Association for Public Policy Analysis & Management

Like studies focused on the detection of a main or total effect, a principal consideration in the design of studies examining mediation is the power with which mediation effects can be detected if they exist. However, unlike studies concerning the detection of main effects, literature has not established power formulas for detecting mediation effects in multilevel designs or described precisely how changes in parameter values can influence and even undermine a study’s power to detect mediation effects.

In this study, we developed a framework and formulas to help researchers design multilevel mediation studies by deriving formulas to assess the power of a design, describe the complex and atypical behavior of power in studies of mediation, and delineate the conditions under which it is maximized for a given set of parameter values. More specifically, the purpose of this study was twofold. First, we derived power formulas for multiple tests of multilevel mediation effects (e.g., Sobel test). Second, we investigate the behavior of the power curves as a function of design parameters such as the magnitude of the mediation effect, the decomposition of this effect (i.e., relative magnitude of the a and b paths), intraclass correlation, and sample sizes. The results indicated that unlike the power to detect total effects, the power to detect mediation effects is not a monotonic function of effect size but rather a complex function governed by the decomposition of the total effect. This phenomenon is present in each of the tests considered and we outline the conditions under which power is maximized and the rate with which it declines as a function of the magnitude of path coefficients and use these results to make recommendations for the design of cluster randomized trials.