Two-stage exams have gained traction in education as a means of creating collaborative active-learning experiences in the classroom in a manner that advances learning, positively increases student engagement, and reduces test anxiety. Published analyses have focused almost exclusively on the increase in student scores from the first individual stage to the second collaboration stage and have shown clear positive effects on gains in student scores. Missing from these analyses is a comprehensive evaluation of the effects of individual preparation, the characteristics of questions, and small group composition on the outcomes two-stage exams. I developed a simple quantitative framework that provides a flexible approach for estimating and evaluating the effects of individuals, questions, and groups on student performance. Additionally, the framework yields statistics appropriate for making inferences about productive collaboration, consensus-building, and counter-productive interaction that happens within small groups. Analyses of 12 exams across two courses and 2 years using the quantitative framework revealed considerable variation for all three of these effects within and among exams. Overall, the results highlight the value of quantitative estimation of two-stage exams for gaining perspective on the effects of individuals, questions, and groups on student performance, and facilitates data-driven revision of assessments, curricula, and teaching strategies towards achieving gains in students' collaborative skills.
