Consider a two-way ANOVA design. Generally, interactions are characterized by the difference between two measures of effect size. Typically the measure of effect size is based on the difference between measures of location, with the difference between means being the most common choice. This paper deals with extending extant results to two robust, heteroscedastic measures of effect size. The first is a robust, heteroscedastic analogue of Cohen's d. The second characterizes effect size in terms of the quantiles of the null distribution. Simulation results indicate that a percentile bootstrap method yields reasonably accurate confidence intervals. Data from an actual study are used to illustrate how these measures of effect size can add perspective when comparing groups.

中文翻译：

---

双向方差分析：基于效应大小的稳健测量的交互作用推论

考虑一个双向 ANOVA 设计。通常，交互作用的特征在于两个效应大小测量值之间的差异。通常，效应大小的测量基于位置测量之间的差异，其中均值之间的差异是最常见的选择。本文涉及将现有结果扩展到两个稳健的、异方差的效应大小度量。第一个是 Cohen 的d的稳健的异方差类比。第二个根据零分布的分位数来表征效应大小。模拟结果表明，百分位自举法产生相当准确的置信区间。来自实际研究的数据用于说明这些效应量测量如何在比较组时增加视角。