Comparing groups using robust H statistic with adaptive trimmed mean

Abstract

An alternative robust method for testing the equality of central tendency measures was developed by integrating H Statistic with adaptive trimmed mean using hinge estimator, HQ. H Statistic is known for its ability to control Type I error rates and HQ is a robust location estimator. This robust estimator used asymmetric trimming technique, where it trims the tail of the distribution based on the characteristic of that particular distribution. To investigate on the performance (i.e. robustness) of the procedure, some variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Bootstrap method was used to test the hypothesis. The integration seemed to produce promising robust procedure that is capable of addressing the problem of violations to the assumptions. About 20% trimming is the appropriate amount of trimming for the procedure, where this amount is found to be robust in most conditions. This procedure was also proven to be robust as compared to the parametric (ANOVA) and non-parametric (Kruskal-Wallis) methods.