correct_d_bias {psychmeta}

Correct for small-sample bias in Cohen's d values

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

correct_d_bias(d, n)

Arguments

d

Vector of Cohen's d values.

n

Vector of sample sizes.

Details

The bias correction is:

g = d_{c} = d_{obs} \times J

where

J = \frac{\Gamma(\frac{n - 2}{2})}{\sqrt{\frac{n - 2}{2}} \times \Gamma(\frac{n - 3}{2})}

and d_{obs} is the observed effect size, g = d_{c} is the corrected (unbiased) estimate, n is the total sample size, and \Gamma() is the gamma function.

Historically, using the gamma function was computationally intensive, so an approximation for J was used (Borenstein et al., 2009):

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

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