15 - Rank-based and nonparametric methods

Abstract

This chapter focuses on nonparametric and rank-based methods and comparison of two independent groups. Wilcoxon–Mann–Whitney test is the standard rank-based method for comparing two independent groups that is called the Wilcoxon–Mann–Whitney (WMW) test. It was originally derived by Wilcoxon and later it was realized that Wilcoxon's method was the same as a procedure proposed by Mann and Whitney. Sometimes the Wilcoxon–Mann–Whitney test is described as a method for comparing medians. S-PLUS function WMW: using the data stored in the S-PLUS variables x and y, the S-PLUS function WMW (x, y) computes the significance level of the Wilcoxon–Mann–Whitney test. The chapter also discusses ties and heteroscedasticity. A practical concern is that if groups differ, then under general circumstances the wrong standard error is being used by the Wilcoxon–Mann–Whitney test that can result in relatively poor power and an unsatisfactory confidence interval. S-PLUS function cid: The S-PLUS function cid performs the calculations for two independent groups. The Brunner–Munzel procedure: an alternative approach to both tied values and heteroscedasticity stems from the concept from Brunner and Munzel, which is based on midranks for handling tied values.