A Comparison of Methods for Constructing Confidence Intervals for the Squared Multiple Correlation Coefficient.

Four methods for constructing 100(1 - a)% confidence intervals for the population squared multiple correlation coefficient (r2) were compared. In one method the confidence interval was constructed by using the distribution of R². Provided r² > 0 the coverage probability for this method is exactly 1 - a 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 r². The method based on the distribution of R² is recommended.