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Fisher’s Tanh^–1 Transformation of the Correlation Coefficient and a Test for Complete Independence in a Multivariate Normal Population

Alberta Hospital Edmonton

Computer sampling from a multivariate normal spherical population was used to evaluate Type I error rates for a test of P = I based on Fisher’s tanh^–1 variance stabilizing transformation of the correlation coefficient. The range of variates considered was 5 to 25 and Type I error rates were estimated for several sample sizes with 2,500 independent replications. Except for small samples the test was well behaved. After the test converges to an acceptable Type I error rate it is preferable to Box’s test of P = I.

Key Words: correlation • Monte Carlo • multivariate independence • sphericity

Journal of Educational and Behavioral Statistics, Vol. 12, No. 3, 294-300 (1987)
DOI: 10.3102/10769986012003294


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