Glass's delta measures the standardized difference between two means by dividing their difference by a selected reference group's standard deviation. Unlike Cohen's d, it does not pool both groups' standard deviations, so it is useful when the denominator must represent one specific group's variability. section 13.11 section 13.8.3
Use Glass's delta as part of an effect-size workflow:
- Apply it to continuous data alongside a t-test; use it to describe the size of a difference, not to replace significance testing. section 20.3
- Choose it when controlling the standard-deviation denominator matters, rather than using the pooled denominator of Cohen's d or Hedges' g. section 13.11
- Interpret values near 0.2 or below as small, around 0.5 as medium, and 0.8 or above as large. section 20.3
Comparing Gini-index groups in R
Using the effectsize package, glass_delta(ws_giniX$gini_index, ws_giniY$gini_index) returns an estimate of -0.51 with a 95% confidence interval from -0.93 to -0.09. Reversing the groups changes the estimate to 0.31 with an interval from 0.07 to 0.56, illustrating that argument order controls direction and the selected denominator affects the result. section 13.8.3
cohens_d(ws_giniX$gini_index, ws_giniY$gini_index) ## Cohen's d | 95% CI ## ------------------------- ## -0.32 | [-0.70, 0.07] ## ## - Estimated using pooled SD. hedges_g(ws_giniX$gini_index, ws_giniY$gini_index) ## Hedges' g | 95% CI ## ------------------------- ## -0.32 | [-0.70, 0.07] ## ## - Estimated using pooled SD. glass_delta(ws_giniX$gini_index, ws_giniY$gini_index) ## Glass' delta | 95% CI ## ----------------------------- ## -0.51 | [-0.93, -0.09]
Compare Cohen's d, Hedges' g, and Glass's delta outputs for the same two Gini-index vectors. section 13.8.3
