convert_ma: Function to convert meta-analysis of correlations to d values...

In jadahlke/psychmeta: Psychometric Meta-Analysis Toolkit

Function to convert meta-analysis of correlations to d values or vice-versa

Description

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.

Usage

convert_ma(ma_obj, ...)

convert_meta(ma_obj, ...)

Arguments

ma_obj	A meta-analysis object of class r_as_r, d_as_d, r_as_d, or d_as_r
...	Additional arguments.

Details

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}}

Value

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).

jadahlke/psychmeta documentation built on Feb. 11, 2024, 9:15 p.m.