Keywords: effect size, sample size, clinical trial design
Sample size estimation or power analysis is important in planning well-designed studies to address research hypotheses. For a research hypothesis defined in terms of comparing two means, effect size (ES) is normally used in calculating the sample size required for a pre-specified power using a statistical test of the hypothesis. In this work we develop a generalized effect size (GES) that is applicable to both dependent as well as independent samples without any assumptions on the variability of the two underlying distributions being compared. We propose an unbiased estimator of the GES and demonstrate that several of the existing ES estimators are particular cases of the GES estimator. We derive an exact confidence interval and conduct Monte-Carlo simulations to study the properties of the proposed GES estimator. The GES estimator demonstrates consistent performance and provides more appropriate estimates under various variance-covariance assumptions. The application of GES is illustrated with an example of analysis of data from a clinical trial.