, Volume 84, Issue 4, pp 1129–1151 | Cite as

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

  • Edison M. ChoeEmail author
  • Hua-Hua Chang


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.


test overlap item exposure test security pool utilization computerized adaptive testing asymptotic theory 



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Copyright information

© The Psychometric Society 2019

Authors and Affiliations

  1. 1.Graduate Management Admission Council™ (GMAC™)RestonUSA
  2. 2.Purdue UniversityWest LafayetteUSA

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