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I have gathered data from a number of studies where two different groups have performed the same task. For each group in each study, I have number of observations as well as the mean and standard deviation of the performance.

I've been comparing the difference in group means using standard meta-analytic methods, where you convert your data to a Cohen's d as well as a variance for that Cohen's d for each study. However, now I'd like to investigate whether the two groups differ in terms of their respective variances, that is, whether one group has a more narrow distribution of scores around the mean than the other.

I know there are tests of equal variance when it comes to single experiments, but I'm not aware of any meta-analytic approaches for investigation this question. Are there any?

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You probably want to use the log of the ratios of the variances. See

Nakagawa, S., Poulin, R., Mengersen, K., Reinhold, K., Engqvist, L., Lagisz, M., & Senior, A. M. (2015). Meta-analysis of variation: Ecological and evolutionary applications and beyond. Methods in Ecology and Evolution, 6, 143–152.

Disclaimer: I have never done this myself and the reference is taken from the documentation of Wolfgang Viechtbauer's metafor package.

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