Comparison of Local Powers of Some Exact Tests for a Common Normal Mean with Unequal Variances

Abstract

The inferential problem of drawing inference about a common mean μ of several independent normal populations with unequal variances has drawn universal attention, and there are many exact tests for testing a null hypothesis H₀ : μ = μ₀ against both-sided alternatives. In this paper, we provide a review of their local power and a comparison. It turns out that, in the case of equal sample size, a uniform comparison and ordering of the exact tests based on their local power can be carried out even when the variances are unknown.