Nonparametric procedures are more powerful for detecting interaction in two-way ANOVA when the data are non-normal. In this paper, we compute null critical values for the aligned rank-based tests (APCSSA/APCSSM) where the levels of the factors are between 2 and 6. We compare the performance of these new procedures with the ANOVA F-test for interaction, the adjusted rank transform test (ART), Conover's rank transform procedure (RT), and a rank-based ANOVA test (raov) using Monte Carlo simulations. The new procedures APCSSA/APCSSM are comparable with existing competitors in all settings. Even though there is no single dominant test in detecting interaction effects for non-normal data, nonparametric procedure APCSSM is the most highly recommended procedure for Cauchy errors settings.

翻译：当数据非正态时，非参数方法在检测双向方差分析中的交互作用方面更具效力。本文计算了因子水平数介于2至6时对齐秩次检验（APCSSA/APCSSM）的零假设临界值。通过蒙特卡洛模拟，我们将这些新方法的性能与交互作用的ANOVA F检验、调整秩变换检验（ART）、Conover秩变换方法（RT）以及基于秩的方差分析检验（raov）进行比较。在所有设定下，新方法APCSSA/APCSSM均与现有竞争方法表现相当。尽管在非正态数据中检测交互效应时不存在单一的最优检验，但对于柯西误差设定，非参数方法APCSSM是最为推荐的方法。