Correcting for restriction of range in both X and Y when the unrestricted variances are unknown

Abstract

Correction of correlation coefficients that have arisen from range restricted populations is commonly suggested and practiced in research on testing and measurement. Until recently, that research has operated under two important limitations. First, the majority of the research has dealt with range restriction on one variable only, and second, the correction formulas have assumed that the variance of the variable(s) in the unrestricted population was known. This article presents a method for estimating such corrections from the data in the restricted sample and applies the method to a recently developed approximation for restriction on both and Y. The procedure is evaluated and found to produce sufficiently accurate results to be useful in many practical range restriction settings.