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A Nearly Similar Powerful Test for Mediation

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  • Kees Jan van Garderen
  • Noud van Giersbergen

Abstract

This paper derives a new powerful test for mediation that is easy to use. Testing for mediation is empirically very important in psychology, sociology, medicine, economics and business, generating over 100,000 citations to a single key paper. The no-mediation hypothesis $H_{0}:\theta_{1}\theta _{2}=0$ also poses a theoretically interesting statistical problem since it defines a manifold that is non-regular in the origin where rejection probabilities of standard tests are extremely low. We prove that a similar test for mediation only exists if the size is the reciprocal of an integer. It is unique, but has objectionable properties. We propose a new test that is nearly similar with power close to the envelope without these abject properties and is easy to use in practice. Construction uses the general varying $g$-method that we propose. We illustrate the results in an educational setting with gender role beliefs and in a trade union sentiment application.

Suggested Citation

  • Kees Jan van Garderen & Noud van Giersbergen, 2020. "A Nearly Similar Powerful Test for Mediation," Papers 2012.11342, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2012.11342
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    References listed on IDEAS

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    1. Graham Elliott & Ulrich K. Müller & Mark W. Watson, 2015. "Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis," Econometrica, Econometric Society, vol. 83, pages 771-811, March.
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    5. Noud P.A. van Giersbergen, 2014. "Inference about the Indirect Effect: a Likelihood Approach," UvA-Econometrics Working Papers 14-10, Universiteit van Amsterdam, Dept. of Econometrics.
    6. Moreira, Marcelo J. & Mourão, Rafael & Moreira, Humberto Ataíde, 2016. "A critical value function approach, with an application to persistent time-series," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 778, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
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