Some Modifications on the Application of the Exact Wilcoxon–Mann–Whitney Test

Abstract

Despite of its lasting popularity, the application of the exact Wilcoxon–Mann–Whitney (WMW) test has never been free of inappropriateness or unnecessary inefficiency in practice. The goal of this paper is to exemplify some modifications that can be conducted to the application of the exact WMW test in small sample cases to achieve more precise and more powerful estimations and tests. At first, we propose a modified procedure to replace the current generalized Hodges–Lehmann procedure in Proc-StatXact 5^® to correctly derive the exact WMW test based interval estimates for the shift parameter in the presence of ties. We then propose a variance adjustment for the exact WMW test to achieve more powerful exact test as the variance adjusted WMW statistic has less discrete distribution than the conventionally unadjusted WMW statistic. We find that the proposed variance adjusted exact method is noticeably less conservative than the conventional exact WMW method, especially when ties in observation are not very heavy.

Key Words:

• Discreteness
• Hodge–Lehmann Procedure
• Permutation
• Small sample
• Ties
• Variance adjusted statistic

Acknowledgments