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

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 asymptoticχ 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 toο(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.