### 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 language | English (US) |
---|---|

Pages (from-to) | 185-203 |

Number of pages | 19 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 24 |

Issue number | 3-4 |

DOIs | |

State | Published - Jul 1 1986 |

Externally published | Yes |

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### 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

**Confidence Interval Estimation and Hypothesis Testing for a Common Correlation Coefficient.** / Looney, Stephen Warwick.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Confidence Interval Estimation and Hypothesis Testing for a Common Correlation Coefficient

AU - Looney, Stephen Warwick

PY - 1986/7/1

Y1 - 1986/7/1

N2 - 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.

AB - 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.

KW - Correlation matrix

KW - eigenvalues

KW - equicorrelation

KW - normal approximation

KW - power

KW - significance level

UR - http://www.scopus.com/inward/record.url?scp=84954782384&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954782384&partnerID=8YFLogxK

U2 - 10.1080/00949658608810903

DO - 10.1080/00949658608810903

M3 - Article

AN - SCOPUS:84954782384

VL - 24

SP - 185

EP - 203

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 3-4

ER -