Comparing the Performance of Eight Item Preknowledge Detection Statistics

Item preknowledge describes a situation in which a group of examinees (called aberrant examinees) have had access to some items (called compromised items) from an administered test prior to the exam. Item preknowledge negatively affects both the corresponding testing program and its users (e.g., universities, companies, government organizations) because scores for aberrant examinees are invalid. In general, item preknowledge is hard to detect due to multiple unknowns: unknown groups of aberrant examinees (at unknown test centers or schools) accessing unknown subsets of items prior to the exam. Recently, multiple statistical methods were developed to detect compromised items. However, the detected subset of items (called the suspicious subset) naturally has an uncertainty due to false positives and false negatives. The uncertainty increases when different groups of aberrant examinees had access to different subsets of items; thus, compromised items for one group are uncompromised for another group and vice versa. The impact of uncertainty on the performance of eight statistics (each relying on the suspicious subset) was studied. The measure of performance was based on the receiver operating characteristic curve. Computer simulations demonstrated how uncertainty combined with various independent variables (e.g., type of test, distribution of aberrant examinees) affected the performance of each statistic.