P-method post hoc test for adaptive trimmed mean, HQ

Abstract

Adaptive trimmed mean, HQ, which is one of the latest additions in robust estimators, had been proven to be good in controlling Type I error in omnibus test. However, post hoc (pairwise multiple comparison) procedure for HQ was yet to be developed then. Thus, we have taken the initiative to develop post hoc procedure for HQ. Percentile bootstrap method or P-Method was proposed as it was proven to be effective in controlling Type I error rate even when the sample size was small. This paper deliberates on the effectiveness of P-Method on HQ, denoted as P-HQ. The strength and weakness of the proposed method were put to test on various conditions created by manipulating several variables such as shape of distributions, number of groups, sample sizes, degree of variance heterogeneity and pairing of sample sizes and group variances. For such, a simulation study on 2000 datasets was conducted using SAS/IML Version 9.2. The performance of the method on various conditions was based on its ability in controlling Type I error which was benchmarked using Bradley's criterion of robustness. The finding revealed that P-HQ could effectively control Type I error for almost all the conditions investigated.