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Related Experiment Videos

Estimation of the average correlation coefficient for stratified bivariate data.

L M Rubenstein1, C S Davis

  • 1Department of Preventive Medicine, University of Iowa, Iowa City, IA 52242, USA. linda-rubenstein@uiowa.edu

Statistics in Medicine
|April 21, 1999
PubMed
Summary
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This study introduces an improved estimator for the Cochran-Mantel-Haenszel (CMH) correlation statistic, enhancing its accuracy for analyzing associations between variables, especially with non-normal data.

Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • The Cochran-Mantel-Haenszel (CMH) correlation statistic (QC) is used for stratum-adjusted analysis of associations between ordered categorical variables.
  • Its application extends to continuous variables, particularly within K I x J contingency tables.

Purpose of the Study:

  • To derive and evaluate an estimator for the average correlation coefficient in K I x J tables.
  • To assess two variance estimates for this average correlation coefficient: a restricted and an unrestricted variance.

Main Methods:

  • Derivation of an average correlation coefficient estimator.
  • Study of restricted variance (based on null hypothesis cell frequencies) and unrestricted variance (based on asymptotic variance).
  • Application and comparison of methods using continuous non-normal (bivariate gamma) and normal distributions.

Related Experiment Videos

Main Results:

  • The proposed estimator performs well across various table margins, sample sizes, and correlation patterns.
  • Restricted variance confidence intervals are preferred for zero/small correlations and small cell frequencies.
  • Unrestricted confidence intervals are superior for larger correlations and cell frequencies.
  • CMH and normal theory statistics show comparable size and power.
  • The proposed estimator outperforms normal theory estimators for small, skewed sample sizes.

Conclusions:

  • The developed estimator and variance estimates offer robust tools for analyzing stratified associations.
  • Confidence interval performance varies based on correlation strength, sample size, and data distribution.
  • No single confidence interval method is universally optimal across all conditions.