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Equivalence tests for comparing correlation and regression coefficients.

Alyssa Counsell1, Robert A Cribbie

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The British Journal of Mathematical and Statistical Psychology
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This summary is machine-generated.

Equivalence tests can demonstrate a lack of association between variables. New methods for correlation and regression coefficients show better accuracy but require large sample sizes for sufficient power.

Keywords:
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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Traditional difference-based tests are common for hypothesis testing.
  • Equivalence tests are alternatives to demonstrate a lack of association.
  • Limited research exists on equivalence methods for correlation or regression coefficients.

Purpose of the Study:

  • To propose novel equivalence tests for correlation and regression coefficients.
  • To evaluate the performance of these new tests using simulations.
  • To compare the proposed tests against traditional difference-based tests.

Main Methods:

  • Development of equivalence tests based on the TOST method and Anderson-Hauck method.
  • Simulation study to assess test performance and accuracy.
  • Comparison with the inappropriate method of using non-rejection of the null hypothesis in difference-based tests.

Main Results:

  • Equivalence tests demonstrate more accurate probabilities of declaring equivalence than difference-based tests.
  • The Anderson-Hauck equivalence test is recommended over the TOST method.
  • Equivalence tests require large sample sizes to achieve adequate statistical power.

Conclusions:

  • Novel equivalence tests provide a more accurate approach for evaluating the similarity of correlation or regression coefficients.
  • The Anderson-Hauck method is superior to TOST for this application.
  • Researchers should consider the sample size requirements when planning studies using equivalence tests.