Standard Errors of Multivariate Range-Corrected Validities

Abstract

The multivariate rather than the univariate range correction is used for estimating unrestricted applicant population validities in many military test validity studies but not uniformly. A Monte Carlo approach compared the standard errors of range-corrected validities under various experimental conditions adhering to the assumptions underlying correction accuracy. The multivariate corrected validities had smaller standard errors than both the univariate-corrected validities and the unrestricted validities. We conclude that using the univariate correction could fail to reveal the most valid selection instrument and that the multivariate correction should be used when scores for relevant predictors are available for the unrestricted population.

Notes

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¹The regression weights for all ASVAB tests in the sample are used in the multivariate correction even though only one composite of a small number of tests is applied as the explicit selector.

² Unbiased is used here to mean that the expected value equals the population value. Strictly speaking, none of the estimators discussed in this article are unbiased, although their biases are negligible. Indeed, the ordinary uncorrected sample correlation is a biased estimator of its restricted population value, but the bias decreases as the sample size increases, which is to say, the sample correlation is a consistent estimator.