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Modified Wilcoxon–Mann–Whitney Test and Power Against Strong Null

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  • Youyi Fong
  • Ying Huang

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 under-appreciated among some practitioners is that the FP test can also be used to test the strong null like the WMW. In this article, 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 for this article are available online.

Suggested Citation

  • Youyi Fong & Ying Huang, 2019. "Modified Wilcoxon–Mann–Whitney Test and Power Against Strong Null," The American Statistician, Taylor & Francis Journals, vol. 73(1), pages 43-49, January.
    • Handle: RePEc:taf:amstat:v:73:y:2019:i:1:p:43-49
    DOI: 10.1080/00031305.2017.1328375
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    Cited by:

    1. Wosnitza, Jan Henrik, 2022. "Calibration alternatives to logistic regression and their potential for transferring the dispersion of discriminatory power into uncertainties of probabilities of default," Discussion Papers 04/2022, Deutsche Bundesbank.
    2. Justyna Zabawa & Cyprian Kozyra, 2020. "Eco-Banking in Relation to Financial Performance of the Sector—The Evidence from Poland," Sustainability, MDPI, vol. 12(6), pages 1-23, March.
    3. Liu, Jiamin & Ma, Shuangge & Xu, Wangli & Zhu, Liping, 2022. "A generalized Wilcoxon–Mann–Whitney type test for multivariate data through pairwise distance," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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