(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
in a thousand people has a prevalence for a particular heart disease.
There is a test to detect this disease. The test is 100%
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).