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Probability-of-Coverage Tolerance Intervals for the Beta Binomial

Published online by Cambridge University Press:  01 January 2025

David Jarjoura
David Jarjoura*
Affiliation:
Northeastern Ohio Universities College of Medicine
*
Requests for reprints should be sent to David Jarjoura, Division of Community Health Sciences, Northeastern Ohio Universities College of Medicine, PO Box 95, Rootstown, OH 44272.
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Abstract

True score tolerance intervals, which are designed to cover a chosen proportion of the conditional distribution of true scores given an observed score, are suggested as alternatives to true score confidence intervals. Using large sample theory, a tolerance interval estimator for the beta binomial is derived. An example indicates that with moderate sample sizes, tolerance intervals with high probability of coverage will not be much wider than when the two beta true score parameters are known.

Keywords

beta binomialtolerance intervalstrue score intervals
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 137 - 141
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

The author acknowledges valuable comments from Richard Sawyer.

Most work was completed while the author was at the American College Testing Program.

References

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