Experimental Power for Indirect Effects in Group-randomized Studies with Group-level Mediators

Mediation analyses have provided a critical platform to assess the validity of theories of action across a wide range of disciplines. Despite widespread interest and development in these analyses, literature guiding the design of mediation studies has been largely unavailable. Like studies focused on the detection of a total or main effect, an important design consideration is the statistical power to detect indirect effects if they exist. Understanding the sensitivity to detect indirect effects is exceptionally important because it directly influences the scale of data collection and ultimately governs the types of evidence group-randomized studies can bring to bear on theories of action. However, unlike studies concerned with the detection of total effects, literature has not established power formulas for detecting multilevel indirect effects in group-randomized designs. In this study, we develop closed-form expressions to estimate the variance of and the power to detect indirect effects in group-randomized studies with a group-level mediator using two-level linear models (i.e., 2-2-1 mediation). The results suggest that when carefully planned, group-randomized designs may frequently be well positioned to detect mediation effects with typical sample sizes. The resulting power formulas are implemented in the R package PowerUpR and the PowerUp!-Mediator software (causalevaluation.org).