Approximations to the Power of Rank Tests

Abstract

Proposed is a method for approximating the distribution of the ranks, which is the basis for evaluating the power of an arbitrary rank test (see definition of "rank test" in Section 2 below). The method involves, in essence, a transformation of the original distributions, by means of interpolating polynomials, into distributions defined on the unit interval (0, 1). A somewhat detailed discussion is given to the problem of testing the hypothesis that two populations are identical against the alternative hypothesis that they have two specified (non-identical) distributions. Explicit formulas for approximating the distributions of the ranks under the alternative hypothesis are given. A few tables are computed for the case where both distributions are normal with the same variance but different means. The last section is devoted to the investigation of the asymptotic power efficiency of certain rank tests.