Evaluating Statistical Power, Type I Error, and Sample Size Requirements for Representative Moderated Mediation Models

The moderated mediation models simultaneously account for both the causal process linking an independent variable to a dependent variable and the contextual variables that influence the strength and direction of this process. Despite their extensive use, relatively few studies have examined which testing methods are most appropriate or what sample sizes ensure valid inference. This study compares the power and Type I error rates of the index of moderated mediation across different testing methods in two representative moderated mediation models, and explores the minimum required sample sizes, providing practical guidelines for researchers. Study 1 indicated that the powers ranked from highest to lowest, in the order of bias-corrected bootstrap (BCBS), percentile bootstrap (PBS), robust maximum likelihood (MLR), and maximum likelihood (ML). Under large effect sizes, PBS performance declined while MLR improved. Study 2 revealed a substantial inflation of the Type I error rate under certain conditions of PBS. These findings indicate that PBS may not be the most appropriate testing method in such cases, and that BCBS or MLR—both of which exhibited higher power and better control of Type I error—should be considered as alternatives depending on the conditions. In Study 3, assuming a medium effect size, sample sizes of 200 to 230 achieved over 80% power. These findings enhance understanding of key statistical considerations in moderated mediation models, and help researchers select appropriate testing methods.