A tutorial on using the paired t test for power calculations in repeated measures ANOVA with interactions

• Published in: Behavior research methods Vol. 55; no. 5; pp. 2467 - 2484
• Main Authors: Langenberg, Benedikt, Janczyk, Markus, Koob, Valentin, Kliegl, Reinhold, Mayer, Axel
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2023; Springer Nature B.V
• Subjects: Behavioral Science and Psychology; Cognitive Psychology; Psychology; Within-subjects design; Interactions; Repeated measures ANOVA; Power; Effect sizes
• ISSN: 1554-3528; 1554-351X; 1554-3528
• DOI: 10.3758/s13428-022-01902-8

The a priori calculation of statistical power has become common practice in behavioral and social sciences to calculate the necessary sample size for detecting an expected effect size with a certain probability (i.e., power). In multi-factorial repeated measures ANOVA, these calculations can sometimes be cumbersome, especially for higher-order interactions. For designs that only involve factors with two levels each, the paired t test can be used for power calculations, but some pitfalls need to be avoided. In this tutorial, we provide practical advice on how to express main and interaction effects in repeated measures ANOVA as single difference variables. In particular, we demonstrate how to calculate the effect size Cohen’s d of this difference variable either based on means, variances, and covariances of conditions or by transforming η p 2 or ω p 2 from the ANOVA framework into d . With the effect size correctly specified, we then show how to use the t test for sample size considerations by means of an empirical example. The relevant R code is provided in an online repository for all example calculations covered in this article.