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

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

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