H-statistic with winsorized modified one-step M-estimator for two independent groups design

Abstract

Two-sample independent t-test is a classical method which is widely used to test the equality of two groups. However, this test is easily affected by any deviation in normality, more obvious when heterogeneity of variances and group sizes exist. It is well known that the violation in the assumption of these tests will lead to inflation in Type I error rate and depression in statistical test power. In mitigating the problem, robust methods can be used as alternatives. One such method is H-statistic. When used with modified one-step M-estimator (MOM), this test statistic (MOM-H) produce good control of Type I error even under small sample size but inconsistent across certain conditions investigated. Furthermore, power of the test is low which might be due to the trimming process. In this study, MOM is winsorized (WMOM) to sustain the original sample size. The H-statistic with WMOM as the central tendency measures (denoted as WMOM-H) showed better control of Type I error as compared to MOM-H especially under balance design regardless of the shapes of distribution investigated in the study. It also performed well under highly skewed and heavy tailed distribution for unbalanced design. In general, this study demonstrated that winsorization process (WMOM) could improve the performance of H-statistic in terms of Type I error rate control.