Bayesian Hierarchal Models of Final Exam Grades in Statistics Classes: A Two-University Study

• Activity Number: 353
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Education
• Author(s): Lawrence V. Fulton*+ and Rasim Musal and Lana Ivanitskaya and Salma Haidar and Carl Lee
• Companies: Texas State University and Texas State University and Central Michigan University and Central Michigan University and Central Michigan University
• Keywords: statistics ; Bayesian ; zero-inflated ; education ; hierarchical

Abstract

In this two university, IRB-approved study of business statistics courses, we use Bayesian hierarchical modeling to search for the effects of pre-existing ability, demographics, manipulated homework certification standards, "cramming," and other covariates on the probability that a student achieves a particular grade. The significance of our research is that we are able to determine probabilistically the grade that students should expect given fixed covariate values. This information is valuable to both professors and students in realistically appraising likely performance. Our model is nonlinear in parameters and reflects a zero-inflated distribution, accounting for the population of students who did not have an economically rational reason to take the final examination. We identify the distinct number of student grade groups and employ mixed beta distributions in modeling the examination scores. By using Bayesian hierarchical modeling, we are able to obtain the examination grade probability distribution that any student "i" will obtain given covariate values. As part of our research, we conduct cross-validation and evaluate model fit.