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arXiv · 2305.12366

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

Rand R. Wilcox·Guillaume A. Rousselet
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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.

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Rand R. Wilcox, Guillaume A. Rousselet. 2023-05-21. A Quantile Shift Approach To Main Effects And Interactions In A 2-By-2 Design. https://arxiv.org/abs/2305.12366

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