Component Analysis When Testing for Fixed Effects in Unbalanced ANOVAs

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, 2025, vol. 8, issue 2, 1-14

Abstract: In possibly unbalanced fixed effects in ANOVAs, we examine both parametric and nonparametric tests for main and two-way interaction effects when the levels of each factor may be ordered or unordered. For main effects, we decompose the factor sum of squares into one degree of freedom components involving contrasts, albeit not necessarily orthogonal contrasts. For interactions, we develop what we call coefficients. These are an extension of part of the interaction sum of squares in potentially unbalanced designs. They may be used to test nonparametrically for focused interaction effects. The tests developed here provide focused and objective assessments of main and interaction effects and augment traditional methods.

Keywords: degree-degree coefficients; exploratory data analysis; orthogonal polynomials; level-degree coefficients; level-level coefficients; pairwise comparisons; unbalanced designs (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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