I want to meta-analyze the interaction effect of a 2x2 ANOVA.

(I am not talking about an interaction in the meta-regression, as in this question but about an interaction as the focal effect that should be meta-analytically summarized).

What is the best way to code the interaction effect size for a subsequent meta-analysis? (preferably in the metafor package)

  • $\begingroup$ What kind of information do you have? Means, SDs, and cell sizes of all four cells? Just F-values and the degrees of freedom? Do you want a 'standardized' effect size? $\endgroup$ – Wolfgang Nov 25 '14 at 21:16
  • $\begingroup$ I have both situations, as you wrote: a) Means, SDs, sample size and b) only F and dfs. "Standardized": If possible. $\endgroup$ – Felix S Nov 26 '14 at 18:48

In a 2x2 ANOVA with factors A and B you can easily turn it into one number. Calculate the effect for A, the effect for B, and subtract them. And, of course, you need the error term for the interaction. This may not be included but can be derived in the case of a reported F and means. Going through ANOVA hand calculations you can derive the numerator to the F from means and N and therefore the MSE can also be derived.

  • $\begingroup$ Thanks. I hoped that someone has done these hand calculations before and could provide me the final formulas ;-) $\endgroup$ – Felix S Nov 26 '14 at 18:50

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