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Hypergeometric Family and Item Overlap Rates in Computerized Adaptive Testing

Published online by Cambridge University Press:  01 January 2025

Hua-Hua Chang  and
Jinming Zhang
Hua-Hua Chang
Affiliation:
University of Texas at Austin
Jinming Zhang*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Jinming Zhang, MS 02-T, Educational Testing Service, Princeton, NJ 08541. E-Mail: [email protected]
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Abstract

A computerized adaptive test (CAT) is usually administered to small groups of examinees at frequent time intervals. It is often the case that examinees who take the test earlier share information with examinees who will take the test later, thus increasing the risk that many items may become known. Item overlap rate for a group of examinees refers to the number of overlapping items encountered by these examinees divided by the test length. For a specific item pool, different item selection algorithms may yield different item overlap rates. An important issue in designing a good CAT item selection algorithm is to keep item overlap rate below a preset level. In doing so, it is important to investigate what the lowest rate could be for all possible item selection algorithms. In this paper we rigorously prove that if every item has an equal possibility to be selected from the pool in a fixed-length CAT, the number of overlapping items among any α randomly sampled examinees follows the hypergeometric distribution family for α ≥ 1. Thus, the expected values of the number of overlapping items among any randomly sampled α examinees can be calculated precisely. These values may serve as benchmarks in controlling item overlap rates for fixed-length adaptive tests.

Keywords

computerized adaptive testinghypergeometric distributionitem exposure rateitem selectionstratificationSympson-Hetter methoditem overlap ratetest security
Type
Articles
Information
Psychometrika , Volume 67 , Issue 3 , September 2002 , pp. 387 - 398
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The research reported in this paper is collaborative in every respect, and the order of authorship is alphabetical. The authors wish to thank the three anonymous reviewers for their useful comments on earlier versions of this manuscript. The publication of this manuscript was supported in part by funds from Educational Testing Service and National Board of Medical Examiners.

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