Asymptotic Behavior of Some Rank Tests for Analysis of Variance

Abstract

The $H$ test and the median test have been proposed for testing the hypothesis of the equality of $c$ probability distributions. Assuming translation-type alternatives, we find the limiting distributions of the $H$ and median test statistics. These results are used to derive general formulas for the asymptotic relative efficiencies of these tests with respect to one another and to the classical $F$ test. A short discussion of the computation of approximate power functions of these tests is also included.