psychmeta (version 2.7.0)

correct_glass_bias: Correct for small-sample bias in Glass' \(\Delta\) values

Description

Correct for small-sample bias in Glass' \(\Delta\) values.

Usage

correct_glass_bias(delta, nc, ne, use_pooled_sd = rep(FALSE, length(delta)))

Value

Vector of d values corrected for small-sample bias.

Arguments

delta

Vector of Glass' \(\Delta\) values.

nc

Vector of control-group sample sizes.

ne

Vector of experimental-group sample sizes.

use_pooled_sd

Logical vector determining whether the pooled standard deviation was used (TRUE) or not (FALSE; default).

Details

The bias correction is estimated as:

$$\Delta_{c}=\Delta_{obs}\frac{\Gamma\left(\frac{n_{control}-1}{2}\right)}{\Gamma\left(\frac{n_{control}-1}{2}\right)\Gamma\left(\frac{n_{control}-2}{2}\right)}$$

where \(\Delta\) is the observed effect size, \(\Delta_{c}\) is the corrected estimate of \(\Delta\), \(n_{control}\) is the control-group sample size, and \(\Gamma()\) is the gamma function.

References

Hedges, L. V. (1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128. tools:::Rd_expr_doi("10.2307/1164588")

Examples

correct_glass_bias(delta = .3, nc = 30, ne = 30)