Abstract
It is generally believed that correlations and standard deviations measured within an explicitly selected group must be smaller than those within an applicant population. A small data set is used to show that this is not always true, and that both validity and reliability estimates within a selected group can exceed those within the applicant population. The increase in correlation within the explicitly selected group is tied to an increase in standard deviation of the predictor in the selected group. This conclusion extends Levin's (1972) result for the case of incidental selection, selection on an unmeasured third variable. If possible, theoretical derivations should not be limited to the case where the predictor standard deviation in the applicant population exceeds that in the selected group. When such a situation occurs in observed data, it cannot be immediately dismissed as an artifact.
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References
Callender, J. C., & Osburn, H. G. (1981). Testing the constancy of validity with computer-generated sampling distributions of the multiplicative model variance estimate: Results for petroleum industry validation research.Journal of Applied Psychology, 66, 274–281.
Davis, F. B. (1944). A note on correcting reliability coefficients for range.Journal of Educational Psychology, 35, 500–502.
Gulliksen, H. (1950).Theory of Mental Tests. New York: Wiley.
Levin, J. (1972). The occurrence of an increase in correlation by restriction of range.Psychometrika, 37, 93–97.
Lord, F. M., & Novick, M. L. (1968).Statistical Theories of Mental Test Scores. Reading, MA: Addison-Wesley.
Pearson, K. (1903). Mathematical contributions to the theory of evolution XI—On the influence of natural selection on the variability and correlation of organs.Philosophical Transactions, A, 200, 1–66.
Pearson, K. (1912). On the general theory of the influence of selection on correlation and variation.Biometrika, 8, 437–443.
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The author would like to thank Mark L. Davison and other reviewers for their comments on earlier drafts of the paper. An anonymous reviewer provided a better example than the original one, resulting in a more general conclusion.
This work was supported in part by a Dissertation Fellowship from the University of Minnesota.
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McGuire, D.P. The occurrence of an increase in correlation with explicit selection. Psychometrika 51, 331–333 (1986). https://doi.org/10.1007/BF02293989
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DOI: https://doi.org/10.1007/BF02293989