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This study introduces new statistical tests for comparing correlations in bilateral data. The asymptotic score test and two exact tests demonstrate robustness and accuracy for various data sizes.

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Area of Science:

  • Statistics
  • Biostatistics
  • Correlation Analysis

Background:

  • Comparing correlations is crucial in statistical analysis.
  • Existing methods may be limited for small or bilateral datasets.
  • Dallal's model provides a framework for analyzing such data.

Purpose of the Study:

  • To develop and evaluate methods for testing the equality of correlations in multiple bilateral data.
  • To compare the performance of asymptotic and exact statistical tests.

Main Methods:

  • Derivation of three asymptotic test statistics for large samples.
  • Development of conditional and unconditional exact methods for small samples.
  • Numerical simulations to assess Type I Error Rates (TIEs) and statistical power.

Main Results:

  • The asymptotic score test exhibited the highest robustness across simulations.
  • Two proposed exact tests demonstrated satisfactory TIEs and powers.
  • The study identified reliable methods for correlation equality testing.

Conclusions:

  • The developed asymptotic and exact tests are effective for comparing correlations in bilateral data.
  • The asymptotic score test and specific exact tests are recommended for practical application.
  • Real-world examples confirm the utility of these statistical approaches.