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Understanding Power Anomalies in Mediation Analysis.

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This study explains puzzling statistical power anomalies in mediation analysis. Theoretical derivations and simulations reveal why power for indirect effects can unexpectedly decrease with effect size, offering crucial insights for researchers.

Keywords:
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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Previous research noted anomalies in statistical power for indirect effects in mediation models.
  • Observed power for indirect effects can stagnate or decline as effect size increases.
  • Power for indirect effects can exceed that of total or direct effects, even with equal magnitudes.

Purpose of the Study:

  • To theoretically explain the observed power anomalies in mediation analysis.
  • To derive the limiting distributions of statistics and their non-centralities.
  • To provide a mathematical basis for understanding power behavior in indirect effect testing.

Main Methods:

  • Derivation of limiting distributions for relevant statistics.
  • Calculation of non-centrality parameters for power analysis.
  • Computer simulations to validate theoretical findings.

Main Results:

  • Theoretical results successfully explain the observed power anomalies in mediation analysis.
  • The derivations provide a framework for understanding the behavior of statistical power.
  • Simulations confirmed the validity of the derived limiting distributions.

Conclusions:

  • The study resolves puzzling anomalies in statistical power for indirect effects.
  • Understanding these power dynamics is crucial for accurate mediation analysis.
  • Theoretical insights aid in interpreting and improving power calculations in research.