Asymptotic Behavior of Some Rank Tests for Analysis of Variance

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.