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Comparing Examinees to a Control

Published online by Cambridge University Press:  01 January 2025

Rand R. Wilcox
Rand R. Wilcox*
Affiliation:
University of California at Los Angeles
*
Requests for reprints should be sent to Rand R. Wilcox, Center for the Study of Evaluation, UCLA Graduate School of Education, 145 Moore Hall, Los Angeles, CA 90024.
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Abstract

When comparing examinees to a control, the examiner usually does not know the probability of correctly classifying the examinees based on the number of items used and the number of examinees tested. Using ranking and selection techniques, a general framework is described for deriving a lower bound on this probability. We illustrate how these techniques can be applied to the binomial error model. New exact results are given for normal populations having unknown and unequal variances.

Keywords

setting standardsindifference zonestrong true-score models
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 1 , March 1979 , pp. 55 - 68
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

The work upon which this publication is based was performed pursuant to a grant [Grant No. NIE-G-76-0083] with the National Institute of Education, Department of Health, Education and Welfare. Points of view or opinions stated do not necessarily represent official NIE position or policy.

The author would like to thank Shelley Niwa for writing the computer programs used in this study.

References

Reference Note

Wilcox, R. R. Comparing normal populations to a control, 1977, Los Angeles: Center for the Study of Evaluation, University of California.Google Scholar

References

Aitchison, J., & Aitken, C. G. G. Multivariate binary discrimination by the kernel method. Biometrika, 1976, 63, 413–420.CrossRefGoogle Scholar
Aitchison, J., & Dunsmore, I. R. Statistical prediction analysis, 1975, Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Bahadur, R. R. A representation of the joint distribution of responses to n dichotomous items. In Solomon, H.(Eds.), Studies in item analysis and prediction, 1961, Stanford: Stanford University Press.Google Scholar
Barr, D. R., & Rizvi, M. H. An introduction to ranking and selection. Journal of the American Statistical Association, 1966, 61, 640–646.CrossRefGoogle Scholar
Dudewicz, E. J., & Dalal, S. R. Allocation of observations in ranking and selection with unequal variances. Sankhya, 1975, 37, 28–78.Google Scholar
Dudewicz, E. J., Ramberg, J. S., & Chen, H. J. New tables for multiple comparisons with a control (unknown variances). Biometrische Zeitschrift, 1975, 17, 13–26.CrossRefGoogle Scholar
Freeman, M. F., & Tukey, J. W. Transformations related to the angular and the square root. The Annals of Mathematical Statistics, 1950, 21, 607–611.CrossRefGoogle Scholar
Gupta, S., & Sobel, M. On selecting a subset which contains all populations better than a standard. The Annals of Mathematical Statistics, 1958, 29, 235–244.CrossRefGoogle Scholar
Huynh, H. Statistical consideration of mastery scores. Psychometrika, 1976, 41, 65–78.CrossRefGoogle Scholar
IBM Application Program, System/360. Scientific subroutines package (360-CM-03X) Version III, programmer's manual, 1971, White Plains, NY: IBM Corporation Technical Publications Department.Google Scholar
Johns, M. V. An empirical Bayes approach to non-parametric two-way classification. In Solomon, H.(Eds.), Studies in item analysis and prediction, 1961, Stanford: Stanford University Press.Google Scholar
Keats, J. A., & Lord, F. M. A theoretical distribution for mental test scores. Psychometrika, 1962, 27, 59–72.CrossRefGoogle Scholar
Lord, F. M. A strong true-score theory, with applications. Psychometrika, 1965, 30, 239–270.CrossRefGoogle Scholar
Lord, F. M., & Novick, M. R. Statistical theories of mental test scores, 1968, Reading, MA: Addison-Wesley.Google Scholar
Mosteller, F., & Tukey, J. W. Data analysis, including statistics. In Lindzey, G., & Aronsen, E.(Eds.), The handbook of social psychology, 1968, Reading, MA: Addison-Wesley.Google Scholar
Mosteller, F., & Youtz, C. Tables of the Freeman-Tukey transformations for the binomial and Poisson distributions. Biometrika, 1961, 48, 433–440.CrossRefGoogle Scholar
Ott, J., & Kronmal, R. A. Some classification procedures for multivariate binary data using orthogonal functions. Journal of the American Statistical Association, 1976, 71, 391–399.CrossRefGoogle Scholar
Tong, Y. L. On partitioning a set of normal populations by their locations with respect to a control. The Annals of Mathematical Statistics, 1969, 40, 1300–1324.CrossRefGoogle Scholar
Wilcox, R. R. Applying ranking and selection techniques to determine the length of a mastery test. Educational and Psychological Measurement, in press, 1979.CrossRefGoogle Scholar