Bayes theorem and how we talk about medical tests

Bayes' theorem reveals that medical test results are probabilistic, not binary. Using celiac disease testing as an example, a positive result with 93% sensitivity and 96% specificity actually means only a 19% chance of having the disease in the general population—an 80% false positive rate. The key insight is that test accuracy depends heavily on prior probability: the same positive test jumps to 72% accuracy when symptoms suggest a 10% baseline risk instead of 1%. Understanding conditional probability helps interpret what test results actually mean for individual patients.