Hedges' G

A standardised effect size measure similar to Cohen's d but corrected for small sample size bias.

Source: Hedges 1981

Hedges' g is a standardised effect size much like Cohen's d, expressing the difference between two group means in units of their pooled standard deviation, but with a correction applied for small samples. That correction matters because Cohen's d tends to overstate the true effect when samples are small, and Hedges' g scales it down to remove this upward bias. This makes it the safer choice for small studies and for meta-analyses combining them. Correcting the small-sample bias in a standardised difference is its purpose. Borenstein and colleagues (2009) describe this measure.

Source: Borenstein et al. 2009

Hedges' g is calculated much like Cohen's d, as the difference between the two group means divided by a pooled standard deviation, but then multiplied by a correction factor that depends on the sample size and reduces the small-sample bias, bringing the estimate closer to the true effect. So Hedges' g is calculated by taking the standardised mean difference and applying a correction that shrinks it slightly, with the correction being larger for smaller samples and negligible for large ones, which yields a standardised effect size that is approximately unbiased and thus more suitable than the uncorrected Cohen's d when sample sizes are small.

Source: Hedges 1981

Hedges' g differs from Cohen's d in applying a correction for small-sample bias: Cohen's d, the standardised mean difference, tends to overestimate the effect in small samples, and Hedges' g multiplies it by a factor that removes most of this bias. In large samples the two are nearly identical. So Hedges' g and Cohen's d are closely related standardised mean differences, differing chiefly in the small-sample correction, with Hedges' g preferred when samples are small because it is approximately unbiased, while the two converge as the sample size grows, so the distinction matters most for small studies.

Source: Hedges 1981

Hedges' g is preferred when sample sizes are small, since Cohen's d overestimates the effect in small samples and Hedges' g corrects for this bias, and it is commonly used in meta-analysis, where combining studies of varying, sometimes small, sizes makes the correction valuable. So Hedges' g is preferred for small studies and for meta-analytic synthesis, because its bias correction gives a more accurate standardised effect size when samples are limited, which is why it is often the default standardised mean difference in meta-analysis, ensuring that effect sizes from small studies are not systematically overstated.

Source: Hedges 1981

The small-sample correction in Hedges' g is important because the uncorrected standardised mean difference is biased upward when samples are small, so without correction effect sizes from small studies would be systematically overstated, distorting their interpretation and their contribution to a meta-analysis. So the small-sample correction matters for accuracy, since it removes most of the upward bias, giving a more truthful estimate of the effect size in small studies and preventing the overestimation that would otherwise occur, which is particularly important when synthesising evidence across studies of different sizes, where uncorrected estimates could bias the combined result.

Source: Hedges 1981