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Correction for range restriction: an expanded typology.

A common research problem is the estimation of the population correlation between x and y from an observed correlation rxy obtained from a sample that has been restricted because of some sample selection process. Methods of correcting sample correlations for range restriction in a limited set of conditions are well-known. An expanded classification scheme for range-restriction scenarios is developed that conceptualizes range-restriction scenarios from various combinations of the following facets: (a) the variable(s) on which selection occurs (x, y and/or a 3rd variable z), (b) whether unrestricted variances for the relevant variables are known, and (c) whether a 3rd variable, if involved, is measured or unmeasured. On the basis of these facets, the authors describe potential solutions for 11 different range-restriction scenarios and summarize research to date on these techniques.