A Relative Measure of Effect Size for Paired Data Generalizing the Wilcoxon Matched-Pairs Signed-Ranks Test Statistic

• Activity Number: 610
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: WNAR
• Author(s): Robert Gordon Newcombe*+
• Companies: Cardiff University
• Keywords: effect size ; paired ; Wilcoxon statistic ; ridit ; confidence interval ; 1-parameter logistic regression

Abstract

The Wilcoxon matched-pairs signed-ranks test statistic can be re-expressed as a relative measure of effect size psi. Psi is formulated in terms of ridit ranks 0.5, 1.5 ..., n-0.5, not 1, 2, ..., n. Extreme values +1 or -1 occur when all differences have the same sign. Psi is conveniently modeled by 1-parameter logistic regression with back-transformation to the scale of psi. The MLE coincides with the empirical estimate. Likelihood and score CIs are derived in the usual manner. Coverage and width properties are evaluated by simulation using symmetrical and skewed beta models. Both methods tend to give slightly anticonservative coverage, the score interval is preferable in most parts of the parameter space. The usual trade-off between coverage and narrowness applies generally, not invariably. The likelihood interval, readily obtained using SAS, has more symmetrical coverage properties.