Power of Mediation Effects Using Bootstrap Resampling
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Mediation analyses are a statistical tool for testing the hypothesis about how the relationship between two variables may be direct or indirect via a third variable. Assessing statistical significance has been an area of active research; however, assessment of statistical power has been hampered by the lack of closed form calculations and the need for substantial amounts of computational simulations. The current work provides a detailed explanation of implementing large scale simulation procedures within a shared computing cluster environment. In addition, all results and code for implementing these procedures is publicly available. The resulting power analyses compare the effects of sample size and strength and direction of the relationships between the three variables. Comparisons of three confidence interval calculation methods demonstrated that the bias-corrected method is optimal and requires approximately ten less participants than the percentile method to achieve equivalent power. Differing strengths of distal and proximal effects were compared and did not differentially affect the power to detect mediation effects. Suppression effects were explored and demonstrate that in the presence of no observed relationship between two variables, entrance of the mediating variable into the model can reveal a suppressed relationship. The power to detect suppression effects is similar to unsuppressed mediation. These results and their methods provide important information about the power of mediation models for study planning. Of greater importance is that the methods lay the groundwork for assessment of statistical power of more complicated models involving multiple mediators and moderators.
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