TL;DR
This paper reviews existing additivity tests in two-way ANOVA with one observation per cell, evaluates their performance, and proposes a modification to Tukey's test to improve its power against general interactions.
Contribution
A new modification of Tukey's additivity test is developed to better detect interactions in limited data scenarios.
Findings
Tukey and Mandel tests have low power for complex interactions
Simulation shows the modified test improves detection of interactions
All tests are implemented in R package AdditivityTests
Abstract
In this paper we discuss testing for an interaction in the two-way ANOVA with just one observation per cell. The known results are reviewed and a simulation study is performed to evaluate type I and type II risks of the tests. It is shown that the Tukey and Mandel additivity tests have very low power in case of more general interaction scheme. A modification of Tukey's test is developed to resolve this issue. All tests mentioned in the paper have been implemented in R package AdditivityTests.
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