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After a brief consideration of the definition and importance of mediation, statistical tests for mediation are reviewed, including the joint significance of the two effects involved in the mediation, the Sobel test and its variants, resampling with the bootstrap, Bayesian estimation using MCMC simulation, and the effect ratio. A structural-equation-modeling (SEM) perspective on mediation then introduces the alternative scenarios that could yield a false-positive mediation finding. Design-based, partial solutions are advanced for problems of measurement, uncontrolled common causes, and temporal ordering that can confound mediation analysis. Next, the issue of heterogeneity of effects and statistical interactions in mediation analyses are addressed, including a discussion of moderated mediation and mediated moderation. Finally, the relation of mediation analysis to experimentation is discussed, with attention to the possibility of creatively integrating SEM-based mediation analysis and experimental design.
Erik Z. Woody (Sun,) studied this question.