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A robust Pearson correlation test for a general point null using a surrogate bootstrap distribution.

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Summary
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This study introduces a robust bootstrap test for hypotheses about correlation coefficients (ρ). The novel surrogate bootstrap distribution ensures accurate Type I error control across various scenarios, enhancing statistical reliability.

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Area of Science:

  • Statistics
  • Statistical Inference
  • Hypothesis Testing

Background:

  • Accurate hypothesis testing is crucial for reliable statistical inference.
  • Existing methods for testing correlation coefficients (ρ) may lack robustness in certain distributional scenarios.
  • The studentized permutation test offers exactness and asymptotic correctness for ρ = 0.

Purpose of the Study:

  • To present a robust bootstrap test for the general hypothesis H0: ρ = ρ0.
  • To evaluate the Type I error control of the proposed bootstrap test.
  • To demonstrate the test's robustness across diverse distributional assumptions.

Main Methods:

  • Development of a novel surrogate bootstrap distribution.
  • Application of the surrogate bootstrap for hypothesis testing of correlation coefficients.
  • Comparison of Type I error rates under various distributional conditions.

Main Results:

  • The proposed bootstrap test demonstrates good Type I error control.
  • The test maintains robustness across a variety of distributional scenarios.
  • The surrogate bootstrap distribution facilitates reliable hypothesis testing for ρ = ρ0.

Conclusions:

  • The robust bootstrap test provides a reliable method for testing hypotheses about correlation coefficients.
  • The surrogate bootstrap approach enhances the accuracy and generalizability of statistical tests.
  • This method offers improved Type I error control compared to existing techniques in diverse settings.