# convert_ma: Function to convert meta-analysis of correlations to d values... In psychmeta: Psychometric Meta-Analysis Toolkit

 convert_ma R Documentation

## 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:

(sqrt(1 / (p * (1-p))) * r) / sqrt(1 - r^2)

The formula used to convert d values to correlations is:

d / sqrt(1 / (p * (1-p)) + d^2)

To approximate the variance of correlations from the variance of d values, the function computes:

var_r ~= 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 = -1 / ((d^2 * (p - 1) * p - 1) * sqrt(d^2 + 1 / (p - p^2)))

To approximate the variance of d values from the variance of correlations, the function computes:

var_d ~= 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 = sqrt(1 / (p - p^2)) / (1 - r^2)^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).

psychmeta documentation built on Aug. 26, 2022, 5:14 p.m.