Robust percentile bootstrap test with modified one-step M-estimator (MOM): An alternative modern statistical analysis - Nurul Hanis, Harun (2015)
Normality and homoscedasticity are two main assumptions that must be fulfilled when dealing with classical parametric tests for comparing groups. Any violation of the assumptions will cause the results to be invalid. However, in reality, these assumptions are hardly achieved. To overcome such problem, this study proposed to modify a method known as Parametric Bootstrap test by substituting the usual mean, with a highly robust location measure, modified one step M-estimator (MOM). MOM is an asymmetric trimmed mean. The substitution will make the Parametric Bootstrap test more robust for comparing groups. For this study, the trimming criteria for MOM employed two highly robust scale estimators namely MADn and Tn. A simulation study was conducted to investigate on the performance of the proposed method based on Type I error rates. To highlight the strength and weakness of the method, five variables: number of groups, balanced and unbalanced sample sizes, types of distributions, variances heterogeneity and nature of pairings of sample sizes and group variances were manipulated to create various conditions which are common to real life situations.The performance of the proposed method was then compared with the most frequently used parametric and non parametric tests for two (independent sample t-test and Mann Whitney respectively) and more than two independent groups (ANOVA and Kruskal Wallis respectively). The finding of this study indicated that, for two groups, the robust Parametric Bootstrap test performed reasonably well under the conditions of heterogeneous variances with normal or skewed distributions. While for more than two groups, the test generate good Type I error control under heterogeneous variances and skewed distributions. In comparison with the parametric and non parametric methods, the proposed test outperforms its counterparts under non-normal distribution and heterogeneous variances. The performance of each procedure was also demonstrated using real data. In general, the performance of Type I error for the proposed test is very convincing even when the assumptions of normality and homoscedasticity are violated.