When two correlation coefficients are calculated from a single sample, rather than from two samples, they are not statistically independent, and the usual methods for testing equality of the population correlation coefficients no longer apply. This article considers tests to be made using a sample from a multivariate normal distribution. Small sample level of significance and power are obtained using Monte Carlo methods for Hotelling's test of , Williams's modification of Hotelling's test, and for two tests of , based on Fisher's z transformation.