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.

翻译：摘要：在比较两个独立组时，分位数偏移函数本质上是通过比较多个分位数而非单一位置参数来深入理解分布差异的技术。已有多种变体方法被提出和研究。本文将这些方法扩展至组间二因素二水平设计中的主效应与交互作用分析。研究采用两种方法：其一通过比较分布十分位数，其二与Wilcoxon-Mann-Whitney方法存在特定关联。对于两种方法，我们提出基于Harrell-Davis分位数估计器结合百分位数自助法的实现方案，并报告了关于假阳性率和真阳性率的模拟结果。