Default Bayes factors for ANOVA designs

Rouder, Jeffrey N., Morey, Richard D. ORCID: https://orcid.org/0000-0001-9220-3179, Speckman, Paul L. and Province, Jordan M. 2012. Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology 56 (5) , pp. 356-374. 10.1016/j.jmp.2012.08.001

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Abstract

Bayes factors have been advocated as superior to pp-values for assessing statistical evidence in data. Despite the advantages of Bayes factors and the drawbacks of pp-values, inference by pp-values is still nearly ubiquitous. One impediment to the adoption of Bayes factors is a lack of practical development, particularly a lack of ready-to-use formulas and algorithms. In this paper, we discuss and expand a set of default Bayes factor tests for ANOVA designs. These tests are based on multivariate generalizations of Cauchy priors on standardized effects, and have the desirable properties of being invariant with respect to linear transformations of measurement units. Moreover, these Bayes factors are computationally convenient, and straightforward sampling algorithms are provided. We cover models with fixed, random, and mixed effects, including random interactions, and do so for within-subject, between-subject, and mixed designs. We extend the discussion to regression models with continuous covariates. We also discuss how these Bayes factors may be applied in nonlinear settings, and show how they are useful in differentiating between the power law and the exponential law of skill acquisition. In sum, the current development makes the computation of Bayes factors straightforward for the vast majority of designs in experimental psychology.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Psychology
Subjects:	B Philosophy. Psychology. Religion > BF Psychology
Publisher:	Elsevier
ISSN:	0022-2496
Last Modified:	27 Oct 2022 10:07
URI:	https://orca.cardiff.ac.uk/id/eprint/68951

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