Asymptotic Conservativeness and Efficiency of Kruskal-Wallis Test for K Dependent Samples

Abstract The robustness (asymptotic conservativeness) of Kruskal-Wallis test under certain departures from mutual independence of K univariate samples is established. This robustness provides a procedure for testing the equality of K marginal distribution functions based on a broken random sample from a K-variate distribution that satisfies a mild condition. For the unbroken sample, a generalized Kruskal-Wallis (KW) test is proposed for testing the symmetry of a K-dimensional distribution function. The relative efficiency of the K-W test against the aligned rank order test is also examined under the normal shift model.