The Annals of Mathematical Statistics

A Nonparametric Test for the Problem of Several Samples

V. P. Bhapkar

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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].

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Ann. Math. Statist., Volume 32, Number 4 (1961), 1108-1117.

First available in Project Euclid: 27 April 2007

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Bhapkar, V. P. A Nonparametric Test for the Problem of Several Samples. Ann. Math. Statist. 32 (1961), no. 4, 1108--1117. doi:10.1214/aoms/1177704849.

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