Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-08T04:28:57.910Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

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.)

Footnotes

The author acknowledges valuable comments from Richard Sawyer.

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

References

Griffiths, D. A. (1973). Maximum likelihood estimation for the beta binomial distribution and an application to the household distribution of the total number of cases of a disease. Biometrics, 29, 637–648.CrossRefGoogle Scholar
Jarjoura, D. (1985). Tolerance intervals for true scores. Journal of Educational Statistics, 10, 1–17.CrossRefGoogle Scholar
Keats, J. A., Lord, F. M. (1962). A theoretical distribution for mental test scores. Psychometrika, 27, 59–72.CrossRefGoogle Scholar
Kendall, M., Stuart, A. (1977). The advanced theory of statistics 4th ed.,, New York: MacMillan.Google Scholar
Kleinman, J. C. (1973). Proportions with extraneous variance: Single and independent samples. Journal of the American Statistical Association, 68, 46–54.Google Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Proschan, F. (1953). Confidence and tolerance intervals for the normal distribution. Journal of the American Statistical Association, 48, 550–564.CrossRefGoogle Scholar
Rao, C. R. (1973). Linear statistical inference and its applications, New York: Wiley.CrossRefGoogle Scholar
Shenton, L. R. (1950). Maximum likelihood and the efficiency of the method of moments. Biometrika, 37, 111–116.CrossRefGoogle ScholarPubMed
Wald, A. (1942). Setting of tolerance limits when the sample is large. Annals of Mathematical Statistics, 13, 389–399.CrossRefGoogle Scholar