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Detection of Test Collusion via Kullback–Leibler Divergence

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Abstract

The development of statistical methods for detecting test collusion is a new research direction in the area of test security. Test collusion may be described as large-scale sharing of test materials, including answers to test items. Current methods of detecting test collusion are based on statistics also used in answer-copying detection. Therefore, in computerized adaptive testing (CAT) these methods lose power because the actual test varies across examinees. This article addresses that problem by introducing a new approach that works in two stages: in Stage 1, test centers with an unusual distribution of a person-fit statistic are identified via Kullback–Leibler divergence; in Stage 2, examinees from identified test centers are analyzed further using the person-fit statistic, where the critical value is computed without data from the identified test centers. The approach is extremely flexible. One can employ any existing person-fit statistic. The approach can be applied to all major testing programs: paper-and-pencil testing (P&P), computer-based testing (CBT), multiple-stage testing (MST), and CAT. Also, the definition of test center is not limited by the geographic location (room, class, college) and can be extended to support various relations between examinees (from the same undergraduate college, from the same test-prep center, from the same group at a social network). The suggested approach was found to be effective in CAT for detecting groups of examinees with item pre-knowledge, meaning those with access (possibly unknown to us) to one or more subsets of items prior to the exam.

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