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December, 1961 A Nonparametric Test for the Problem of Several Samples
V. P. Bhapkar
Ann. Math. Statist. 32(4): 1108-1117 (December, 1961). DOI: 10.1214/aoms/1177704849


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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V. P. Bhapkar. "A Nonparametric Test for the Problem of Several Samples." Ann. Math. Statist. 32 (4) 1108 - 1117, December, 1961.


Published: December, 1961
First available in Project Euclid: 27 April 2007

zbMATH: 0208.20501
MathSciNet: MR156425
Digital Object Identifier: 10.1214/aoms/1177704849

Rights: Copyright © 1961 Institute of Mathematical Statistics

Vol.32 • No. 4 • December, 1961
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