Confidence Interval Estimation and Hypothesis Testing for a Common Correlation Coefficient

Research output: Contribution to journalArticle

Abstract

Several procedures have been proposed for testing the hypothesis that all off-diagonal elements of the correlation matrix of a multivariate normal distribution are equal. If the hypothesis of equal correlation can be accepted, it is then of interest to estimate and perhaps test hypotheses for the common correlation. In this paper, two versions of five different test statistics are compared via simulation in terms of adequacy of the normal approximation, coverage probabilities of confidence intervals, control of Type I error, and power. The results indicate that two test statistics based on the average of the Fisher z-transforms of the sample correlations should be used in most cases. A statistic based on the sample eigenvalues also gives reasonable results for confidence intervals and lower-tailed tests.

Original languageEnglish (US)
Pages (from-to)185-203
Number of pages19
JournalJournal of Statistical Computation and Simulation
Volume24
Issue number3-4
DOIs
StatePublished - Jul 1 1986
Externally publishedYes

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Interval Estimation
Hypothesis Testing
Correlation coefficient
Confidence interval
Statistics
Test Statistic
Testing
z transform
Multivariate Normal Distribution
Normal Approximation
Type I error
Hypothesis Test
Coverage Probability
Correlation Matrix
Normal distribution
Statistic
Mathematical transformations
Eigenvalue
Estimate
Interval estimation

Keywords

  • Correlation matrix
  • eigenvalues
  • equicorrelation
  • normal approximation
  • power
  • significance level

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

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