Q-SID: Detecting collusion groups from exam question scores with error quantification

Collusion in online exams undermines the integrity of exam results. Existing detection methods identify suspicious student pairs and are often limited to multiple-choice formats. We introduce Question-Score Identity Detection (Q-SID), a statistical algorithm that efficiently detects likely collusion groups and quantifies uncertainty using only graded numeric question scores. This enables Q-SID to support a broad range of multiple-choice and non-multiple-choice exams. Q-SID reports two false-positive rates (FPRs) for each collusion group: (1) an empirical FPR, whose null data are from strictly proctored exam datasets, and (2) a synthetic FPR, whose null data are simulated from a copula-based model. Across 34 unproctored exam datasets, including two benchmark datasets with verified positives and negatives from textual analysis, Q-SID performs robustly across exam formats, class sizes, numbers of questions, and levels of complexity. It is more accurate and substantially faster than widely used pairwise statistics and group-level baselines, including answer similarity at group level (ASIg) and clique detection.