A Quantile Shift Approach To Main Effects And Interactions In A 2-By-2 Design

TL;DR

This paper extends shift function techniques to analyze main effects and interactions in 2-by-2 designs, using quantile comparisons and bootstrap methods for detailed distributional insights.

Contribution

It introduces two novel approaches for quantile-based analysis of effects and interactions in 2-by-2 experimental designs, utilizing the Harrell-Davis estimator and bootstrap.

Findings

Both methods effectively detect distributional differences.

Simulation results show controlled false positive rates.

Methods outperform traditional mean-based comparisons.

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. For both methods, we propose an implementation using the Harrell-Davis quantile estimator, used in conjunction with a percentile bootstrap approach. We report results of simulations of false and true positive rates.