The Robustness of the Modified H-Statistic in the Test of Comparing Independent Groups

The H-statistic is a robust test statistic in comparing the equality of two and more than two independent groups. This statistic is one of a good alternative to the F-statistic in the analysis of variance (ANOVA). The F-statistic is good only when the distribution of data is normal with homogeneous variances. If there is a violation of at least one of these assumptions, it affects the Type I error rate of the test. The main weakness of the F-statistic is its calculation based on the mean. The mean is well-known as a very sensitive central tendency measure with 0 breakdown point, whereas the H-statistic provides a test with fewer assumptions yet powerful. This statistic is readily adaptable to any measure of central tendency, and it appears to give reasonably good results. Hence, this paper provides a detailed study on the robustness of the H-statistic and its performance using different robust central tendency measures such that the modified one-step M (MOM) estimator and Winsorized MOM estimator. Based on the simulation study, this paper also investigates the performance of the H-statistic under various data conditions. The findings reveal that this statistic performs as well as the F-statistic under normal and homogeneous variance, yet it provides better control of Type I error rate under non-normal data or heterogeneous variances or both. Keywords: H-statistic; robust test; mean; modified one-step M-estimator