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Applied Psychological Measurement
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Determining the Significance of Correlations Corrected for Unreliability and Range Restriction

Nambury S. Raju,

Illinois Institute of Technology

Paul A. Brand,

Medina & Thompson, Inc.

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.

Key Words: corrected correlations • range restriction • reliability • standard errors

Applied Psychological Measurement, Vol. 27, No. 1, 52-71 (2003)
DOI: 10.1177/0146621602239476
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N. S. Raju, D. V. Lezotte, B. K. Fearing, and T. C. Oshima
A Note on Correlations Corrected for Unreliability and Range Restriction
Applied Psychological Measurement, March 1, 2006; 30(2): 145 - 149.
[Abstract] [PDF]