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Related Experiment Videos

Inferences about correlations when there is heteroscedasticity.

R R Wilcox1, J Muska

  • 1Department of Psychology, University of Southern California, Seeley G. Mudd Building, Room 501, Los Angeles, CA 90089-1061, USA.

The British Journal of Mathematical and Statistical Psychology
|June 8, 2001
PubMed
Summary

This study compares methods for testing correlation (rho) when data has unequal variances (heteroscedasticity). The nested bootstrap method showed the best Type I error control for Pearson

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • The standard Student's t test for Pearson's correlation (rho) assumes equal conditional variances (homoscedasticity).
  • Heteroscedasticity, or unequal conditional variances, can invalidate the Student's t test, potentially leading to incorrect rejection of the null hypothesis.
  • This issue arises when the variance of one variable changes with the values of the other variable in a bivariate distribution.

Purpose of the Study:

  • To compare the performance of two heteroscedastic methods for testing the null hypothesis of zero population correlation (H0: rho = 0).
  • To evaluate the effectiveness of these methods, including bootstrap techniques, under conditions of heteroscedasticity.
  • To assess Type I error rates and statistical power across different correlation measures and bootstrap methods.

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Main Methods:

  • Simulation study comparing nested bootstrap and adjusted percentile bootstrap methods.
  • Evaluation using Pearson's correlation coefficient (rho) and robust analogues (Spearman's rho, percentage bend correlation).
  • Analysis focused on Type I error probabilities and statistical power under heteroscedasticity.

Main Results:

  • The nested bootstrap method demonstrated superior control of Type I errors in simulations using Pearson's rho.
  • For robust correlation measures, the nested bootstrap offered minimal advantage over the basic percentile method regarding Type I error rates.
  • The adjusted percentile bootstrap generally showed higher power than the nested bootstrap, even when Type I errors were lower with the adjusted method.

Conclusions:

  • The nested bootstrap is recommended for testing Pearson's correlation under heteroscedasticity due to its Type I error control.
  • The choice of correlation measure impacts the effectiveness of bootstrap methods; robust measures may not benefit as much from advanced bootstrapping.
  • Further investigation is needed for confidence interval construction, as current methods show limitations with positive correlations under heteroscedasticity.