Hostname: page-component-6bf8c574d5-b4m5d Total loading time: 0 Render date: 2025-02-23T04:38:08.868Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistical Inference for False Positive and False Negative Error Rates in Mastery Testing

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
University of South Carolina
*
Requests for reprints should be addressed to Huynh Huynh, College of Education, University of South Carolina, Columbia, South Carolina 29208.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper describes an asymptotic inferential procedure for the estimates of the false positive and false negative error rates. Formulas and tables are described for the computations of the standard errors. A simulation study indicates that the asymptotic standard errors may be used even with samples of 25 cases as long as the Kuder-Richardson Formula 21 reliability is reasonably large. Otherwise, a large sample would be required.

Keywords

mastery testingerrors in classificationsdecision errorsdecision accuracybeta-binomial modeltesting for selectionerror rate inference
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 107 - 120
Copyright
Copyright © 1980 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

This work was performed pursuant to Grant No NIE-G-78-0087 with the National Institute of Education, Department of Health, Education and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance of Joseph C. Saunders is gratefully acknowledged.

References

Reference Notes

Huynh, H. Statistical inference for the kappa and kappamax reliability indices based on the beta-binomial model. Paper presented at the annual meeting of the Psychometric Society meeting. University of North Carolina at Chapel Hill, June 16–17, 1977.Google Scholar
Huynh, H. Statistical inference for false positive and false negative error rates in mastery testing (computer program and tables added). Publication Series in Mastery Testing (Res. Memo. 79–6), University of South Carolina, 1979.Google Scholar

References

Abramowitz, M. & Stegun, I. A. Handbook of mathematical functions. Washington, D. C.: National Bureau of Standards Applied Mathematics Series 55, 1968.Google Scholar
Duncan, G. T. An empirical Bayes approach to scoring multiple-choice tests in the misinformation model. Journal of the American Statistical Association, 1974, 69, 50–57.CrossRefGoogle Scholar
Gradshteyn, I. S. & Ryzhik, I. M. Tables of integrals, series, and products, 1965, New York: Academic Press.Google Scholar
Griffiths, D. A. 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, 1973, 29, 637–648.CrossRefGoogle Scholar
Huynh, H. Statistical consideration of mastery scores. Psychometrika, 1976, 41, 65–78.CrossRefGoogle Scholar
Huynh, H. On the reliability of decisions in domain-referenced testing. Journal of Educational Measurement, 1976, 13, 253–264.CrossRefGoogle Scholar
Huynh, H. Two simple classes of mastery scores based on the beta-binomial model. Psychometrika, 1977, 42, 65–78.CrossRefGoogle Scholar
Huynh, H. Reliability of multiple classifications. Psychometrika, 1978, 43, 317–325.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 Publication Department.Google Scholar
IMSL Library 1. Houston: International Mathematical and Statistical Libraries, 1977.Google Scholar
Keats, J. A. & Lord, F. M. A theoretical distribution for mental test scores. Psychometrika, 1962, 27, 59–72.CrossRefGoogle Scholar
Kendall, M. G. & Stuart, A. The advanced theory of statistics, 2nd ed, London: Charles Griffin, 1967.Google Scholar
Lord, F. M. A strong true score theory, with applications. Psychometrika, 1965, 30, 239–270.CrossRefGoogle Scholar
Lord, F. M. Estimating true-score distribution in psychological testing (an empirical Bayes estimation problem). Psychometrika, 1969, 34, 259–299.CrossRefGoogle Scholar
Pearson, K. Tables of the incomplete beta function, 1934, Cambridge: University Press.Google Scholar
Rao, C. R. Linear statistical inference and its applications, 2nd ed., New York: John Wiley, 1973.CrossRefGoogle Scholar
Wilcox, R. R. A note on the length and passing score of a mastery test. Journal of Educational Statistics, 1976, 1, 359–364.CrossRefGoogle Scholar
Wilcox, R. R. Estimating the likelihood of false-positive and false-negative decisions in mastery testing: An empirical Bayes approach. Journal of Educational Statistics, 1977, 2, 289–307.CrossRefGoogle Scholar
Zacks, S. The theory of statistical inference, 1971, New York: John Wiley.Google Scholar