Accuracy of Population Validity and Cross-Validity Estimation: An Empirical Comparison of Formula-Based, Traditional Empirical, and Equal Weights Procedures

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Abstract
An empirical monte carlo study was performed using predictor and criterion data from 84,808 U.S. Air Force enlistees. 501 samples were drawn for each of seven sample size conditions: 25, 40, 60, 80, 100, 150, and 200. Using an eight-predictor model, 500 estimates for each of 9 validity and 11 cross-validity estimation procedures were generated for each sample size condition. These estimates were then compared to the actual squared population validity and cross-validity in terms of mean bias and mean squared bias. For the regression models determined using ordinary least squares, the Ezekiel procedure produced the most accurate estimates of squared population validity (followed by the Smith and the Wherry procedures), and Burket’s formula resulted in the best estimates of squared population cross-validity. Other analyses compared the coefficients determined by traditional empirical cross-validation and equal weights; equal weights resulted in no loss of predictive accuracy and less shrinkage. Numerous issues for future basic research on validation and cross-validation are identified.