Interpretation of the Standardized Mean Difference Effect Size When Distributions Are Not Normal or Homoscedastic

The standardized mean difference (sometimes called Cohen's d) is an effect size measure widely used to describe the outcomes of experiments. It is mathematically natural to describe differences between groups of data that are normally distributed with different means but the same standard deviation. In that context, it can be interpreted as determining several indexes of overlap between the two distributions. If the data are not approximately normally distributed or if they have substantially unequal standard deviations, the relation between d and overlap between distributions can be very different, and interpretations of d that apply when the data are normal with equal variances are unreliable.