Determining the Significance of Correlations Corrected for Unreliability and Range Restriction

Abstract

A new asymptotic formula for estimating the sampling variance of a correlation coefficient corrected for unreliability and range restriction was proposed. A Monte Carlo assessment of the new sampling variance formula has resulted in the following conclusions. First, the formula-based (analytical) sampling variances were very close to the empirically derived sampling variances based on 5,000 replications. Second, the sampling variance formula was quite robust against committing Type I errors. Third, the statistical power was low to moderate in distinguishing between two unattenuated and unrestricted population correlations. Fourth, the new formula produced smaller sampling variances; was closer to nominal alpha levels; and was more powerful when sample size increased, when the population correlation coefficient increased, when range restriction was less severe, and when both the criterion and predictor reliabilities increased.