A Quantile Shift Approach to Main Effects and Interactions in a 2-by-2 Design

Abstract

When comparing two independent groups, shift functions are basically techniques that compare multiple quantiles rather than a single measure of location, the goal being to get a more detailed understanding of how the distributions differ. Various versions have been proposed and studied. This paper deals with extensions of these methods to main effects and interactions in a between-by-between, 2-by-2 design. Two approaches are studied, one that compares the deciles of the distributions, and one that has a certain connection to the Wilcoxon–Mann–Whitney method. There are many quantile estimators, but for reasons summarized in the paper, the focus is on using the Harrell–Davis quantile estimator used in conjunction with a percentile bootstrap method. Included are results comparing two methods aimed at controlling the probability of one or more Type I errors.

Keywords

• shift function
• deciles
• factorial design
• interaction
• quantile estimation