A Realistic Mathematics Education Approach to Diagnostic Probability and ROC Analysis in Undergraduate Health Science Education

This study investigated the effectiveness of a modeling-based instructional sequence grounded in Realistic Mathematics Education (RME) for supporting undergraduate health science students’ understanding of diagnostic probability and receiver operating characteristic (ROC) analysis. A quasi-experimental pretest–posttest design was implemented with ninety undergraduate health science students enrolled in a biostatistics course, including a control group receiving traditional lecture-based instruction (n = 41) and an experimental group completing five modeling activities supported by MATLAB-based visualization (n = 49). The pretest assessed students’ general probability knowledge prior to the intervention, whereas the posttest evaluated diagnostic probability, threshold reasoning, ROC interpretation, and the area under the curve (AUC). Pretest normality was examined using the Shapiro–Wilk test, which indicated nonnormality in the control group (p = 0.017) and normality in the experimental group (p = 0.122). A nonparametric Mann–Whitney U test showed no statistically significant difference in baseline probability performance between groups (U = 929.0, p = 0.540). Posttest distributions satisfied parametric assumptions (Shapiro–Wilk p = 0.485 and p = 0.220), permitting the use of an independent-samples t-test, which revealed significantly higher posttest scores for the experimental group (p < 0.001). Effect size estimates, including Cohen’s d, Hedges’ g, and Glass’s Δ, all exceeded 1.10, indicating a large educational effect. Students in the modeling-based group achieved higher posttest scores on items involving threshold-dependent interpretation, ROC analysis, and distribution-based reasoning. The findings suggest that an RME-based modeling sequence incorporating visualization and guided representational transitions may support students’ learning of diagnostic probability concepts in undergraduate health science education. Further research is needed to examine the durability of these gains and the relative contributions of RME, modeling, visualization, and digital tools.