Asymptotic Confidence Limits for the Difference Between Two Squared Multiple Correlations: A Simplified Approach

This article develops equations for determining the asymptotic confidence limits for the difference between 2 squared multiple correlation coefficients. The present procedure uses the delta method described by I. Olkin and J. D. Finn (1995) but does not require the variance-covariance matrix and the partial derivatives for all the zero-order correlations that enter into the expression for the difference, as does their procedure. This simplified approach can lead to an extreme reduction in the calculations required, as well as a reduction in the mathematical complexity of the solution. This approach also demonstrates clearly that in some cases, it may be inappropriate to use the asymptotic confidence limits in tests of significance.