Comparing Two Groups

Abstract

This chapter describes robust methods for comparing two distributions. Compared with traditional methods for comparing means, modern robust methods offer substantial gains in power under fairly general conditions. Included are methods for comparing both independent and dependent groups. The corresponding shift function provides a detailed sense of where the distributions differ and by how much. This is followed by methods for comparing trimmed means, M-estimators, and measures of scale, including a level robust method for comparing the usual variances. Recent advances when measuring effect size are described. Modern rank-based methods are covered as well that have the advantage of using a correct estimate of the standard error even when the distributions differ. The Wilcoxon–Mann–Whitney test uses a correct estimate of the standard when the distributions being compared are identical. But under general conditions, it uses the wrong standard, which can negatively impact power and result in inaccurate confidence intervals. Comparing two independent binomials is covered as well. The final section covers methods for comparing dependent groups. Recent results on handling missing values are covered. Relevant R functions are described and illustrated.Level robust methods, robust estimators, Bootstrap methods, tied values, effect size, rank-based methods, binomial distribution.