Cited by 350Advanced Causal Inference TechniquesMeta-analysis and systematic reviewsPsychometric Methodologies and Testing

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Monotonicity of effect sizes: questioning kappa-squared as mediation effect size measure

Wen, Zhonglin, Fan, Xitao·2015·Psychological Methods

DOI 10.1037/met0000029

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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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Authors: Wen, Z., & Fan, X.
Affiliations: South China Normal University (CN)
University of Macau (MO)
ORCID: Wen, Zhonglin
Fan, Xitao
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 2015
Volume: 20
Issue: 2
Pages: 193-203
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/met0000029
OpenAlex: W2155202060
Cited by: 350
References: 23
Citations by year: 2026: 20 · 2025: 23 · 2024: 28 · 2023: 31 · 2022: 43 · 2021: 41 · 2020: 30 · 2019: 47 · 2018: 33 · 2017: 38 · 2016: 14 · 2015: 2
FWCI: 25.81
Type: journal article
Language: en
Update notices: correction (2015-05-11)
Open access: closed
Locations: Psychological Methods (publishedVersion)
PubMed (publishedVersion)
Funders: National Natural Science Foundation of China (31271116 and 31400909)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Keywords: indirect effects, rank preservation, monotonicity, multiple mediation, effect size measures, mediation analysis
MeSH terms: Behavioral Sciences, Humans, Statistics as Topic, Models, Statistical, Confidence Intervals

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Monotonicity of effect sizes: questioning kappa-squared as mediation effect size measure

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