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

[Filippo Gambarota]

Thank you as always Wolfgang.
I'm wondering if this could work. Assuming that all studies used a common
measure (let's say reaction times on a computer task). Ideally, If I have
the interaction parameter and the standard error (e.g., from a mixed model
output) I could directly use that measure.
Alternatively and following your suggestion I should standardize the
numerator using the same quantity ( sqrt(MSE) ) but this quantity is
influenced by the repeated measure design (i.e., the correlation).
Thank you

On Mon, 8 Aug 2022 at 14:53, Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> 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
>


-- 
*Filippo Gambarota*
PhD Student - University of Padova
Department of Developmental and Social Psychology
Website: filippogambarota <https://filippogambarota.netlify.app/>
Research Group: Colab <http://colab.psy.unipd.it/>   Psicostat
<https://psicostat.dpss.psy.unipd.it/>

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