extremely skewed distribution.