We report findings from a longitudinal study of students' beliefs about empirical arguments and mathematical proof. We consider the influence of an 'Introduction to Proof (ITP)' course and the consequences of the observed changes in behaviour. Consistent with recent literature, our findings suggest that a majority of the thirty-eight undergraduate students in this study do not find empirical arguments convincing, even at the beginning of their ITP course. We use Sankey diagrams to show that, while many were unconvinced by these arguments at the start and end of the course, others began the course endorsing empirical arguments as similar to their own, shifting toward deductive-symbolic arguments by the end. Finally, we consider the value of Sankey diagrams for understanding changes in population behaviours, and the consequences of our work for future research on the role of empirical arguments in the classroom.