Bootstrap Standard Error and Confidence Intervals for the Difference Between Two Squared Multiple Correlation Coefficients

A typical question in multiple regression analysis is to determine if a set of predictors gives the same degree of predictor power in two different populations. Olkin and Finn (1995) proposed two asymptotic-based methods for testing the equality of two population squared multiple correlations, rho(2)(1) and rho(2)(2). Simulation results indicated that these methods failed to perform accurately under certain model conditions (Algina & Keselman, 1999). In the present study, a unified bootstrap procedure is proposed for estimating the standard error of R-1(2) - R-2(2) and constructing the confidence interval for rho(2)(1) - r(2)(2). A simulation study was conducted to examine the empirical performance of the proposed procedure under different levels of rho(2), sample sizes, numbers of predictors, and types of data distribution. Results indicated that the asymptotic method, in general, can only work well with normal data. The bootstrap procedure, on the other hand, performs satisfactorily with both normal and nonnormal data. However, both methods fail when rho(2)(1) and r(2)(2) are zero.