# Is it more accurate to convert t-test statistic to pearson's r or means and SDs to cohen's d to pearson's r when extracting data for a meta-analysis?

I am completing a meta analysis and the common metric I am using is pearson's r. For studies that report comparisons of means rather than correlations should I convert the t-test statistic the author has reported into r using the equations I have seen in many meta-analysis books, or is it more accurate to use the means and standard deviations they have reported in order to calculate cohen's d effect size and then convert this to pearson's r (also well established in the meta analysis literature)?

I would suggest using biserial correlation, which you can generate from the means and standard deviations.

Check out metafor::escalc(), specifically the argument measure = "RBIS". That will return a biserial correlation and a variance.

I received this advice from the R meta-analysis email list (https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis), which is active and full of very smart people.

You can also check out "Estimation of the biserial correlation and its sampling variance for use in meta-analysis" by Jacobs & Viechtbauer (2017) in Research Synthesis Methods as a reference for this.

When I did a meta-analysis, I then transformed that biserial correlation using the standard r-to-z transformation and used the delta method to transform the variance. Example code for that variance transformation is:

zvar <- function(yi, vi) {
vi/(1 - yi^2)^2
}


where yi is the biserial correlation and vi is the variance, both returned from metafor::escalc()

• If the study does not report the mean and SD, is it then preferable to calculate r by converting the effect size they have reported (e.g. cohen's d to r) or to calculate r from a significance test value they have reported (e.g. from a t-test)? – Bobby Feb 24 '18 at 20:44