The Effects of Nonnormal Distributions on Confidence Intervals around the Standardized Mean Difference: Bootstrap and Parametric Confidence Intervals

The standardized group mean difference, Cohen’s d, is among the most commonly used and intuitively appealing effect sizes for group comparisons. However, reporting this point estimate alone does not reflect the extent to which sampling error may have led to an obtained value. A confidence interval expresses the uncertainty that exists between d and the population value, δ, it represents. A set of Monte Carlo simulations was conducted to examine the integrity of a noncentral approach analogous to that given by Steiger and Fouladi, as well as two bootstrap approaches in situations in which the normality assumption is violated. Because d is positively biased, a procedure given by Hedges and Olkin is outlined, such that an unbiased estimate of δ can be obtained. The bias-corrected and accelerated bootstrap confidence interval using the unbiased estimate of δ is proposed and recommended for general use, especially in cases in which the assumption of normality may be violated.