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：在比较两个独立组群时，偏移函数本质上是通过比较多个分位数而非单一位置度量来深入理解分布差异的技术。目前已有多类变体被提出并研究。本文重点探讨这些方法在组间二乘二设计中主效应与交互效应的扩展应用。研究采用两种方法：一种比较分布十分位数，另一种与Wilcoxon-Mann-Whitney方法存在特定关联。针对这两种方法，我们提出基于Harrell-Davis分位数估计器与百分位数引导法相结合的实施方案，并展示了关于假阳性率与真阳性率的模拟实验结果。