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Statistical Consideration of Mastery Scores

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
Boston College
*
Requests for reprints should be addressed to Huynh Huynh, Division of Educational Research, Boston College, Chestnut Hill, Massachusetts 02167.
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Abstract

The kind of mastery score problem often encountered in educational and psychological testing may be roughly described as follows: given that a certain unit of instruction must be mastered by a subject, a test is administered at the end of this unit and, on the basis of the observed score or an estimate of the true score, a decision is made about the grant of the mastery status. If the subject is declared master of the unit, he will be allowed to proceed to the next unit of instruction. Otherwise, remedial work will be given. Given relevant consequences of misclassification, the problem is to determine an optimum decision rule.

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 1 , March 1976 , pp. 65 - 78
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

Part of this work was completed while the author was Visiting Researcher at the Learning Research and Development Center, University of Pittsburgh in the summer of 1973. Gratitude is extended to Robert Glaser for the invitation and to Anthony Nitko for helpful comments and suggestions.

References

Atkinson, R. C. Computer-based instruction in initial reading. In Proceedings of the 1967 Invitational Conference on Testing Problems, 1968, Princeton, New Jersey: Educational Testing Service.Google Scholar
Berkson, J. A statistical precise and relatively simple method of estimating the bio-assay with quantal response, based on the logistic function. Journal of the American Statistical Association, 1953, 48, 565–599.Google Scholar
Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M. and Novick, M. R. (Eds.), Statistical theories of mental test scores, 1968, Reading, Massachusetts: Addison-Wesley Publishing Company.Google Scholar
Cochran, W. G. Experiments for nonlinear functions. Journal of the American Statistical Association, 1973, 68, 771–781.Google Scholar
Ebel, R. L. Criterion-referenced measurements: limitations. School Review, 1971, 69, 282–288.CrossRefGoogle Scholar
Emrick, J. A. An evaluation model for mastery testing. Journal of Educational Measurement, 1971, 8, 321–326.CrossRefGoogle Scholar
Ferguson, R. L. Computer assistance for individualizing measurement, 1971, Pittsburgh: University of Pittsburgh Learning Research and Development Center.CrossRefGoogle Scholar
Ferguson, T. S. Mathematical statistics: a decision theoretic approach, 1967, New York: Academic Press.Google Scholar
Flanagan, J. C. Functional education for the seventies. Phi Delta Kappan, 1967, 49, 27–32.Google Scholar
Glaser, R. Adapting the elementary school curriculum to individual performance. In Proceedings of the 1967 Invitational Conference on Testing Problems, 1968, Princeton, New Jersey: Educational Testing Service.Google Scholar
Glaser, R. and Nitko, A. J. Measurement in learning and instruction. In Thorndike, R. L. (Eds.), Educational measurement, 1971, Washington: American Council on Education.Google Scholar
Hambleton, R. K. Testing and decision-making procedures for selected individualized instructional programs. Review of Educational Research, 1974, 44, 371–400.CrossRefGoogle Scholar
Hambleton, R. K. and Novick, M. R. Toward an integration of theory and method for criterion-referenced tests. Journal of Educational Measurement, 1973, 10, 159–170.CrossRefGoogle Scholar
IBM Application Program, System/360. Scientific subroutines package (360-CM-03X) Version III, programmer's manual, 1971, White Plains, New York: IBM Corporation Technical Publications Department.Google Scholar
Keats, J. A. and Lord, F. M. A theoretical distribution for mental test scores. Psychometrika, 1962, 27, 59–72.CrossRefGoogle Scholar
Lord, F. M. Tailored testing, an application of stochastic approximation. Journal of the American Statistical Association, 1971, 66, 707–711.CrossRefGoogle Scholar
Lord, F. M. and Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Massachusetts: Addison-Wesley Publishing Company.Google Scholar
Novick, M. R. and Jackson, P. H. Statistical methods for educational and psychological research, 1974, New York: McGraw-Hill.Google Scholar
Pearson, K. Tables of the incomplete beta function, 1934, Cambridge: University Press.Google Scholar
Rudin, W. Real and complex analysis, 1966, New York: McGraw-Hill.Google Scholar
Schlaifer, R. Analysis of decisions under uncertainty, 1969, New York: McGraw-Hill.Google Scholar