A Nonparametric Test for the Problem of Several Samples

In this paper, a new nonparametric test for the problem of c samples is offered. It is based upon the numbers of c-plets that can be formed by choosing one observation from each sample such that the observation from the ith sample is the least, i = 1, 2, \⋯, c. The asymptotic distribution of the new test statistic is derived by an application of the extension of Hoeffding's theorem [4] on U-statistics to the case of c samples. The asymptotic power and the asymptotic efficiencies of this test relative to the Kruskal-Wallis H-test [7] and the Mood-Brown M-test [10] are computed in standard fashion along the lines of Andrews' paper [1].