A comparison of methods for constructing confidence intervals for the squared multiple correlation coefficient

Four methods for constructing 100(1 - alpha)% confidence intervals for the population squared multiple correlation coefficient (rho(2)) were compared. In one method the confidence interval was constructed by using the distribution of R-2. Provided rho(2) > 0 the coverage probability for this method is exactly 1 - alpha when the data are multivariate normal. The other three methods are based on results in Olkin and Finn (1995) and are approximate. Results show that each of the approximate methods works very poorly for some combinations of rho(2). The method based on the distribution of R-2 is recommended.