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

Area of Science:

• Methodology
• Statistics
• Social Sciences

Background:

• Mediation analyses are vital across disciplines for testing theories of action.
• A lack of guidance exists for designing mediation studies, particularly regarding statistical power.
• Detecting indirect effects is key, influencing data collection and the evidence from group-randomized studies.

Purpose of the Study:

• To develop power formulas for detecting multilevel indirect effects in group-randomized designs.
• To provide closed-form expressions for estimating the variance and power of indirect effects.
• To address the gap in literature concerning power calculations for mediation in complex designs.

Main Methods:

• Development of closed-form expressions for variance and power.
• Application of two-level linear models (2-2-1 mediation).
• Implementation of formulas in R package PowerUpR and PowerUp!-Mediator software.

Main Results:

• Group-randomized designs, when planned carefully, can possess adequate statistical power to detect mediation effects.
• The developed formulas enable precise estimation of power for indirect effects in multilevel settings.
• Typical sample sizes may be sufficient for detecting mediation effects with appropriate design.

Conclusions:

• The study provides essential tools for researchers designing group-randomized mediation studies.
• Accurate power estimation can optimize data collection and strengthen causal inference.
• The findings support the feasibility of detecting mediation effects in well-designed group-randomized studies.