Testing for Level–Degree Interaction Effects in Two-Factor Fixed-Effects ANOVA When the Levels of Only One Factor Are Ordered

J. C. W. Rayner () and G. C. Livingston
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J. C. W. Rayner: National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia
G. C. Livingston: School of Information and Physical Sciences, University of Newcastle, Newcastle, NSW 2308, Australia

Stats, 2024, vol. 7, issue 2, 1-11

Abstract: In testing for main effects, the use of orthogonal contrasts for balanced designs with the factor levels not ordered is well known. Here, we consider two-factor fixed-effects ANOVA with the levels of one factor ordered and one not ordered. The objective is to extend the idea of decomposing the main effect to decomposing the interaction. This is achieved by defining level–degree coefficients and testing if they are zero using permutation testing. These tests give clear insights into what may be causing a significant interaction, even for the unbalanced model.

Keywords: balanced and unbalanced designs; exploratory data analysis tool; orthogonal contrasts; orthogonal polynomials; pairwise comparisons (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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