Improved Approximation to the Non-Null Distribution of the Correlation Coefficient
HELENA CHMURA KRAEMER · Journal of the American Statistical Association · 1973
If r is the correlation coefficient based on a sample of n observations randomly drawn from a population having a bivariate normal distribution with correlation coefficient ρ, it is shown that is approximately distributed as t with (n − 2) degrees of freedom where ρ′ is a function of ρ and n satisfying certain constraints.