[R-meta] Effect Size & Variance from ANOVA when data available

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu Aug 25 18:19:21 CEST 2022

Dear Pia,

For a factor with 3 levels, there isn't just one effect size, but two (using one of the three levels as the reference level). This is like the 'multiple treatment' case discussed by Gleser & Olkin:


One could do the same for the interaction, although working this out would take a bit of effort.

But given that you have the raw data and all studies used the same response scale, I would suggest to just conduct an 'individual participant data meta-analysis' (IPDMA), that is, to analyze the raw data. Briefly, you throw all data into a single dataset with a 'study identifier' variable. Then one can add random intercepts for studies to account for the nesting of observations within studies. One might also want to add random effects for the factors, which is analogous to allowing factor main effects (and their interaction) to vary across studies.

There is an entire book on IPDMA that may be worth checking out: https://www.ipdma.co.uk/textbook


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Katharina Paul
>Sent: Friday, 19 August, 2022 12:16
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Effect Size & Variance from ANOVA when data available
>Dear all,
>I have a question on how to calculate (Standardised) Effect Sizes and
>Sampling Variance for the effects tested in an ANOVA (3x3, checking main
>effects and interactions).
>Unfortunately, I could not find any details on this (as most info was on
>correlations or condition differences).
>The good thing is that I have the single-subject data from the studies so I
>could calculate everything I need (instead of estimating it) . The scale of
>the data (and number of factors tested) is the same across them.
>However I don't know what to calculate to run the Meta-Analysis and hope
>you can help me out here!
>I hope this question is appropriate,
>Thanks so much,

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