Hostname: page-component-6766d58669-bkrcr Total loading time: 0 Render date: 2026-05-21T09:55:11.871Z Has data issue: false hasContentIssue false
  • English
  • Français

Relating Tests Given to Different Samples

Published online by Cambridge University Press:  01 January 2025

Donald B. Rubin  and
Dorothy Thayer
Donald B. Rubin*
Affiliation:
Educational Testing Service
Dorothy Thayer
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Donald B. Rubin, Educational Testing Service, Princeton, New Jersey 08540.
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose a collection of standard tests is given to all subjects in a random sample, but a different new test is given to each group of subjects in nonoverlapping subsamples. A simple method is developed for displaying the information that the data set contains about the correlational structure of the new tests. This is possible to some extent, even though each subject takes only one new test. The method uses plausible values of the partial correlations among the new tests given the standard tests in order to generate plausible simple correlations among the new tests and plausible multiple correlations between composites of the new tests and the standard tests. The real data example included suggests that the method can be useful in practical problems.

Keywords

correlationsincomplete datamissing datainestimable parametersmaximum likelihood estimation

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 3 - 10
Copyright
Copyright © 1978 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Reference Note

Beaton, A. E. The use of special matrix operations in statistical calculus, 1964, Princeton, N. J.: Educational Testing Service.Google Scholar

References

Anderson, T. W. Maximum likelihood estimates for a multivariate normal distribution when some observations are missing. Journal of the American Statistical Association, 1957, 52, 200–203.CrossRefGoogle Scholar
Dempster, A. P. Elements of Continuous Multivariate Analysis, 1969, Reading, Mass.: Addison-Wesley Publishing Company.Google Scholar
Edgett, G. L. Multiple regression with missing observations among the independent variables. Journal of the American Statistical Association, 1956, 51, 122–131.10.1080/01621459.1956.10501315CrossRefGoogle Scholar
Hartley, H. O. & Hocking, R. R. The analysis of incomplete data. Biometrics, 1971, 27, 783–823.CrossRefGoogle Scholar
Lord, F. M. Equating test scores—A maximum likelihood solution. Psychometrika, 1955, 20, 193–200.CrossRefGoogle Scholar
Lord, F. M. Estimation of parameters from incomplete data. Journal of the American Statistical Association, 1955, 50, 870–876.CrossRefGoogle Scholar
Lord, F. M. & Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley Publishing Company.Google Scholar
Rubin, D. B. Characterizing the estimation of parameters in incomplete-data problems. Journal of the American Statistical Association, 1974, 69, 467–474.CrossRefGoogle Scholar
Rubin, D. B. Comparing regressions when some predictor values are missing. Technometrics, 1976, 18, 201–205.CrossRefGoogle Scholar
Rubin, D. B. Inference and missing data. Biometrika, 1976, 63, 581–592.10.1093/biomet/63.3.581CrossRefGoogle Scholar