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Two rather surprising anomalies relating to statistical power occur in testing mediation. First, in a model with no direct effect for which the total effect and indirect effect are identical, the power for the test of the total effect can be dramatically smaller than the power for the test of the indirect effect. Second, when there is a direct effect of a causal variable on the outcome controlling for the mediator, the power of the test of the indirect effect is often considerably greater than the power of the test of the direct effect, even when the two are of the same magnitude. We try to explain the reasons for these anomalies and how they affect practice.