Tests of Location Equality Under Non-Identical Distributions

Abstract

The ANOVA-F test is the most known procedure for comparing at least three population means. However, this conventional test might give misleading results when it’s underlying assumptions are violated. In this study, Welch’s test with trimmed mean, Welch’s test with trimmed mean and a bootstrap-t, newly proposed test and ANOVA-F test were compared in terms of actual Type I error rates under not only non-normality and heteroscedasticity, but also with non-identical distribution shapes. The newly proposed method outperformed ANOVA-F and other alternatives under various situations.