Can an effect size be calculated for an interaction effect in general and more specifically using the F-statistic and its associated degrees of freedom? If yes, should this be done and what is the appropriate interpretation of the effect size given the nature of interaction effects? Initially, I assumed the answer is "no." However, a quick Google search turned up statements about computing effect sizes for interaction terms. Any assistance in clarifying this issue will be greatly appreciated!
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2 Answers
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Looking into classic old texts (like Geoffrey Keppel's Design and Analysis: A Researcher's Handbook and Fredric Wolf's Meta-Analysis: Quantitative Methods for Research Synthesis), I've seen several options, including omega, phi, and the square of each. But most widely interpretable and simplest to obtain from most software packages' output is the incremental contribution that the interaction makes to r-squared. Partial eta squared (explained variance not shared with any other predictor in the model) is another option, and in fact for an interaction tested in a sequential model, it should be the same as the increment in r-squared. I realize I'm not answering your question about specifically using F and df; if that is that essential to you maybe others can address it. Wolf shows how to convert F to r for the 2-group case only, and I'm not the strongest when it comes to formulas.
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Yes, an effect size for an interaction can be computed, though I don't think I know any measures of effect size that you can compute simply from the F and df values; usually you need various sums-of-squares values to do the computations. If you have the raw data, the "ezANOVA" function in the "ez" package for R will give you generalized eta square, a measure of effect size that, unlike partial-eta square, generalizes across design types (eg. within-Ss designs vs between-Ss designs).
answered Feb 3, 2011 at 0:02