Statistical Analysis of Item Preknowledge in Educational Tests: Latent Variable Modelling and Statistical Decision Theory
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Tests are a building block of our modern education system. Many tests are high-stake, such as admission, licensing, and certification tests, that can significantly change one's life trajectory. For this reason, ensuring fairness in educational tests is becoming an increasingly important problem. This paper concerns the issue of item preknowledge in educational tests due to item leakage. That is, a proportion of test takers have access to leaked items before a test is administrated, which leads to inflated performance on the set of leaked items. We develop methods for the simultaneous detection of cheating test takers and compromised items based on data from a single test administration, when both sets are completely unknown. Latent variable models are proposed for the modelling of (1) data consisting only of item-level binary scores and (2) data consisting of both item-level binary scores and response time, where the former is commonly available in paper-and-pencil tests and the latter is widely encountered in computer-based tests. The proposed model adds a latent class model component upon a factor model (also known as item response theory model) component, where the factor model component captures item response behavior driven by test takers' ability and the latent class model component captures item response behavior due to item preknowledge. We further propose a statistical decision framework, under which compound decision rules are developed that control local false discovery/nondiscovery rates. Statistical inference is carried out under a Bayesian framework. The proposed method is applied to data from a computer-based nonadaptive licensure assessment.
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