Comparing the "typical score" across independent groups based on different criteria for trimming

Abstract

Nonnormality and variance heterogeneity affect the validity of the traditional tests for treatment group equality (e.g. ANOVA F-test and t-test), particularly when group sizes are unequal. Adopting trimmed means instead of the usual least squares estimator has been shown to be mostly affective in combating the deleterious effects of nonnormality. There are, however, practical concerns regarding trimmed means, such as the predetermined amount of symmetric trimming that is typically used. Wilcox and Keselman proposed the Modified One- Step M-estimator (MOM) which empirically determines the amount of trimming. Othman et al. found that when this estimator is used with Schrader and Hettmansperger's H statistic, rates of Type I error were well controlled even though data were nonnormal in form. In this paper, we modified the criterion for choosing the sample values for MOM by replacing the default scale estimator, MADn, with two robust scale estimators, Sn and Tn , suggested by Rousseeuw and Croux (1993). To study the robustness of the modified methods, conditions that are known to negatively affect rates of Type I error were manipulated. As well, a bootstrap method was used to generate a better approximate sampling distribution since the null distribution of MOM-H is intractable. These modified methods resulted in better Type I error control especially when data were extremely skewed.