Bayesian meta-analysis: effect sizes
I would like to run a Bayesian meta-analysis on my results from three studies. I am aware that I need an effect size, standard error of the effect size, and upper and lower confidence intervals for each study in order to achieve this. But I have a question about this: from my Bayesian ANCOVAs, there doesn't seem to be an output table that provides all of the details I need. Can I use R squared as a standardised effect size? If I do, the 'model averaged R squared' output gives me the mean and intervals, but not the standard error. I can calculate the standard error from the intervals – is this the correct approach? If not, what is the alternative?
Many thanks,
Eugene
Comments
Hi Eugene,
I think the assumptions underlying standard meta-analytic models are violated if you use the output of any Bayesian model-averaged analysis per study. More generally, using R-squared as an effect size in meta-analysis is not appropriate because standard frequentist and Bayesian meta-analytic models require that each study provides a normally-distributed effect size (e.g., Fisher's z, Cohen's d or log odds ratio).
Maybe you can use a standard frequentist ANCOVA per study and extract an appropriate effect size such as Cohen's d as discussed here: https://www.researchgate.net/post/Calculating_cohens_d_from_ANCOVA_what_is_R_in_the_formula
I never applied meta-analysis in an ANCOVA context, but I think it matters whether you want to aggregate the effect of the discrete factor, the effect of the continuous covariate, or both.
Best,
Daniel
Ok thanks Daniel