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Correlation and Prediction in Ordinal Test Theory

Published online by Cambridge University Press:  01 January 2025

Robert S. Schulman
Robert S. Schulman*
Affiliation:
Virginia Polytechnic Institute and State University
*
Requests for reprints should be sent to Robert S. Schulman, Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.
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Abstract

Based on the test theory model for ordinal measurements proposed by Schulman and Haden, the present paper considers correlations between tests, attenuation, regressions involving true and observed scores, and prediction of test reliability.

The population correlation between tests is shown to be related to the expected sample correlation for samples of size n1 and n2. Errors of estimation, measurement and prediction are found to be similar to their counterparts in interval test theory, while attenuation is identical to its counterpart. The bias in estimating population reliability from sample data is compared for Kendall's tau and Spearman's rho.

Keywords

attenuationerror of estimationerror of measurementerror of predictionreliability estimation

Information

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 3 , September 1976 , pp. 329 - 340
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

The author wishes to thank the referees for their helpful comments on an earlier draft of this paper, and in particular, for the suggested alternative methods of establishing some of the presented results.

References

Cochran, W. G. Sampling techniques, 1963, New York: John Wiley & Sons, Inc..Google Scholar
Durbin, J. & Stuart, A. Inversions and rank correlation coefficients. Journal of the Royal Statistical Society, Series B, 1951, 13, 303–309.CrossRefGoogle Scholar
Kendall, M. G. Rank correlation methods, 1970, London: Charles Griffin & Company.Google Scholar
Lord, F. M. & Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Schulman, R. S. & Haden, R. L. A test theory model for ordinal measurements. Psychometrika, 1975, 40, 455–472.CrossRefGoogle Scholar
Sen, P. K. The Hájek-Rènyi inequality for sampling from a finite population. Sankhyã, Series A, 1970, 32, 181–188.Google Scholar