Better Scrutiny of the Wilcoxon-Mann-Whitney Test

• Activity Number: 622
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): George Divine*+
• Companies: Henry Ford Hospital
• Keywords: Wilcoxon-Mann-Whitney test ; Fligner-Policello test ; Brunner-Munzel test ; robustness

Abstract

A 2009 Statistics in Medicine paper by Fagerland and Sandvik documents limitations of the Wilcoxon-Mann-Whitney (WMW) test when employed as a test of medians or means. However, the simulations reported in that paper failed to include the natural WMW null hypothesis: P(X< Y)=0.5. For that situation, (and contrary to the authors' implications), simulations demonstrate that the WMW test does indeed perform well as a test of P(X< Y)=0.5, even when the distributions being compared are skewed, as long as the sample sizes and variances of the two groups being compared are similar. Additionally, as their originators intended, the Fligner-Policello and Brunner-Munzel variations of the WMW test (which take into account potentially unequal variances), appear to perform well when variances and sample sizes are unequal. The Brunner-Munzel test performed best in the circumstances covered in the simulations undertaken for this report.