On the Use of the Shapiro-Wilk Test in Two-Stage Adaptive Inference for Paired Data

• Activity Number: 468
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Weiwen Miao*+ and Joseph L. Gastwirth and Boris Freidlin
• Companies: Macalester College and George Washington University and National Cancer Institute
• Keywords: Adaptive tests ; Paired data ; power robustness ; Shapiro-Wilk test

Abstract

Paired data arises in a wide variety of applications where the underlying distribution of the paired differences is often unknown. When the differences are normally distributed, the t-test is optimum. If the differences are not normal, the t-test can have substantially less power than the appropriate optimum test that depends on the unknown distribution. In textbooks, when the normality of the differences is questionable, typically the nonparametric Wilcoxon signed-rank test is suggested. An adaptive procedure that uses the Shapiro-Wilk test of normality to decide whether to use the t-test or the Wilcoxon signed-rank test has been employed in several studies. The U.S. Environmental Protection Agency (EPA) introduced another approach: applying both the sign and t-tests on the paired differences in its analysis, the alternative hypothesis is accepted if either test is significant. We investigate the statistical properties of the current adaptive test and the EPA's method and suggests an alternative adaptive test. The new procedure is easy to use and generally has higher empirical power, especially when the differences are heavy-tailed, than the currently used methods.