Mediator Models As a Novel Method for Increasing Statistical Power

Introduction: Mediation analysis is often used in prevention research as a way of assessing the efficacy of an intervention program. Researchers test the significance of the mediated effect, which is the relationship between the independent variable X and the mediator M (a path) and the relationship between M and the dependent variable Y (b path). Previous research has shown that including additional variables in the relationship between X and Y can increase power to detect effects over a bivariate relation. Although previous research has studied power in mediation models, the inclusion of multiple mediators as a method for increasing power has not been investigated. This study will calculate the actual power to detect the mediated effect as compared with power of the total effect between X and Y for a two mediator model.

 Methods: A Monte Carlo simulation was written using the SAS programming language. The program calculated empirical power to detect the total mediated and specific mediated effects for a two mediator model for different combinations of parameters and sample sizes using the joint significance test for mediation (MacKinnon et al., 2002) and product of coefficients tests of mediation using multivariate delta standard errors (MacKinnon, 2008; Sobel, 1982), as well as power for the test of the total effect of X to Y. Path coefficients corresponding to zero, small, medium, and large effect sizes were used, and sample sizes of 50, 100, 200, 500, and 1000 were used. In addition, programs were written to calculate analytical power of the specific and total mediated effects for comparison.

Results: Results indicated that including two mediators increased power over a bivariate relation in small samples when both specific mediated effects were large and in large samples when both specific mediated effects were small. This trend was maintained and was more pronounced for cases where power of the test of the total mediated effect exceeded Cohen’s (1988) guidelines of 0.80 for adequate statistical power and the test of the total effect of X to Y did not.

Conclusion: Explanations for why this pattern of results occurs are discussed, as well as implications of the results for future research.