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Powering the Circumplex: A Practical Guide to Sample Size for the Structural Summary Method.

Kimberly J Gilbert1

  • 1Fordham University, Bronx, NY, USA.

Assessment
|May 11, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces power analysis for the Structural Summary Method (SSM) in circumplex models. It provides validated formulas for amplitude and angular displacement, aiding researchers in designing studies with confidence.

Keywords:
Monte Carlo simulationangular displacementeffect sizeinterpersonal circumplexpower analysisstructural summary method

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Area of Science:

  • Psychology
  • Quantitative Psychology
  • Social Psychology

Background:

  • The Structural Summary Method (SSM) is a key framework for analyzing circumplex models.
  • Existing SSM guidance focuses on retrospective analysis, lacking tools for prospective power analysis.
  • A priori power analysis is crucial for robust study design and valid inference.

Purpose of the Study:

  • To extend the Structural Summary Method (SSM) to support prospective power analysis.
  • To derive and validate power functions for amplitude and angular displacement within SSM.
  • To provide researchers with reliable tools for planning studies using circumplex models.

Main Methods:

  • Developed analytical power functions for amplitude and angular displacement.
  • Conducted two studies to derive and validate these power functions.
  • Employed simulation and resampling techniques across multiple datasets for validation.

Main Results:

  • Established reliable power functions for amplitude, showing modest sample sizes suffice for detecting interpersonal differentiation.
  • Demonstrated that displacement precision is critically dependent on amplitude, impacting displacement-focused hypotheses.
  • Validated formulas confirmed their utility for guiding study design in SSM.

Conclusions:

  • The extended SSM now supports a priori inference, enhancing its utility for research planning.
  • Distinct inferential properties of amplitude and displacement are clarified.
  • This work strengthens the SSM as a comprehensive tool for circumplex model research.