Correcting for range restriction when the population variance is unknown

Abstract

Correction of correlations diminished by range restriction is a commonly suggested psychometric technique. Such corrections may be appropriate in applied settings, such as educational or personnel selection, or in more theoretical applications, such as meta-analysis. However, an important limitation on the practice of range restriction corrections exists-an estimate of the unrestricted population variance is required. This article outlines and examines the accuracy of a method for estimating the unrestricted variance of a variable from the restricted sample itself. This method is based on the observation that it is possible to table a function of the truncated normal distribution that will allow the extent or point of truncation to be estimated (Cohen, 1959). The correlation of the truncated variable with other variables may then be corrected by standard restriction of range formulas. The method also allows for correction of the mean of the restricted variable.