Open Access
December, 1963 Use of the Wilcoxon Statistic for a Generalized Behrens-Fisher Problem
Richard F. Potthoff
Ann. Math. Statist. 34(4): 1596-1599 (December, 1963). DOI: 10.1214/aoms/1177703894

Abstract

Heretofore, the ordinary Wilcoxon statistic for the two-sample problem [9], [5] has been used only to test the null hypothesis that the two parent populations are identical. This paper presents a technique for utilizing the Wilcoxon statistic to test a broader type of null hypothesis, like that encountered in the Behrens-Fisher problem: we show that the usual Wilcoxon test, with $(m + n + 1)/12mn$ replaced by $1/\lbrack 4 \min(m, n)\rbrack$, may be used to test the null hypothesis of the equality of the medians of two symmetrical (continuous) distributions which are of the same form but which have different (unknown) scale parameters; more generally, the test still works for testing the equality of the medians of any two symmetrical distributions.

Citation

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Richard F. Potthoff. "Use of the Wilcoxon Statistic for a Generalized Behrens-Fisher Problem." Ann. Math. Statist. 34 (4) 1596 - 1599, December, 1963. https://doi.org/10.1214/aoms/1177703894

Information

Published: December, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0225.62061
MathSciNet: MR155393
Digital Object Identifier: 10.1214/aoms/1177703894

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 4 • December, 1963
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