A Nonparametric Test for the Problem of Several Samples

Abstract

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 $i$th sample is the least, $i = 1, 2, \cdots, c$. 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].