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December, 1965 Small Sample Power of the One Sample Wilcoxon Test for Non-Normal Shift Alternatives
Harvey J. Arnold
Ann. Math. Statist. 36(6): 1767-1778 (December, 1965). DOI: 10.1214/aoms/1177699805

Abstract

The power of the one sample Wilcoxon test is computed for the hypothesis that the median is zero against various shift alternatives for samples drawn from several different non-normal distributions. A recursive scheme given by Klotz [2] simplifies the problem of power computations and allows investigating samples to size $n = 10$ on a large computer. The power for selected type I errors $\alpha$ are compared with the power of a best signed-rank procedure obtained by sorting the probabilities in decreasing order for all possible sample configurations for fixed $n$ and adding up the probabilities associated with the most probable 100 $\alpha$% of the configurations. The non-normal distributions selected for study are the $t$ distribution with degrees of freedom $\frac{1}{2}$, 1, 2, and 4. The one sample Wilcoxon test, found to be powerful for normal shift alternatives by Klotz [2], deteriorates badly in power for the long-tailed distributions studied as does the one sample $t$ test. However, the Wilcoxon test remains more powerful than the $t$ test. The sign test is still more powerful than either Wilcoxon or $t$. No asymptotic results are obtained.

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Harvey J. Arnold. "Small Sample Power of the One Sample Wilcoxon Test for Non-Normal Shift Alternatives." Ann. Math. Statist. 36 (6) 1767 - 1778, December, 1965. https://doi.org/10.1214/aoms/1177699805

Information

Published: December, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0136.40404
MathSciNet: MR183077
Digital Object Identifier: 10.1214/aoms/1177699805

Rights: Copyright © 1965 Institute of Mathematical Statistics

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Vol.36 • No. 6 • December, 1965
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