Effect size, statistical power, and sample size for assessing interactions between categorical and continuous variables

The reporting and interpretation of effect size estimates are widely advocated in many academic journals of psychology and related disciplines. However, such concern has not been adequately addressed for analyses involving interactions between categorical and continuous variables. For the purpose of improving current practice, this article presents fundamental features and theoretical developments for the variance of standardized slopes as a desirable standardized effect size measure for the degree of disparity between several slope coefficients. To estimate the effect size, a consistent and nearly unbiased estimator is described and a simple refinement is emphasized for extreme situations whenever appropriate. The essential problems of power and sample size calculations for testing the equality of slope coefficients are also considered. According to the analytic justification and empirical assessment, the exact approach has a clear advantage over the approximate methods. Both SAS and R computer codes are provided to facilitate practical accessibility of the proposed techniques in interaction studies.