title: When the test of mediation is more powerful than the test of the total effect.
abstract: Although previous research has studied power in mediation models, the extent to which the inclusion of a mediator will increase power has not been investigated. To address this deficit, in a first study we compared the analytical power values of the mediated effect and the total effect in a single-mediator model, to identify the situations in which the inclusion of one mediator increased statistical power. The results from this first study indicated that including a mediator increased statistical power in small samples with large coefficients and in large samples with small coefficients, and when coefficients were nonzero and equal across models. Next, we identified conditions under which power was greater for the test of the total mediated effect than for the test of the total effect in the parallel two-mediator model. These results indicated that including two mediators increased power in small samples with large coefficients and in large samples with small coefficients, the same pattern of results that had been found in the first study. Finally, we assessed the analytical power for a sequential (three-path) two-mediator model and compared the power to detect the three-path mediated effect to the power to detect both the test of the total effect and the test of the mediated effect for the single-mediator model. The results indicated that the three-path mediated effect had more power than the mediated effect from the single-mediator model and the test of the total effect. Practical implications of these results for researchers are then discussed.
authors.affiliation: Department of Psychology, Arizona State University, P.O. Box 871104, 950 S. McAllister Ave. Room 237, Tempe, AZ, 85287-1104, USA, holly.orourke@asu.edu.
authors.forename: Holly P
authors.initials: HP
authors.lastname: O'Rourke
authors.forename: David P
authors.initials: DP
authors.lastname: MacKinnon
mesh_terms: D015984:Causality; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D008962:Models, Theoretical; D017008:Negotiating