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Detection of Item Preknowledge Using Likelihood Ratio Test and Score Test

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  • Sandip Sinharay

    (Pacific Metrics Corporation)

Abstract

An increasing concern of producers of educational assessments is fraudulent behavior during the assessment (van der Linden, 2009). Benefiting from item preknowledge (e.g., Eckerly, 2017; McLeod, Lewis, & Thissen, 2003) is one type of fraudulent behavior. This article suggests two new test statistics for detecting individuals who may have benefited from item preknowledge; the statistics can be used for both nonadaptive and adaptive assessments that may include either or both of dichotomous and polytomous items. Each new statistic has an asymptotic standard normal n distribution. It is demonstrated in detailed simulation studies that the Type I error rates of the new statistics are close to the nominal level and the values of power of the new statistics are larger than those of an existing statistic for addressing the same problem.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:42:y:2017:i:1:p:46-68
    DOI: 10.3102/1076998616673872
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    References listed on IDEAS

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    1. Tom Snijders, 2001. "Asymptotic null distribution of person fit statistics with estimated person parameter," Psychometrika, Springer;The Psychometric Society, vol. 66(3), pages 331-342, September.
    2. Zhan Shu & Robert Henson & Richard Luecht, 2013. "Using Deterministic, Gated Item Response Theory Model to Detect Test Cheating due to Item Compromise," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 481-497, July.
    3. Mauricio Romero & Ã lvaro Riascos & Diego Jara, 2015. "On the Optimality of Answer-Copying Indices," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 435-453, October.
    4. Robert Mislevy & Hua-Hua Chang, 2000. "Does adaptive testing violate local independence?," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 149-156, June.
    5. C. Glas & Anna Dagohoy, 2007. "A Person Fit Test For Irt Models For Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 159-180, June.
    6. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.
    7. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    8. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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    Keywords

    cheating; fraud; test security;
    All these keywords.

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