Modified Wilcoxon–Mann–Whitney Test and Power Against Strong Null. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Fong, Youyi; Huang, Ying
• Is Part Of: American statistician. Volume 73:Issue 1(2019)
• Page Start: 43
• Page End: 49
• Publication Date: 2019-01-02
• Subjects: Wilcoxon rank sum test -- Mann–Whitney U test -- Behrens–Fisher problem -- Two-sample location problem -- Unequal variances; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2017.1328375
• Languages: English
• ISSNs: 0003-1305

Abstract

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.