# How do I calculate the standard error of a converted effect size (r to d)?

Background : I am doing a meta-analysis using Cohen's d, using R (package = metafor; function = rma). I am calculating the effect size of having a higher BMI on social cognition abilities. Some studies have a high BMI group and a control "normal weight" control group, and the effect size calculation is pretty straightforward. For studies that used a single group design and reported a simple bivariate r-stats between BMI and my "outcome" measure (social cognition), I used an r-to-d conversion using the following formula:

d = 2r/ √(1-r2)

[Friedman, H. (1968). "Magnitude of experimental effect and a table for its rapid estimation," Psychological Bulletin, 70(4): 245-251.]

My question . (1) Firstly, I'm hoping I used the r-to-d equation appropriately and that it makes sense that I'm doing this. Any feedback on this point and my methodology would be helpful!
(2) Secondly, in order to complete my meta-analysis, I need to calculate a standard error (SE) of the converted (r to d) effect sizes. Most standard error equations assume the study design uses two groups, rather than a single group study design. I just know r-values, sample size, and means/SDs of BMI & the outcome (social cognition) variables. Does anyone know how to calculate the standard error in this situation? The solution could be a programming function someone knows of and/or just an equation.

Thanks so much!!

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