The Wilcoxon-Mann-Whitney Procedure: What Does It Really Test?

• Activity Number: 43
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Education
• Author(s): George Divine and Anna Baron and Elizabeth Juarez-Colunga and Harry James Norton*+
• Companies: Henry Ford Health System and Univ of Colorado Denver and University of Colorado Denver and Carolinas Medical Center
• Keywords: Wilcoxon rank sum test ; Statistical Education ; Non-parametric tests ; WMWodds

Abstract

Have you ever read in an introductory statistics book that the null hypothesis for the Wilcoxon-Mann-Whitney test is that "The medians are equal"? We will present an example from a recently published randomized clinical trial where the medians of 2 groups are identical, but the p-value for the WMW test is highly statistically significant. In contrast to the potential for such an unfortunate result with the median, as noted by Ralph O'Brien and others, the WMWodds (Wilcoxon-Mann-Whitney odds) directly reflects the quantity that the rank sum procedure actually tests, and thus it can be a superior summary measure. Unlike the means and medians, the WMWodds will have a direct one-to-one correspondence to the WMW test result. Several examples will be presented demonstrating that WMWodds can go in the opposite direction from the difference in the group medians, and that the WMW test is not transitive. We will discuss how our presentation of the WMW test has been employed in both a classroom lecture and in a seminar presentation, and students' reactions.