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Inferential procedures based on the weighted Pearson correlation coefficient test statistic.

Han Yu1, Alan D Hutson1

  • 1Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, NY, USA.

Journal of Applied Statistics
|February 19, 2024
PubMed
Summary
This summary is machine-generated.

The common t-test inflates Type I errors when using weighted Pearson correlation. A studentized permutation test robustly controls errors, even with small samples and non-normal data.

Keywords:
Permutation testcomputational methodslinear associationsmall sampletype i error control

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Area of Science:

  • Statistics
  • Biostatistics

Background:

  • The t-test is widely used for hypothesis testing.
  • Weighted Pearson correlation is employed in various analyses.
  • Existing t-test methods show poor Type I error control with weighted Pearson correlation.

Purpose of the Study:

  • To evaluate the Type I error control of the t-test for weighted Pearson correlation.
  • To propose novel methods for accurate hypothesis testing in this context.

Main Methods:

  • Derived the large sample variance of the weighted Pearson correlation coefficient.
  • Developed an asymptotic test and studentized permutation tests.
  • Conducted extensive simulation studies with varying sample sizes and distributions.

Main Results:

  • The standard t-test demonstrates severely inflated Type I error rates.
  • The proposed studentized permutation test, particularly using Fisher's Z statistic, effectively controls Type I errors.
  • Robust performance was observed even in small sample sizes and non-normal data scenarios.

Conclusions:

  • The studentized permutation test offers a reliable solution for hypothesis testing with weighted Pearson correlation.
  • This method ensures accurate statistical inference, addressing limitations of standard t-tests.