Instructors new to active learning classrooms frequently ask how they should best structure groups in the classroom to ensure optimum learning. Groups within classrooms are complex social systems with many variables, so unfortunately there is no easy answer. Existing group-formation algorithms do not specify how groups should be structured; they only provide a way for instructors to specify their own algorithm based on factors like GPA or Gender. There are many dimensions of student thinking, motivation, and experience that may be relevant, but here we focus on one measurement that is relatively easy to measure: prior preparation. There have been some studies investigating the role of preparation in cooperative grouping, but each study seems to come to a different conclusion. Here we provide some evidence as to why that might be the case by investigating outcomes based on different measures of preparation and investigating the effects of cooperative grouping for different groups of students. We find that groups that are heterogeneous with respect to physics preparation tend to perform better. Additionally, we find that this effect is particularly pronounced for women and underrepresented students, but not for white men. This would seem to suggest that a reason for disagreements in the literature could be sensitive to how preparation is measured as well as the demographics of the study population.