On the Power of Two-Sample Rank Tests on the Equality of Two Distribution Functions

Abstract

This paper is a comparative study of the power functions of two-sample rank tests of the hypothesis of equal distributions,H0:H = G.Numerical results are given for the alternative of two extreme distributions,H1:H= l-(1- F)k,G=Fk, withFan unspecified continuous cumulative distribution function,k =2, 3, 4, sample sizesm = n≤ 6, significance levels 0·01, 0·05, 0·10. Randomized decision rules are employed when necessary to attain the exact significance level. Some results are also given for unequal sample sizes. The tests considered are the most powerful rank test, Terry's test, one- and two-sided Wilcoxon tests, one- and two-sided median tests, the Wald-Wolfowitz runs test, and two new tests, called the Gamma and Psi tests. These are derived herein as the locally most powerful rank tests against slight variations of the alternative of two extreme distributions. Comparisons are made with the power of these same tests against normal alternatives differing only in location.