[R-meta] Meta-Analysis using different correlation coefficients

[Lena Pollerhoff]

Hello,

We are currently conducting a meta-analysis based on correlation coefficients.
We have received a huge amount of raw datasets, so that we are able to calculate effect sizes/correlations coefficients on our own for many datasets, and  we have other correlations extracted from the original pubs. Therefore I have a couple of questions:

1. If one variable is dichotomous and the other variable is continuous but not normally distributed, what kind of coefficient should be calculated? We’d go for point-biserial if the variable is naturally dichotomous (not artificially dichotomized), and for biserial correlation if the dichotomous variable was artificially dichotomized, but are worried that both require normal distribution of the continuous variable? 

2. We are wondering how to best integrate person’s product moment correlation coefficients (both continuous, normally distributed variables), (point-) biserial correlation coefficients (for 1 (artificial) dichotomous and 1 continuous variable) and spearman rang correlation coefficients (for non-parametric, both continuous variables) in one meta-analysis? Just use the raw values? Or is it better to transform them in a homogenous way (I’ve read Fisher’s z makes less sense for anything else than Pearson’s r as a variance-stabilizing procedure?)? Can spearman rho be converted using fisher’s z transformation? I’ve also read that it is not advisable to include product-moment correlation and point-biserial correlation in one meta-analysis, is there a way to convert the point-biserial correlation to something that can be integrated with Pearson’s r and Spearman’s rho?

3. I have multiple effect sizes within one sample and I want to aggregate them, how do I define rho in the aggregate function from the metafor package? Is it possible to calculate rho based on the raw datasets? Or would it better to think in a conservative way and assume perfect redundancy (i.e., rho = 0.9)?

Thanks in advance for your time and effort!
Best,
Lena