Predicting student performance in introductory statistics using a measure of perception of cognitive competence in statistics: An analysis using Bayesian networks

Many undergraduates are required to take a course in introductory statistics to satisfy a university major requirement. These students are usually from non-quantitative majors, and they often have difficulty with the course. Many of these students do not believe they have the cognitive competence to succeed in introductory statistics. For such students to succeed, it is often necessary for the instructor or teaching assistants to offer additional resources. Since there are typically hundreds of students taking the course, it would be useful if instructors were able to identify students that are likely to fail the course early enough in the term to offer them assistance.One goal of this study was to explore how well students' course grades can be predicted from test scores, demographic variables, and a measure of their perceptions of their cognitive competence in statistics (PCCS) using Bayesian networks. In particular, how well do the models identify students who fail the course, and how reliable are their predictions? This study uses a survey developed by Lenaburg (2007) to measure students' perceptions of their cognitive competence in statistics, which has been shown to correlate with achievement. The structure was proposed for two Bayesian networks, and the structures of four more were learned from the data using two learning algorithms. When the final exam score is unknown, Bayesian networks offered acceptable prediction, and generally outperformed regression models. In addition, the PCCS scores helped improve the prediction that could be achieved with exam scores alone.The second goal of the study was to see how well PCCS scores and item responses can be predicted under various missing data situations using Bayesian networks. The structure for two networks was provided, and two more networks were learned from the data. Methods of regression and substituting the mean of the non-missing items performed better than the Bayesian networks for predicting PCCS scores. However, the Bayesian networks learned from the Greedy Thick-Thinning algorithm performed better than these methods for predicting the responses to missing items. Overall, Bayesian networks are a useful tool for prediction and for understanding the relationships among variables of interest.