Takes a meta-analysis class object of d values or correlations (classes r_as_r, d_as_d, r_as_d, and d_as_r; second-order meta-analyses are currently not supported) as an input and uses conversion formulas and Taylor series approximations to convert effect sizes and variance estimates, respectively.
convert_ma(ma_obj, ...)convert_meta(ma_obj, ...)
A meta-analysis object of class r_as_r, d_as_d, r_as_d, or d_as_r
Additional arguments.
A meta-analysis converted to the d value metric (if ma_obj was a meta-analysis in the correlation metric) or converted to the correlation metric (if ma_obj was a meta-analysis in the d value metric).
The formula used to convert correlations to d values is: $$d=\frac{r\sqrt{\frac{1}{p\left(1-p\right)}}}{\sqrt{1-r^{2}}}$$
The formula used to convert d values to correlations is: $$r=\frac{d}{\sqrt{d^{2}+\frac{1}{p\left(1-p\right)}}}$$
To approximate the variance of correlations from the variance of d values, the function computes: $$var_{r}\approx a_{d}^{2}var_{d}$$ where \(a_{d}\) is the first partial derivative of the d-to-r transformation with respect to d: $$a_{d}=-\frac{1}{\left[d^{2}p\left(1-p\right)-1\right]\sqrt{d^{2}+\frac{1}{p-p^{2}}}}$$
To approximate the variance of d values from the variance of correlations, the function computes: $$var_{d}\approx a_{r}^{2}var_{r}$$ where \(a_{r}\) is the first partial derivative of the r-to-d transformation with respect to r: $$a_{r}=\frac{\sqrt{\frac{1}{p-p^{2}}}}{\left(1-r^{2}\right)^{1.5}}$$