Wilcoxon-Mann-Whitney or T-Test? On Assumptions for Hypothesis Tests and Multiple Interpretations of Decision Rules

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael P. Fay*+
• Companies: National Institute of Allergies and Infectious Diseases
• Keywords: Hypothesis test ; Wilcoxon rank sum test ; Behrens-Fisher problem ; Welch's t-test ; permutation test ; Location shift

Abstract

Traditionally, a decision rule is coupled with only one set of assumptions which demarcates the null and alternative hypotheses. Here we associate a single decision rule with several sets of assumptions, each of which can define a valid or approximately valid test when associated with the decision rule. We call such a decision rule, a multiple perspective decision rule (MPDR), with each perspective providing a different interpretation to the same accept/reject decision. This allows the consumer of the decision rule to try on several sets of assumptions depending on perspective, all without recalculating the p-value associated with the decision rule. We explore this idea by reviewing the many hypotheses that have been associated with the two sample t-tests and the Wilcoxon-Mann-Whitney test, and show how the MPDR outlook may be helpful in this situation.