Monotonicity of Effect Sizes: Questioning Kappa-Squared as Mediation Effect Size Measure

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Abstract

Mediation analysis is important for research in psychology and other social and behavioral sciences. Great progress has been made in testing mediation effects and in constructing their confidence intervals. Mediation effect sizes have also been considered. Preacher and Kelley (2011) proposed and recommended κ2 as an effect size measure for a mediation effect. In this article, we argue that κ2 is not an appropriate effect size measure for mediation models, because of its lack of the property of rank preservation (e.g., the magnitude of κ2 may decrease when the mediation effect that κ2 represents increases). Furthermore, κ2 can lead to paradoxical results in multiple mediation models. We show that the problem of κ2 is due to (a) the improper calculation of the maximum possible value of the indirect effect, and (b) mathematically, the maximum possible indirect effect is infinity, implying that the definition of κ2 is mathematically incorrect. At this time, it appears that the traditional mediation effect size measure PM (the ratio of the indirect effect to the total effect), together with some other statistical information, should be preferred for basic mediation models. But for inconsistent mediation models where the indirect effect and the direct effect have opposite signs, the situation is less clear. Other considerations and suggestions for future research are also discussed.

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