Explanations for Accuracy of the General Multivariate Formulas in Correcting for Range Restriction

Univariate and multivariate corrections for range re striction were compared using Navy applicant scores on the Armed Services Vocational Aptitude Battery (ASVAB). Two Navy school ASVAB selector composites were used separately and together to simulate three selection situations for nine selection ratios (SRs). The selectors then were used as predictors. Composite va lidities (the ASVAB Mechanical Comprehension test was the criterion) were corrected using the univariate and the general multivariate formulas. In general, multivariate corrections were more accurate than univariate correc tions, notably when the univariate explicit selection variable was negatively skewed and correction viola tions (linearity and homoscedasticity) did not offset each other. Multivariate correction accuracy was attributed to the inclusion of variables with adequate distributional properties, the compensatory effects of regression weights, and the related psychometric principle that differentially weighting a large number of correlated predictor variables has little impact on a multiple cor relation. Index terms: correction formulas, explicit selection, incidental selection, multivariate correction formulas, restriction in range, validation studies.