Psychologists have asked physicians several variants of the following question: "*An invariably fatal disease affects one person in 100. Patients can be treated with a risky procedure: it saves 80% of those with the disease, but if used on healthy people, 20% of them will die. Fortunately, there is a screening test that is 95% reliable: it is positive for 95% of people with the disease and negative for 95% of healthy people. A person is chosen at random and given the test, which comes back positive. In your opinion, should this person be advised to undergo treatment?*"
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Test reliability and the base rate -----------------------------------
Most of the physicians surveyed recommended treatment. The usual argument is that, since the test is reliable, the person who tested positive is very likely to have the disease and will therefore die if left untreated.
The trouble is that many physicians estimate the probability that the person is actually infected at around 95%, because the test is 95% reliable.