Cohen’s d measures the practical size of a difference between two group means. It divides the difference in means by the groups’ average, pooled standard deviation, expressing the separation as a number of standard deviations. A result farther from 0 indicates a larger effect; the sign depends on the order in which the two groups are supplied. section 7.4.3 section 13.8.3
Use Cohen’s d alongside—not instead of—a t-test when comparing continuous outcomes for two groups. A t-test addresses statistical significance and a null hypothesis, while Cohen’s d describes magnitude. Because Cohen’s d does not consider record counts, a statistically significant result can have a negligible effect, and a statistically insignificant result can still have a large effect. section 7.0 section 20.3
Read a Cohen’s d result in three parts:
- d estimate: the signed number of standard deviations separating the means; reversing argument order reverses its sign. section 12.7.3
- qualitative rating: output can classify the magnitude as negligible, small, medium, or large. section 13.8.3
- confidence interval: the R output reports a 95% interval around the estimate. section 7.4.3
- practical interpretation: an estimate near 0 signals little difference relative to typical variation; values around 0.5 are medium and values at or above 0.8 are large. section 13.8.3 section 20.3
In R, call cohen.d() from the effsize package with the same two numeric vectors used in a t-test. The effectsize package also provides cohens_d(). Cohen’s d commonly uses pooled standard deviation; Hedges’ g and Glass’s delta are alternative effect-size measures for continuous data, with Glass’s delta allowing control over the denominator standard deviation. section 12.7.3 section 13.8.3
Home and road foul calls
Comparing 2018–19 road and home personal fouls produces d estimates of 0.089 in the regular season and 0.158 in the postseason, both rated negligible. The estimates quantify a direction, but their small magnitudes indicate that the group means differ little relative to their variation—even where t-test conclusions differ. section 7.4.3 section 7.0
Salary inequality and winning
For NBA teams split by regular-season winning percentage, a Gini-coefficient d estimate of 0.621 is rated medium. The positive result reflects the higher average Gini coefficient in the first group passed to cohen.d(), linking a meaningful standardized difference to greater salary inequality among winning teams. section 12.8.2 section 12.8.1
cohen.d(fouls1819reg$pfR, fouls1819reg$pfH) ## ## Cohen's d ## ## d estimate: 0.08907251 (negligible) ## 95 percent confidence interval: ## lower upper ## 0.009960997 0.168184021 cohen.d(fouls1819post$pfR, fouls1819post$pfH) ## ## Cohen's d ## ## d estimate: 0.158254 (negligible) ## 95 percent confidence interval: ## lower upper ## -0.1506272 0.4671351
This pair of cohen.d() calls shows the minimal R workflow and the returned d estimate, qualitative rating, and 95% confidence interval for road-versus-home foul calls. section 7.4.3
