Issues in Using Wilcoxon Rank Sum Test and Hodges-Lehmann CI

• Activity Number: 668
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Ruji Yao*+ and Yijie Zhou and Bo Yang and Jinglan Pei and Wenling Kuo
• Companies: Merck Research Laboratories and Merck Research Laboratories and Merck Research Laboratories and Merck Research Laboratories and Merck Research Laboratories
• Keywords: Wilcoxon Rank Sum Test ; Hodges-Lehmann CI ; Median

Abstract

Wilcoxon rank sum test and Hodges-Lehmann confidence interval are often used to compare the treatment effects between two groups when data are not normally distributed. Three statistics are typically reported together for statistical inference of the between-group difference: point estimator as the difference between group medians; p-value based on Wilcoxon rank sum test; and confidence interval using Hodges-Lehmann method. In most cases, these statistics yield consistent results. In this article, we will present an example where the results from these three statistics are not entirely consistent. Motivated by this example, we investigate the relation among the three statistics, and more importantly the underlying assumption for the theoretical consistency among the three statistics. We reveal that Wilcoxon rank sum test and Hodges-Lehmann confidence interval are based on median of the difference between two groups, rather than on the difference between two group medians. In addition, we propose alternative analysis approaches based on bootstrap method and contingency tables as partial solutions to address such inconsistency.