A Monte Carlo study of formulas for the bias and variance of double-corrected correlation coefficients

Date

1987

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Abstract

Monte Carlo approach was employed to investigate the accuracy of Bobko's (1983) formulas for the bias and variance of correlations corrected for range restriction and criterion unreliability, and of formulas for the standard error of correlations corrected for range restriction alone (Bobko & Rieck, 1980; Kelly, 1923). A computer program was written to generate 100 samples (N = 200 and N = 100) from each of 80 distributions of rxy (derived by crossing various levels of true validity, criterion reliability, and selection ratio). Results indicate Bobko's (1983) bias formula is conservative, but too inaccurate to be of practical value. Bobko's variance formula, on the other hand, is moderately accurate and useful in practical applications. The standard error formulas proposed by Kelly for the correlation corrected for range restriction are conservative but relatively inaccurate. The Bobko and Rieck (1980) formula is much more accurate than the Kelly (1923) formulas and useful in practical applications. The standard error formula for the observed correlation generally underestimates the actual standard error to a slight extent. These standard error formulas can be used to compute confidence intervals for the true correlation, and have applications in validity generalization studies. Limitations of these formulas are also discussed.

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Keywords

Employee selection, Psychological tests, Evaluation, Mathematical models

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