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Bayesian t-tests for correlations and partial correlations.

Min Wang1, Fang Chen2, Tao Lu2

  • 1Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX, USA.

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|June 16, 2022
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Summary
This summary is machine-generated.

This study introduces new Bayesian tests for correlation and partial correlation. These tests align with frequentist methods, offering an accessible alternative for data analysis.

Keywords:
Bayes factorZellner's g-priorrestricted most powerful Bayesian testsstatistical evidencet-test

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Area of Science:

  • Statistics
  • Bayesian inference
  • Correlation analysis

Background:

  • Traditional frequentist methods are widely used for correlation and partial correlation testing.
  • Bayesian approaches offer an alternative framework for statistical inference.
  • Integrating Bayesian methods with frequentist procedures can enhance analytical flexibility.

Purpose of the Study:

  • To develop novel Bayes factor-based testing procedures for detecting correlation and partial correlation.
  • To create Bayesian tests that are computationally accessible and easily integrated into existing workflows.
  • To demonstrate the concordance between the proposed Bayesian tests and established frequentist paradigms.

Main Methods:

  • Development of Bayes factor-based testing procedures for correlation and partial correlation.
  • Restriction of alternative hypotheses to maximize rejection probability for a given Bayes factor threshold.
  • Leveraging frequentist t-statistics and critical values for straightforward calculation.
  • Implementation using standard spreadsheet software like Excel.

Main Results:

  • The proposed Bayesian tests are shown to be simple to calculate, relying on frequentist t-statistics.
  • These Bayesian tests can yield identical decisions to frequentist tests when thresholds are aligned.
  • The procedures are validated through both simulated data and real-world examples.
  • The method offers a practical extension to standard frequentist correlation analysis.

Conclusions:

  • The developed Bayesian testing procedures provide a computationally efficient and accessible alternative for correlation and partial correlation analysis.
  • These methods bridge Bayesian and frequentist paradigms, offering consistent decision-making.
  • The ease of implementation makes these tests valuable for researchers across various fields.