Hostname: page-component-89b8bd64d-nlwjb Total loading time: 0 Render date: 2026-05-10T06:11:16.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Ability Estimation for Conventional Tests

Published online by Cambridge University Press:  01 January 2025

Jwa K. Kim  and
W. Alan Nicewander
Jwa K. Kim*
Affiliation:
Middle Tennessee State University
W. Alan Nicewander
Affiliation:
University of Oklahoma
*
Requests for reprints should be sent to Jwa K. Kim, Department of Psychology, Middle Tennessee State University, Murfreesboro, Tennessee 37132.
Get access Rights & Permissions [Opens in a new window]

Abstract

Five different ability estimators—maximum likelihood [MLE (θ)], weighted likelihood [WLE (θ)], Bayesian modal [BME (θ)], expected a posteriori [EAP (θ)] and the standardized number-right score [Z (θ)]—were used as scores for conventional, multiple-choice tests. The bias, standard error and reliability of the five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. The results indicated that ability estimates based on BME (θ), EAP (θ) or WLE (θ) were reasonably unbiased for the range of abilities corresponding to the difficulty of a test, and that their standard errors were relatively small. Also, they were as reliable as the old standby—the number-right score.

Keywords

item response theoryability estimationreliability

Information

Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 4 , December 1993 , pp. 587 - 599
Copyright
Copyright © 1993 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.)

Article purchase

Temporarily unavailable

References

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M. & Novick, M. R. (Eds.), Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Lord, F. M. (1980). Application of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-form reliability. Psycholmetrika, 48, 233–245.CrossRefGoogle Scholar
Mislevy, R. J., & Bock, R. D. (1986). PC-BILOG: Item analysis and test scoring with binary logistic models [Computer program], Moorseville, IN: Scientific Software.Google Scholar
Samejima, F. (1969). Estimation of latent ability using a pattern of graded scores. Psychometric Monograph No. 17, 34(4, Pt. 2).Google Scholar
Stroud, A. H., & Sechrest, D. (1966). Gaussian quadrature formulas, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Tsutakawa, R. K., & Soltys, M. J. (1988). Approximation for Bayesian ability estimation. Journal of Educational Statistics, 13, 117–130.CrossRefGoogle Scholar
Warm, A. W. (1989). Weighted likelihood estimation of ability in item response theory with tests of finite length. Psychometrika, 54, 427–450.CrossRefGoogle Scholar
Yen, W. M. (1987). A comparison of the efficiency and accuracy of BILOG and LOGIST. Psychometrika, 52, 275–291.CrossRefGoogle Scholar