[R-meta] 2*2 ANOVA and meta-analysis

robert ross robross45 at yahoo.com.au
Mon Dec 4 18:29:16 CET 2017

Dear all,

I’m performing a meta-analysis using the standardised mean difference. In most cases, effect sizes are calculated by comparing a control group and an experimental group using a t-test. However, a small number of relevant studies have two manipulations and use a 2*2 between subjects factorial ANOVA to test for a predicted crossover interaction. Popular effect sizes calculators for two way ANOVAs include a “treatment factor” and an “other factor” and generate an effect size in terms of the treatment factor. For example:


With the studies I’m examining it doesn’t seem appropriate to treat one of the main effects as pertaining to the “treatment factor” and the other as pertaining to the “other factor” because both factors were of equal theoretical interest and both were manipulated.

Is it possible (and appropriate) to use the interaction term from the studies with 2*2 factorial design in a meta-analysis that focuses on studies with simpler t-test based designs? If so, how could this be done? If it would not possible or appropriate, are there any alternatives? In some cases I have access to raw data, so I would be able to calculate effect sizes not reported in papers.

Any comments (or pointers to relevant literature) would be much appreciated.


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