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

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...

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Bibliographic Details
Published in:Stats (Basel, Switzerland) Switzerland), 2024-06, Vol.7 (2), p.481-491
Main Authors: Rayner, J. C. W., Livingston, G. C.
Format: Article
Language:English
Subjects:
balanced and unbalanced designs
Eigenvalues
Eigenvectors
exploratory data analysis tool
orthogonal contrasts
orthogonal polynomials
pairwise comparisons
Statistics
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Summary: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.
ISSN:2571-905X
2571-905X
DOI:10.3390/stats7020029