Wednesday, February 11, 2009
02.04.09. If a disease is rare, even a very accurate test will produce results in which a significant fraction of the positives are false positives--cases where the test reports that a patient has the disease when he or she actually does not. For example, if 1% of a population has a disease, half of the positive results from a test that is 99% accurate will be false positives! We simulated this phenomenon with a game in which students had a 1/10 chance of having a disease (one of ten tiles was drawn from a bag), they were subjected to a test that was accurate 5/6 of the time (a die was rolled), and we computed the fraction of the positive test results that was due to false positives. We then went through a calculation of the theoretical fraction using the formula p = x(1-d)/[x(1-d)+d(1-x)], where p is the false positive fraction, d is the disease prevalence (1/10 in the game), and x is the test error rate (1/6 in the game). This led to an interesting discussion of the difference between experimental and theoretical probabilities.