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Distribution of the Determinant of the Sample Correlation Matrix: Monte Carlo Type One Error Rates

John R. Reddon, Douglas N. Jackson and Donald Schopflocher
Journal of Educational Statistics
Vol. 10, No. 4 (Winter, 1985), pp. 384-388
DOI: 10.2307/1164667
Stable URL: http://www.jstor.org/stable/1164667
Page Count: 5
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Distribution of the Determinant of the Sample Correlation Matrix: Monte Carlo Type One Error Rates
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Abstract

Computer sampling from a multivariate normal spherical population was used to evaluate the type one error rates for a test of sphericity based on the distribution of the determinant of the sample correlation matrix. The range of variates considered was 5 to 25, and the range of observations considered was 10 to 1,000. The type one error rates were estimated in each condition with 5,000 replications. The c. d. f. obtained from the asymptotic χ 2 resulted in excessive type one errors in the conditions where the ratio of the sample size to the number of variates was small. The c. d. f. with finite sample corrections involving terms up to o (N-3) performed much better in small samples but resulted in a biased test when the sample size was less than twice the number of variates.

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