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

Abstract

Univariate and multivariate corrections for range restriction 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 validities (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 corrections, notably when the univariate explicit selection variable was negatively skewed and correction violations (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 correlation. Index terms: correction formulas, explicit selection, incidental selection, multivariate correction formulas, restriction in range, validation studies.Since Pearson (1903) developed the correction formulas for restriction in range and Thorndike

An Improved Correction for Range Restricted Correlations Under Extreme, Monotonic Quadratic Nonlinearity and Heteroscedasticity

“…Note that γ 1 < 0 in Equation 24 is consistent with prior research (Held & Foley, 1994;Kobrin et al, 2011;Lee & Foley, 1986). It is important to note several properties of the normal distribution.…”

“…Furthermore, unlike the correction in Equation 1, Assumption 2 allows the prediction errors to be a function of test scores, h (X ). When nonconstant error variance has been detected, prior empirical personnel psychology and educational testing research consistently identified patterns of heteroscedasticity that declines with X (Held & Foley, 1994;Kobrin et al, 2011;Lee & Foley,1986). That is, prediction errors are smaller for higher test scores.…”

Data pruning in consumer choice models

“…Finally, the statistics and economics literature considers the classical "restrictionof-range" problem (DeMets and Halperin, 1977;Duan and Dunlap, 1997;Johnson and Ree, 1994;Held and Foley, 1994;Mendoza et al 1991;Hanges et al 1991;Holmes, 1990). In this literature, correlations, or more generally regression coefficients are shown to be affected by focusing the analysis on a small slice of the population.…”

Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods

“…This issue of the accuracy of the correction for the range restriction formula under different conditions has been extensively addressed in the literature (e.g., Brewer & Hills, 1969;Greener & Osburn, 1979Gross & Fleischman, 1983;Held & Foley, 1994;Holmes, 1990). It should be noted that no normality assumption is required for range restriction correction formulas (Lawley, 1944;Sackett & Yang, 2000).…”