Degenerate Power in Multilevel Mediation: The Non-Monotonic Relationship between Power & Effect Size

Kelcey, Ben

Society for Research on Educational Effectiveness

Abstract:

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 (e.g., Raudenbush, 1997). However, unlike studies concerning the detection of main effects, literature has not established power formulas for detecting mediation effects in multilevel designs and described precisely how changes in parameter values can influence and even undermine a study’s power to detect mediation effects. The purpose of this study was twofold. First, the author derived power formulas for multilevel mediation effects. Second formulas were developed that delineate the conditions under which power is maximized and the rate with which it declines as a function of the magnitude of path coefficients and used these results to investigate the behavior of power as a function of design parameters. 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. Although the study presented focused on inferences drawn from the Sobel test for multilevel mediation, the results extend to other designs and tests including single level designs and bootstrapped confidence intervals. In this way, the findings from this study expand the scope and quality of designs for studies of mediation because they equip researchers with the tools to consider how study features and design choices impact the probability with which they can detect effects. Tables and figures are appended.

Degenerate Power in Multilevel Mediation- The Non-Monotonic Relationship between Power & Effect Size

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