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Validating a Selection Test, a Predictive Probability Approach

Published online by Cambridge University Press:  01 January 2025

Alan L. Gross  and
Philippa Perry
Alan L. Gross*
Affiliation:
The City University of New York
Philippa Perry
Affiliation:
The City University of New York
*
Requests for reprints should be sent to Professor Alan L. Gross, Graduate Center, The City University of New York, Ph.D. Program in Educational Psychology, 33 W. 42 Street, New York, N.Y., 10036
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Abstract

The problem of inferring the validity of a selection test (x) as a predictor of some criterion (y) when complete xy data are not available is investigated. The basic approach is to construct the predictive probability distribution of the unobserved y scores and then derive interval estimates of the least squares regression weights, the difference in average y scores for selected and unselected cases, and the residual variance in predicting y from x. Further, an approximation to the predictive distribution of the squared correlation between x and y in a future group is derived.

Keywords

restriction of rangepredictive probability distribution
Type
Article
Information
Psychometrika , Volume 48 , Issue 1 , March 1983 , pp. 113 - 127
Copyright
Copyright © 1983 The Psychometric Society

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References

Reference Notes

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Gulliksen, H. Theory of Mental Tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Lawley, D. N. A note on Karl Pearson's selection formulae. Royal Society of Edinburgh Proceedings, Section A, 1943, 62, 28–30.Google Scholar
Lord, F. M. & Novick, M. R. Statistical Theories of Mental Test Scores, Reading, Massachusetts: Addison-Wesley, 1968.Google Scholar
Novick, M. R. & Jackson, P. H. Statistical Methods for Educational and Psychological Research, New York: McGraw-Hill, 1974.Google Scholar
Patnaik, P. B. The noncentral x2 and F-distributions and their approximations. Biometrika, 1949, 36, 202–232.Google Scholar
Press, S. J. Applied Multivariate Analysis, New York: Holt, Rinehardt & Winston, Inc., 1972.Google Scholar
Roe, R. A. The correction for restriction in range and the difference between intended and actual selection. Educational and Psychological Measurement, 1979, 39, 551–559.CrossRefGoogle Scholar
Rubin, D. B. Inference and Missing Data. Biometrika, 1976, 63, 581–592.CrossRefGoogle Scholar
Rubin, D. B. Formalizing Subjective Notions of Non-Response. Journal of the American Statistical Association, 1977, 72, 538–543.CrossRefGoogle Scholar
Rydberg, S. Bias in Prediction, Stockholm: Almquist and Wiksell, 1963.Google Scholar
Zellner, A. & Chetty, V. K. Prediction and decision problems in regression models from the Bayesian point of view. Journal of the American Statistical Association, 1965, 60, 608–616.CrossRefGoogle Scholar
Box, G. E. P. & Tiao, G. C. Bayesian inference in statistical analysis, Reading, Massachusetts: Addison-Wesley, 1973.Google Scholar
Cohen, A. C. Restriction and selection in samples from bivariate normal distributions. Journal of the American Statistical Association, 1955, 50, 884–893.Google Scholar
Cohen, A. C. Jr. Restriction and selection in multinormal distributions. Annals of Mathematical Statistics, 1957, 28, 731–741.CrossRefGoogle Scholar
Furst, E. J. & Roelfs, P. J. Validation of the Graduate Record Examination and the Miller analogue test in a doctoral program in education. Educational and Psychological Measurement, 1979, 39, 147–151.CrossRefGoogle Scholar
Graybill, F. A. An Introduction to Linear Statistical Models, Volume I, New York: McGraw-Hill, Inc., 1961.Google Scholar
Gulliksen, H. Theory of Mental Tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Lawley, D. N. A note on Karl Pearson's selection formulae. Royal Society of Edinburgh Proceedings, Section A, 1943, 62, 28–30.Google Scholar
Lord, F. M. & Novick, M. R. Statistical Theories of Mental Test Scores, Reading, Massachusetts: Addison-Wesley, 1968.Google Scholar
Novick, M. R. & Jackson, P. H. Statistical Methods for Educational and Psychological Research, New York: McGraw-Hill, 1974.Google Scholar
Patnaik, P. B. The noncentral x2 and F-distributions and their approximations. Biometrika, 1949, 36, 202–232.Google Scholar
Press, S. J. Applied Multivariate Analysis, New York: Holt, Rinehardt & Winston, Inc., 1972.Google Scholar
Roe, R. A. The correction for restriction in range and the difference between intended and actual selection. Educational and Psychological Measurement, 1979, 39, 551–559.CrossRefGoogle Scholar
Rubin, D. B. Inference and Missing Data. Biometrika, 1976, 63, 581–592.CrossRefGoogle Scholar
Rubin, D. B. Formalizing Subjective Notions of Non-Response. Journal of the American Statistical Association, 1977, 72, 538–543.CrossRefGoogle Scholar
Rydberg, S. Bias in Prediction, Stockholm: Almquist and Wiksell, 1963.Google Scholar
Zellner, A. & Chetty, V. K. Prediction and decision problems in regression models from the Bayesian point of view. Journal of the American Statistical Association, 1965, 60, 608–616.CrossRefGoogle Scholar

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