H-statistic with winsorized modified one-step M-estimator as central tendency measure

Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbalanced group sizes exist. It is well known that the violation in the assumption of the tests will lead to
inflation in Type I error rate and decreasing in the power of test. Nonparametric procedures like Mann-Whitney and Kruskal-Wallis may be the alternative to the parametric procedures, however, loss of information occur due to the ranking data. In mitigating these problems, robust procedures can be used as the other alternative. One of the procedures is H-statistic. When used with modified one-step M-estimator (MOM), the test statistic (MOM-H) produces good control of Type I error rate even
under small sample size but inconsistent under certain conditions investigated. Furthermore, power of test is low which might be due to the trimming process. In this study, MOM was winsorized (WMOM) to retain the original sample size. The Hstatistic when combines with WMOM as the central tendency measure (WMOM-H) shows better control of Type I error rate as compared to MOM-H especially under balanced design regardless of the shape of distributions. It also performs well under highly skewed and heavy tailed distribution for unbalanced design. On top of that, WMOM-H also generates better power value, as compared to MOM-H and ANOVA under most of the conditions investigated. WMOM-H also has better control of Type I error rates with no liberal value (>0.075) compared to the parametric (t-test and ANOVA) and nonparametric (Mann-Whitney and Kruskal-Wallis) procedures. In
general, this study demonstrates that winsorization process (WMOM) is able to improve the performance of H-statistic in terms of controlling Type I error rate and increasing power of test.