Statistical Modeling to Better Understand CS Students.

While educational data mining has often focused on modeling behavior at the level of individual students, we consider developing statistical models to give us insight into the dynamics of student populations. In this talk, we consider two case studies in this vein. The first involves analyzing the evolution of gender balance in a college computer science program, showing that focusing on percentages of underrepresented groups in the overall population may not always provide an accurate portrayal of the impact of various program changes. We propose a new statistical model based on Fisher's Noncentral Hypergeometric Distribution that better captures how program changes are impacting the dynamics of gender balance in a population, especially in the case where the overall population is rapidly increasing (as has been the case in CS in recent years). Our second study looks at the performance of student populations in an introductory college programming course during the past eight years to better understand the evolving mix of students' abilities given the rapid growth in the number of students taking CS courses. Often accompanying such growth is a concern from faculty that the additional students choosing to pursue computing may not have the same aptitude for the subject as was seen in prior student populations. To directly address this question, we present a statistical analysis of students' performance using mixture modeling. Importantly, in this setting many variables that would normally confound such a study are directly controlled for. We find that the distribution of student performance during this period, as reflected in their programming assignment scores, remains remarkably stable despite the large growth in course enrollments. The results of this analysis also show how conflicting perceptions of students' abilities among faculty can be consistently explained. The presentation includes work done jointly with Sarah Evans, Chris Piech, and Katie Redmond.