# Animating Bayes

(Animations by Younas Chentouf and Norman Fenton)

The classic medical diagnosis fallacy is to grossly overestimate the probability that a patient has a disease if he/she tests positive for that disease.  Consider the following problem:

"One in a thousand people has a prevalence for a particular heart disease. There is a test to detect this disease. The test is 100% accurate for people who have the disease and is 95% accurate for those who don't (this means that 5% of people who do not have the disease will be wrongly diagnosed as having it).

If a randomly selected person tests positive what is the probability that the person actually has the disease?"

This question was put to 60 students and staff at Harvard Medical School.

Almost half gave the response 95%. The 'average' answer was 56%. To show how wrong these answers are you can use Bayes Theorem, but most people find this hard to understand. So below we give two alternative visualisations. In each case you can enter any values for the given probabilities (so, to calculate the the correct answer to the above problem you should enter 0.1% for the probability of random person having the disease, 100% for the probability of a person with the disease testing positive, and 5% for the probability of a person without the disease testing positive).