A d estimate is the signed standardized difference between two group means: the mean difference divided by a pooled standard deviation. It expresses separation in standard deviation units, so values farther from zero indicate larger effects. section 12.7.3 section 13.8.3
Interpret a d estimate by checking its direction, magnitude, and relationship to other tests:
- Read the sign from the argument order: a negative estimate means the first group's mean is lower than the second group's mean. section 12.7.3
- Use the magnitude as a signal-to-noise ratio: negligible, small, medium, or large effects correspond to increasingly distant estimates from zero. section 13.8.3
- Use Cohen's d alongside a t-test because d does not account for record counts and therefore does not replace significance testing. section 13.8.3
Comparing Gini indexes
Comparing giniX and giniY with cohen.d() produced d = -0.633, classified as a medium effect, with a 95% confidence interval from -1.012 to -0.254. The negative sign indicates that giniX has the lower mean.
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 with Hedges' g and Glass's delta, including their confidence intervals, using the same Gini-index groups. section 13.8.3
