Risk Savvy: How to Make Good Decisions

by Gerd Gigerenzer

Figure 2-5. What does a positive HIV test mean? The answer depends on the prevalence and the false-positive rate. Left tree: The false-positive rate is 5 in 100,000 according to Amy’s doctor. The prevalence is 1 in 10,000 for women with no known risk factors. Among 100,000 women who take the test, 10 will likely be infected, and also correctly test positive. Among the 99,990 not infected, the test is likely to err in five cases—that is, result in a false positive. Thus, we expect that 15 persons will test positive but only 10 will actually be infected. Right tree: Here, the false-positive rate is 1 in 250,000, corresponding to the most recent studies using better tests. Among 250,000 women who take the test, 25 are likely to be infected, and also correctly test positive. Among the 249,975 not infected, the test is likely to err in one case. In other words, out of every 26 who test positive, we expect that 1 will in fact not be infected. The numbers vary by country, risk group, and quality of test.