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On Maximizing Item Information and Matching Difficulty with Ability

Published online by Cambridge University Press:  01 January 2025

Peter Bickel ,
Steven Buyske ,
Huahua Chang  and
Zhiliang Ying
Peter Bickel
Affiliation:
Department of Statistics, University of California at Berkeley
Steven Buyske
Affiliation:
Department of Statistics, Rutgers University
Huahua Chang
Affiliation:
National Board of Medical Examiners
Zhiliang Ying*
Affiliation:
Department of Statistics, Rutgers University
*
Requests for reprints should be sent to Zhiliang Ying, Department of Statistics, Hill Center, Busch Campus, Rutgers University, Piscataway NJ 08854-8019. E-Mail: [email protected]
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Abstract

An important assumption in IRT model-based adaptive testing is that matching difficulty levels of test items with an examinee's ability makes a test more efficient. According to Lord, “An examinee is measured most effectively when the test items are neither too difficult nor too easy for him”. This assumption is examined and challenged through a class of one-parameter IRT models including those of Rasch and the normal ogive. It is found that for a specific model, the validity of the fundamental assumption is closely related to the so-called van Zwet tail ordering of symmetric distributions. In this connection, the cosine distribution serves as the borderline between those satisfying the assumption and those violating the assumption. Graphic and numerical illustrations are presented to demonstrate the theoretic results.

Keywords

item response theoryitem characteristic curvecomputerized adaptive testingRasch modelnormal ogiveone-parameter IRT modelitem informationvan Zwet tail ordering
Type
Articles
Information
Psychometrika , Volume 66 , Issue 1 , March 2001 , pp. 69 - 77
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

Research by Peter Bickel supported by NSF Grant DMS 95-04955. Research by Steven Buyske supported by ETS Psychometric Fellowship. Research by Huahua Chang supported by ETS research allocation PJ 79427. Research by Zhiliang Ying supported by ETS Visiting Scholar Program, NSF Grant DMS 96-26750, and NSA Grant MDA 96-1-0034.

We would like to thank the Associate Editor and two referees for their helpful and constructive comments, which led to many improvements. We also thank Ming-Mei Wang and Eiji Muraki for relating our work to Samejima (1979), Fumiko Samejima for sending us her manuscript, and Charles Davis for helpful conversations.

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