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The purpose of this study was twofold. First, we derived power formulas for multilevel mediation effects. Second, we developed formulas that delineate the functional relationships between power and the magnitude of path coefficients. 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 (see for example Figure 1). The non-monotonic form of power traverses common tests of multilevel mediation including the Sobel test and those based on bootstrapping.
Benjamin Kelcey, University of Cincinnati
Zuchao Shen, University of Cincinnati
Jessaca K. Spybrook, Western Michigan University
Nianbo Dong, University of Missouri - Columbia