A Relatively Simple Form of the Distribution of the Multiple Correlation Coefficient

Summary A series is obtained for the cumulative distribution function of the multiple correlation coefficient in which the coefficients are interpretable as binomial probabilities. When N−p is even (N is the sample size and p is the number of components in the underlying multivariate normal distribution) the series is finite with 12(n−p)+1 terms. Other series are also considered. A comparatively simple approximation to the general distribution of the multiple correlation coefficient is presented which, in particular for p = 2, is more accurate than Fisher's z-transform over a large set of values of the parameters involved.