Comparing Two Squared Multiple Correlation Coefficients: A Bootstrap Approach

Professor Chan Wai
Department of Psychology
The Chinese University of Hong Kong

Abstract

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, and . Empirical results based on reported simulation studies indicated that these methods failed to perform accurately under certain model conditions. In this presentation, a unified bootstrap procedure is proposed for estimating the standard error of - and constructing the confidence interval for and . A simulation study involving both normal and nonnormal data was conducted to examine the empirical performance of the proposed procedure under different levels of and sample size. Results indicated that while the bootstrap and the asymptotic standard-error estimates both perform satisfactorily with normal data, the bootstrap estimate is more accurate when data are nonnormal. The bootstrap percentile interval also provides an accurate coverage probability for -.