Even with a positive test result, the probability you actually have the disease can be surprisingly low
Suppose there is a test for a rare disease. Even if the test is 99% accurate, if the disease itself is very rare, the "probability that you actually have the disease when you receive a positive result" can be much lower than you might expect. Change the conditions with the sliders and see it directly in the tree diagram.
How to read the tree: The first branch shows the probability of "having the disease / not having the disease" (prevalence), and the second branch shows the probability of getting a "positive / negative" test result in each case (test accuracy). Multiply the probabilities along a path to get the final probability of that path.
Prevalence (proportion of people with the disease)1%
Test accuracy (simplified as sensitivity = specificity)99%
Probability of actually having the disease when you receive a positive result
50.3%
💡 This kind of calculation is called Bayes' theorem. It shows that even a highly accurate test can produce more "false positives" than "true positives" when the disease being tested for is extremely rare — which is why a positive result on an initial screening test is usually followed by a more detailed second test.