Nonparametric tests for interaction in two-way ANOVA with balanced replications

TL;DR

This paper evaluates nonparametric rank-based tests for detecting interaction in two-way ANOVA with balanced data, comparing their performance to traditional and other rank-based tests through simulations.

Contribution

It introduces null critical values for aligned rank-based tests (APCSSA/APCSSM) and compares their effectiveness with existing methods in non-normal data scenarios.

Findings

APCSSA/APCSSM perform comparably with existing tests.

No single test dominates in all non-normal settings.

APCSSM is recommended for Cauchy error distributions.

Abstract

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.