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An Asymptotic |chi2 Test for the Equality of Two Correlation Matrices

Robert I. Jennrich
Journal of the American Statistical Association
Vol. 65, No. 330 (Jun., 1970), pp. 904-912
DOI: 10.2307/2284596
Stable URL: http://www.jstor.org/stable/2284596
Page Count: 9
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An Asymptotic |chi2 Test for the Equality of Two Correlation Matrices
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Abstract

An asymptotic χ2 test for the equality of two correlation matrices is derived. The key result is a simple representation for the inverse of the asymptotic covariance matrix of a sample correlation matrix. The test statistic has the form of a standard normal theory statistic for testing the equality of two covariance matrices with a correction term added. The applicability of asymptotic theory is demonstrated by two simulation studies and the statistic is used to test the difference in the factor patterns resulting from a set of tests given to retarded and non-retarded children. Two related tests are presented: a test for a specified correlation matrix and a test for equality of correlation matrices in two or more populations.

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