Suppose a test can determine with 99 percent accuracy whether someone has a certain disease, which only affects one out of every 10,000 people in the population. If a given person’s test comes back positive, what are the approximate odds that the person has the disease?
Test your math skills or your instincts by giving your best answer above, before reading on for the correct answer.
See Answer and ExplanationThe false positive paradox is a type of base rate fallacy, where prior probability information, in this case the incidence of the disease in the population, is ignored. This is a real problem in the field of medicine, as surveys indicate that many patients and even physicians simply do not understand how to interpret information such as cancer screening statistics.
I’d like to believe this however how did you come to the assumption that only 1 out of 10,000 people who take the test will actually have the virus? That was stated as fact and used to prove the equation.
Thanks for the question Steven. The brainteaser as posed is a hypothetical example. Any real world situations would have different data to start with and thus different results. A test might only be 90% effective, or 99.9% effective. A disease might affect one in 1,000 people, or 1 in 100,000 people. This would change the results. The point is that in order to understand false positives, we need to take into account the effectiveness of the test and how rare the thing being tested is.