False Positives

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Suppose you undergo a medical test for a relatively rare disease.

Your doctor tells you that, according to surveys by medical statisticians, the disease has an incidence of 1% among the general population. Thus, before you take the test, and in the absence of any other evidence, your best estimate of your likelihood of having the disease is 1 in 100, i.e. a probability of 0.01.

Then you take the test. Extensive trials have shown that the reliability of the test is 79%. More precisely, although the test does not fail to detect the disease when it is present, it gives a positive result in 21% of the cases where no disease is present -- what is known as a "false positive."

When you are tested, the test produces a positive diagnosis.

Given the result of the test, what is the probability that you actually have the disease?

  •  High ?
  •  Medium ?
  •  Low ?
This page was last changed on February 17, 2008