A New Method for Testing Interaction in Unreplicated Two-Way Analysis of Variance

Abstract

For a two-way ANOVA table, with a single observation per cell, the standard approach is to assume that interaction between the two factors is negligible, and to base inferences about the main factors on the model without interaction. But there is no totally satisfactory method for testing if interaction can be ignored. The classical approach is to specify a functional form for the interaction terms, involving a small number of parameters, and then use an appropriate test. But, such tests have low power if the functional form is inappropriate. This has led researchers to propose tests which do not assume a specific form for the interactions. In this article, we present a new approach for testing interaction which also does not assume a specific form for the interaction. This approach is fairly simple and flexible, and its usefulness is illustrated with several examples. We also present a general result which shows that there is no test of interaction with good power properties against all types of interaction.

Keywords:

• ANOVA
• F-distribution
• Interaction
• Linear model
• Power
• P-value

Mathematics Subject Classification:

• 62J10
• 62K10

Acknowledgments

We are grateful to Dr. Moradshahi, Department of Biology, Shiraz University, for providing the data in Example 2.1. We are also grateful to a referee for his valuable comments. This work was supported by the Research Council of Shiraz University.