Development and modification of H-statistic with winsorized approach means

Student’s t-test and ANOVA F-test are the classical statistical tests for comparing two or more independent groups. Both are powerful tests when data is normally distributed and variances are homogenous. However, the data with these properties sometime is difficult to be met in real-life will affect the Type I error rates control and reduce statistical power of the tests. H-statistic is a robust statistic but performs well only under non-normality dataset. This statistic had been invented with MOM estimator denoted as MOM-H. Therefore, in this study, two modified H-statistic with mean using Winsorizing approach are proposed to handle both violated properties. The proposed statistics are the H-statistic with Winsorized mean (WM) and the H-statistic with adaptive Winsorized mean (AWM) which denoted as WM-H and AWM-H, respectively. Using this modification, the tests perform better not only under non-normality, but also under heterogeneity of variances. The approach use predetermined values of 15% and 25% Winsorization. The WM is Winsorizing symmetrically while the AWM is Winsorizing adaptively according to the shape of distribution based on hinge estimators, HQ and HQ₁. The WM-H statistic consists of 15WM-H and 25WM-H, whereas the AWM-H comprises of 15WHQ-H, 25WHQ-H, 15WHQ₁-H and 25WHQ₁-H. The performances of the proposed tests are evaluated using Type I error rates and power of test based on simulation study. All the results from the proposed tests are compared with the original H-statistic, MOM-H and classical statistical tests. The findings indicate that 15WHQ-H performs the best for two groups case especially under heavy tailed distribution. Under skewed distribution, WM-H has better performance to others but comparable to MOM-H. In overall the proposed tests are able to give better results than the MOM-H and the classical statistical tests under certain conditions. The proposed tests are also validated using real dataset.