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Improved procedures and computer programs for equivalence assessment of correlation coefficients.

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Summary

This study introduces new equivalence tests for correlation coefficients, addressing limitations in current methods. These techniques reliably assess if a correlation falls within a specified range, enhancing correlation analysis.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Correlation coefficients quantify linear relationships between variables.
  • Existing methods focus on significance testing and confidence intervals, neglecting equivalence.
  • Evaluating correlation equivalence is crucial for expanding correlational technique utility.

Purpose of the Study:

  • To develop and propose novel equivalence tests for correlation coefficients.
  • To address the inadequacy of current methods for correlation equivalence appraisal.
  • To enhance the application of correlational techniques.

Main Methods:

  • Focus on Pearson product-moment correlation coefficient and Fisher's z transformation.
  • Development of equivalence tests to determine if a correlation falls within a reference range.
  • Consideration of Type I error rate, power, and sample size determination.

Main Results:

  • Existing methods are demonstrated as inappropriate for correlation equivalence appraisal.
  • Proposed equivalence tests are validated as reliable tools for correlation analysis.
  • The study clarifies the nature and deficiencies of two one-sided tests for detecting lack of association.

Conclusions:

  • Novel equivalence tests provide a reliable framework for assessing correlation equivalence.
  • The proposed methods are essential for accurate and meaningful correlation analysis.
  • This work expands the practical application of correlation coefficients in research.