THE MULTIPLE CORRELATION COEFFICIENT AND FISHER'S A STATISTIC1

Fisher's A statistic, often called the adjusted R² statistic, is shown to be a close approximation to the maximum likelihood estimate of the multiple correlation coefficient, p², based on the marginal distribution of R². Expansions for the estimate are obtained. The same methods lead to maximum marginal likelihood estimators for the noncentrality parameters for noncentral X² and F.