A modification of the kruskal-wallis statistic for the generalized behrens-fisher problem

The problem of testing the equality of the medians of several populations is considered. Standard distribution-free procedures for this problem require that the populations have the same shape in order to maintain their nominal significance level, ever asymptotically, under the null hypothesis of equal medians , A modification of the Kruskal-Wallis test statistic is proposed which is exactly distribution-free under the usual nonparanetric asswnption that the continuous populations are identical with any shape. It is asymptotically distribution-free when the Continuous populations are asswned to be syrmnetric with equal medians.