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

## 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

 1 2 3 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: \mjdeqnd=\fracr\sqrt\frac1p\left(1-p\right)\sqrt1-r^2(sqrt(1 / (p * (1-p))) * r) / sqrt(1 - r^2)

The formula used to convert d values to correlations is: \mjdeqnr=\fracd\sqrtd^2+\frac1p\left(1-p\right)d / sqrt(1 / (p * (1-p)) + d^2)

To approximate the variance of correlations from the variance of d values, the function computes: \mjdeqnvar_r\approx a_d^2var_dvar_r ~= a_d^2 * var_d where \mjeqna_da_d is the first partial derivative of the d-to-r transformation with respect to d: \mjdeqna_d=-\frac1\left[d^2p\left(1-p\right)-1\right]\sqrtd^2+\frac1p-p^2a_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: \mjdeqnvar_d\approx a_r^2var_rvar_d ~= a_r^2 * var_r where \mjeqna_ra_r is the first partial derivative of the r-to-d transformation with respect to r: \mjdeqna_r=\frac\sqrt\frac1p-p^2\left(1-r^2\right)^1.5a_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 June 1, 2021, 9:13 a.m.