Robustness of S1 statistic with Hodges-Lehmann for skewed distributions - Ahad, Nor Aishah; Syed Yahaya, Sharipah Soaad; Lee, Ping Yin (2016)
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 non- normal 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.