A New Approach to Detecting Cluster Aberrancy (RR 16-05)

This report addresses a general type of cluster aberrancy in which a subgroup of test takers has an unfair advantage on some subset of administered items. Examples of cluster aberrancy include item preknowledge and test collusion. In general, cluster aberrancy is hard to detect due to the multiple unknowns involved: Unknown subgroups of test takers have an unfair advantage on unknown subsets of items. The issue of multiple unknowns makes the detection of cluster aberrancy a challenging problem from the standpoint of applied mathematics. This report presents a novel algorithm to detect cluster aberrancy. The algorithm is general and applicable to all types of testing programs: paper-and-pencil testing, computer-based testing, multistage testing, and computerized adaptive testing; it can also be applied in areas outside of psychometrics, such as finance (e.g., detecting financial fraud). Both simulated and real data were used to study the performance of this algorithm.