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

Author

Listed:
  • Edison M. Choe

    (Graduate Management Admission Council™ (GMAC™))

  • Hua-Hua Chang

    (Purdue University)

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.

Suggested Citation

  • Edison M. Choe & Hua-Hua Chang, 2019. "The Asymptotic Distribution of Average Test Overlap Rate in Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1129-1151, December.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09674-5
    DOI: 10.1007/s11336-019-09674-5
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    References listed on IDEAS

    as
    1. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    2. Robert Mislevy & Hua-Hua Chang, 2000. "Does adaptive testing violate local independence?," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 149-156, June.
    3. Hua-Hua Chang & Jinming Zhang, 2002. "Hypergeometric family and item overlap rates in computerized adaptive testing," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 387-398, September.
    4. Edison M. Choe & Justin L. Kern & Hua-Hua Chang, 2018. "Optimizing the Use of Response Times for Item Selection in Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 135-158, April.
    5. Chun Wang & Yi Zheng & Hua-Hua Chang, 2014. "Does Standard Deviation Matter? Using “Standard Deviation” to Quantify Security of Multistage Testing," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 154-174, January.
    6. Wim J. van der Linden & Bernard P. Veldkamp, 2007. "Conditional Item-Exposure Control in Adaptive Testing Using Item-Ineligibility Probabilities," Journal of Educational and Behavioral Statistics, , vol. 32(4), pages 398-418, December.
    Full references (including those not matched with items on IDEAS)

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