Imagine a base rate of 1 percent for a disease, a false positive rate of 10 percent, and a sensitivity rate of 90 percent for the screening test for the disease. Using natural frequencies, which of the following is the closest estimate of the conditional probability that a person actually has the disease given a positive test result?

Question

Quizplus · Accepted Answer

Using natural frequencies, out of 1000 people, 10 will have the disease (1% base rate), and 9 of these will test positive (90% sensitivity). Out of 990 without the disease, 99 will test positive (10% false positive rate). Thus, the probability of having the disease given a positive test is 9/(9+99) = 9/108 ≈ 8.33%, closest to 8%.

Imagine a Base Rate of 1 Percent for a Disease