Approximate Confidence Intervals for Standardized Effect Sizes in the Two-Independent and Two-Dependent Samples Design

Standardized effect sizes and confidence intervals thereof are extremely useful devices for comparing results across different studies using scales with incommensurable units. However, exact confidence intervals for standardized effect sizes can usually be obtained only via iterative estimation procedures. The present article summarizes several closed-form approximations to the exact confidence interval bounds in the two-independent and two-dependent samples design. Monte Carlo simulations were conducted to determine the accuracy of the various approximations under a wide variety of conditions. All methods except one provided accurate results for moderately large sample sizes and converged to the exact confidence interval bounds as sample size increased.