{"title":"Modified Wilcoxon-Mann-Whitney Test and Power against Strong Null.","authors":"Youyi Fong, Ying Huang","doi":"10.1080/00031305.2017.1328375","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00031305.2017.1328375","citationCount":"14","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Statistician","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00031305.2017.1328375","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/5/10 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 14
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.
期刊介绍：
Are you looking for general-interest articles about current national and international statistical problems and programs; interesting and fun articles of a general nature about statistics and its applications; or the teaching of statistics? Then you are looking for The American Statistician (TAS), published quarterly by the American Statistical Association. TAS contains timely articles organized into the following sections: Statistical Practice, General, Teacher''s Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor.
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