# correct_d_bias: Correct for small-sample bias in Cohen's _d_ values In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

Corrects a vector of Cohen's d values for small-sample bias, as Cohen's d has a slight positive bias. The bias-corrected d value is often called Hedges's g.

## Usage

 1 correct_d_bias(d, n) 

## Arguments

 d Vector of Cohen's d values. n Vector of sample sizes.

## Details

The bias correction is: \mjdeqng = d_c = d_obs \times Jg = d_c = d * J

where \mjdeqnJ = \frac\Gamma(\fracn - 22)\sqrt\fracn - 22 \times \Gamma(\fracn - 32)J = \Gamma((n - 2) / 2) / (sqrt(n - 2) * \Gamma((n - 2) / 2))

and \mjeqnd_obsd is the observed effect size, \mjeqng = d_cg = d_c is the corrected (unbiased) estimate, \mjseqnn is the total sample size, and \mjeqn\Gamma()\Gamma() is the gamma function.

Historically, using the gamma function was computationally intensive, so an approximation for \mjseqnJ was used (Borenstein et al., 2009): \mjdeqnJ = 1 - 3 / (4 * (n - 2) - 1)J = 1 - 3 / (4 * (n - 2) - 1

This approximation is no longer necessary with modern computers.

## Value

Vector of g values (d values corrected for small-sample bias).

## References

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press. p. 104

Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. Wiley. p. 27.

## Examples

 1 2 3 correct_d_bias(d = .3, n = 30) correct_d_bias(d = .3, n = 300) correct_d_bias(d = .3, n = 3000) 

psychmeta documentation built on June 1, 2021, 9:13 a.m.