Visualizing Sensitivity, Specificity, and Prevalence

① This GeoGebra example dynamically illustrates how sensitivity (true positive rate) and specificity (true negative rate) interact with disease prevalence to determine predictive values, using rectangular areas to represent true positives, false negatives, true negatives, and false positives. ② Core mathematical concepts include conditional probability, Bayes' theorem, positive predictive value (PPV), negative predictive value (NPV), and the trade-off between sensitivity and specificity under varying prevalence. ③ Construction highlights: using GeoGebra commands such as Point, OrthogonalLine, Intersect, Segment, and Polygon, the applet builds a prevalence line, sensitivity line, specificity line, and rectangles for true positive and true negative regions, with sliders (e.g., c, d, e, f, h) enabling interactive parameter adjustment. ④ Suitable for high school and university students learning probability and statistics, as well as medical education, this tool helps intuitively grasp how prevalence affects diagnostic test performance and the balance between sensitivity and specificity.