Effect Size > Glass’s delta
Glass’s delta (Glass et al. 1981) is a measure of effect size. Glass’s delta uses only the control group’s standard deviation (SDC). This is because Glass argued that if several treatments were compared to a control group, it would be better to use just the standard deviation computed from the control group, so that effect sizes would not differ under equal means and different variances.
The formula is [1]
When to Choose Glass’s Delta
Use Glass’s Delta when standard deviations are significantly different between groups.
If your standard deviations are not significantly different between groups, use Hedges’ g or Cohen’s d instead. If your sample size is small (less than 20) choose Hedges’ g over Cohen’s d. For samples 20 or greater, the two statistics are roughly equivalent.
The reason for using Glass’s delta when standard deviations are significantly different between groups is that Glass’s delta is less sensitive to differences in variance than other effect size measures, such as Cohen’s d and Hedges’ g.
Cohen’s d and Hedges’ g are both calculated by dividing the mean difference between groups by the pooled standard deviation. The pooled standard deviation is a weighted average of the standard deviations of the two groups. This means that if the standard deviations of the two groups are different, the pooled standard deviation will be pulled towards the larger standard deviation. This can result in an underestimation of the effect size if the standard deviation of the control group is larger than the standard deviation of the experimental group.
Glass’s delta, on the other hand, is calculated by dividing the mean difference between groups by the standard deviation of the control group. This means that Glass’s delta is not affected by differences in variance between the two groups.
As a result, Glass’s delta is a more accurate measure of effect size when the standard deviations of the two groups are significantly different.
In the case where the standard deviations of the two groups are not significantly different, Cohen’s d and Hedges’ g are more appropriate measures of effect size. This is because Cohen’s d and Hedges’ g are more sensitive to small differences in means than Glass’s delta.
References
[1] Effect sizes.