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. 2019;73(1):43-49.
doi: 10.1080/00031305.2017.1328375. Epub 2018 May 10.

Modified Wilcoxon-Mann-Whitney Test and Power against Strong Null

Youyi Fong  1 , Ying Huang  1
Affiliations

Modified Wilcoxon-Mann-Whitney Test and Power against Strong Null

Youyi Fong et al. Am Stat. 2019.

Abstract

The Wilcoxon-Mann-Whitney (WMW) test is a popular rank-based two-sample testing procedure for the strong null hypothesis that the two samples come from the same distribution. A modified WMW test, the Fligner-Policello (FP) test, has been proposed for comparing the medians of two populations. A fact that may be underappreciated among some practitioners is that the FP test can also be used to test the strong null like the WMW. In this paper we compare the power of the WMW and FP tests for testing the strong null. Our results show that neither test is uniformly better than the other and that there can be substantial differences in power between the two choices. We propose a new, modified WMW test that combines the WMW and FP tests. Monte Carlo studies show that the combined test has good power compared to either the WMW and FP test. We provide a fast implementation of the proposed test in an open-source software. Supplementary materials are available online.

Keywords: Behrens-Fisher problem; Mann-Whitney U test; Wilcoxon rank sum test; two-sample location problem; unequal variances.

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Figures

Figure 1
Figure 1
Relationship between Var(U) and sy. X ~ Logistic(0, 1), Y ~ Logistic(0, sy). The horizontal lines have heights Vmn, the theoretical variance of U when sy = 1.
Figure 2
Figure 2
Boxplots for the data examples.
See this image and copyright information in PMC

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