title: Model comparison in ANOVA.
abstract: Analysis of variance (ANOVA), the workhorse analysis of experimental designs, consists of F-tests of main effects and interactions. Yet, testing, including traditional ANOVA, has been recently critiqued on a number of theoretical and practical grounds. In light of these critiques, model comparison and model selection serve as an attractive alternative. Model comparison differs from testing in that one can support a null or nested model vis-a-vis a more general alternative by penalizing more flexible models. We argue this ability to support more simple models allows for more nuanced theoretical conclusions than provided by traditional ANOVA F-tests. We provide a model comparison strategy and show how ANOVA models may be reparameterized to better address substantive questions in data analysis.
authors.affiliation: University of Missouri, Columbia, MO, 65211, USA. rouderj@missouri.edu.
authors.forename: Jeffrey N
authors.initials: JN
authors.lastname: Rouder
authors.affiliation: University of Missouri, Columbia, MO, 65211, USA.|CARFAX, inc., Columbia, MO, 65201, USA.
authors.forename: Christopher R
authors.initials: CR
authors.lastname: Engelhardt
authors.affiliation: University of Stirling, Stirling, FK9 4LA, UK.
authors.forename: Simon
authors.initials: S
authors.lastname: McCabe
authors.affiliation: Cardiff University, Cardiff, CF10 3XQ, UK.
authors.forename: Richard D
authors.initials: RD
authors.lastname: Morey
mesh_terms: D000704:Analysis of Variance; D035843:Biomedical Research; D006801:Humans; D015233:Models, Statistical
keywords: ANOVA; Interactions; Model comparison; Order-restricted inference; Statistical models