Detecting Group Collaboration Using Multiple Correspondence Analysis

Abstract

Test takers wishing to gain an unfair advantage often share answers with other test takers, either sharing all answers (a full key) or some (a partial key). Detecting key sharing during a tight testing window requires an efficient, easily interpretable, and rich form of analysis that is descriptive and inferential. We introduce a detection method based on multiple correspondence analysis (MCA) that identifies test takers with unusual response similarities. The method simultaneously detects multiple shared keys (partial or full), plots results, and is computationally efficient as it requires only matrix operations. We describe the method, evaluate its detection accuracy under various simulation conditions, and demonstrate the procedure on a real data set with known test-taking misbehavior. The simulation results showed that the MCA method had reasonably high power under realistic conditions and maintained the nominal false-positive level, except when the group size was very large or partial shared keys had more than 50% of the items. The real data analysis illustrated visual detection procedures and inference about the item responses possibly shared in the key, which was likely shared among 91 test takers, many of whom were confirmed by nonstatistical investigation to have engaged in test-taking misconduct.