Two-stage collaborative exams are an increasingly popular form of formative assessment which have shown promising results in promoting student learning. While the benefit of two-stage collaborative exams is well researched, there is no clear consensus on the best way of implementing them--specifically with respect to forming student groups. In some studies students self-select their groups, and in others they are assigned by the instructor (either randomly or with a specific grouping algorithm). Research has shown that performance and satisfaction in group learning situations improves when faculty, not students, select the groups. Furthermore, studies have demonstrated that students' learning benefits from working in groups with diverse learning styles, abilities, gender, and race. In this study, we report on a controlled experiment conducted during a two-stage collaborative exam in an introductory physics course at Harvard University. For the group stage of the exam, half of the groups were formed by the instructor (based on balancing gender and performance on previous exams) and the other half were student selected. We compared performance on both the individual and group stage of the exam for the instructor-formed versus student-formed groups. We also surveyed students on their experiences during the group exam. We found that female students perform better on two-part collaborative exams when they are in student-formed groups. We also found that in the student-formed groups students (especially female students) felt more comfortable speaking up and felt that their groups were both "more effective and productive" and "more receptive to their ideas" than in the instructor-formed groups. This study provides important insights into best practice implementation of two-stage collaborative exams.