[R-meta] effect size for interaction from mixed designs

[Viechtbauer, Wolfgang (NP)]

Dear Filippo,

yes, measures like eta-squared or omega-squared are typically not a good choice for a meta-analysis as they are directionless. As you found, one can compute effect sizes also for interactions akin to Cohen's d. But yes, the type of design does matter (in particular, with respect to how the sampling variance needs to be computed). What I describe under that link assumes we are dealing with 2x2 ANOVAs with both factors being 'between-subject' factors. Once you have a within-subject factor (either one or two of them), then the correlation between the conditions will start to play a role again. Another issue here is what we put into the denominator when standardizing. In the between-subject case above, the computations assume that we are using sqrt(MSE) from the model. If one wants to combine such effects with those from mixed/fully within designs, one needs to do something analogous there, as otherwise the effects are not comparable.

I think James Pustejovksy has something on his blog (https://www.jepusto.com) where he describes a very general method for computing d-type effect sizes. I assume this would also cover the cases above.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Filippo Gambarota
>Sent: Monday, 08 August, 2022 14:17
>To: R meta
>Subject: [R-meta] effect size for interaction from mixed designs
>
>Hello!
>I'm planning to conduct a meta-analysis focusing on interaction
>effects. Firstly I was thinking about using an interaction-specific
>effect size such as eta-squared or omega-squared. After reading some
>papers and some other posts
>(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-February/000658.html)
>now it's clear that I can simply use a cohen's d like measure to
>standardize the difference between the two simple effects. However,
>I'm wondering if the type of ANOVA-like design matters in terms of
>fully between/within or mixed. In fact, I'm pretty sure that I'll
>encounter different designs from published studies.
>Thank you!
>--
>Filippo Gambarota
>PhD Student - University of Padova
>Department of Developmental and Social Psychology
>Website: filippogambarota
>Research Group: Colab   Psicostat