## The Annals of Mathematical Statistics

### A Nonparametric Test for the Problem of Several Samples

V. P. Bhapkar

#### 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].

#### Article information

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

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704849

Digital Object Identifier
doi:10.1214/aoms/1177704849

Mathematical Reviews number (MathSciNet)
MR156425

Zentralblatt MATH identifier
0208.20501

JSTOR