An Evaluation of Two Techniques for Constructing Confidence Intervals for the Squared Multiple Correlation Coefficient

Abstract

Fowler's (1986) and Helland's (1987) techniques for constructing confidence intervals for the squared multiple correlation coefficient are discussed. It is shown how the techniques may be applied using F tables and a calculator. Recalculation of Fowler's and Helland's examples shows that Helland's limits are closer to exact values than Fowler's limits. Using realistic simulation results it is shown that, generally speaking, the lower limits of .95 confidence intervals are about the same for both techniques. Fowler's upper limits are much lower than Helland's, however. From further examination it is concluded that Helland's upper limits nevertheless are somewhat too low. Finally, many iterations are required if both N and R¹ are small.