IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v84y2019i4d10.1007_s11336-019-09674-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-019-09674-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-019-09674-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. 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.
    3. Robert Mislevy & Hua-Hua Chang, 2000. "Does adaptive testing violate local independence?," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 149-156, June.
    4. 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.
    5. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Edison M. Choe & Jinming Zhang & Hua-Hua Chang, 2018. "Sequential Detection of Compromised Items Using Response Times in Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 650-673, September.
    2. Onur Demirkaya & Ummugul Bezirhan & Jinming Zhang, 2023. "Detecting Item Preknowledge Using Revisits With Speed and Accuracy," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 521-542, August.
    3. Ping Chen & Chun Wang, 2016. "A New Online Calibration Method for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 674-701, September.
    4. Yan Li & Chao Huang & Jia Liu, 2023. "Diagnosing Primary Students’ Reading Progression: Is Cognitive Diagnostic Computerized Adaptive Testing the Way Forward?," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 842-865, December.
    5. Sandip Sinharay, 2016. "Person Fit Analysis in Computerized Adaptive Testing Using Tests for a Change Point," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 521-549, October.
    6. 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.
    7. Ying Cheng, 2009. "When Cognitive Diagnosis Meets Computerized Adaptive Testing: CD-CAT," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 619-632, December.
    8. 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.
    9. Sandip Sinharay, 2017. "Detection of Item Preknowledge Using Likelihood Ratio Test and Score Test," Journal of Educational and Behavioral Statistics, , vol. 42(1), pages 46-68, February.
    10. Wim Linden & Edith Krimpen-Stoop, 2003. "Using response times to detect aberrant responses in computerized adaptive testing," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 251-265, June.
    11. Wim Linden & Hao Ren, 2015. "Optimal Bayesian Adaptive Design for Test-Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 263-288, June.
    12. Chun Wang & Hua-Hua Chang & Keith Boughton, 2011. "Kullback–Leibler Information and Its Applications in Multi-Dimensional Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 13-39, January.
    13. Xiao Li & Hanchen Xu & Jinming Zhang & Hua-hua Chang, 2023. "Deep Reinforcement Learning for Adaptive Learning Systems," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 220-243, April.
    14. Wenyi Wang & Lihong Song & Teng Wang & Peng Gao & Jian Xiong, 2020. "A Note on the Relationship of the Shannon Entropy Procedure and the Jensen–Shannon Divergence in Cognitive Diagnostic Computerized Adaptive Testing," SAGE Open, , vol. 10(1), pages 21582440198, January.
    15. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    16. Steven W. Nydick, 2014. "The Sequential Probability Ratio Test and Binary Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 39(3), pages 203-230, June.
    17. Chun Wang & Gongjun Xu & Zhuoran Shang & Nathan Kuncel, 2018. "Detecting Aberrant Behavior and Item Preknowledge: A Comparison of Mixture Modeling Method and Residual Method," Journal of Educational and Behavioral Statistics, , vol. 43(4), pages 469-501, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09674-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.