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The Asymptotic Distribution of Average Test Overlap Rate in Computerized Adaptive Testing

Published online by Cambridge University Press:  01 January 2025

Edison M. Choe Open the ORCID record for Edison M. Choe [Opens in a new window]  and
Hua-Hua Chang
Edison M. Choe*
Affiliation:
Graduate Management Admission Council™ (GMAC™)
Hua-Hua Chang
Affiliation:
Purdue University
*
Correspondence should be made to Edison M. Choe, Graduate Management Admission Council™ (GMAC™), 11921 Freedom Drive, Suite 300, Reston, VA 20190, USA. Email: echoe@gmac.com
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Abstract

The average test overlap rate is often computed and reported as a measure of test security risk or item pool utilization of a computerized adaptive test (CAT). Despite the prevalent use of this sample statistic in both literature and operations, its sampling distribution has never been known nor studied in earnest. In response, a proof is presented for the asymptotic distribution of a linear transformation of the average test overlap rate in fixed-length CAT. The theoretical results enable the estimation of standard error and construction of confidence intervals. Moreover, a practical simulation study demonstrates the statistical comparison of average test overlap rates between two CAT designs with different exposure control methods.

Keywords

test overlapitem exposuretest securitypool utilizationcomputerized adaptive testingasymptotic theory
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019 , pp. 1129 - 1151
Copyright
Copyright © 2019 The Psychometric Society

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