An Efficient Alternative to the Wilcoxon Signed-Ranks Test for Paired Nonnormal Data

The Wilcoxon signed-ranks test is widely used to analyze paired data when the normality assumption is doubtful and the paired-samples t test is inappropriate. An alternative procedure was investigated: It performs an independent-samples Student t test on ranks replacing the initial scores and corrects the t statistic by a function of the sample correlation coefficient. The procedure maintains the significance level for normal and eight kinds of nonnormal distributions, despite nonindependence of sample observations, and it has more power to detect alternatives than the Wilcoxon test does, especially for small sample sizes.