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

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.