Steven Pinker -- How the Mind Works - Hampshire High Italian ...

344 HOW THE MIND WORKS• This problem was given to sixty students and staff members at HarvardMedical School: "If a test to detect a disease whose prevalence is1/1000 has a false positive rate of 5%, what is the chance that a personfound to have a positive result actually has the disease, assuming youknow nothing about the person's symptoms or signs?" The most popularanswer was .95. The average answer was .56. The correct answer is .02,and only eighteen percent of the experts guessed it. The answer, accordingto Bayes' theorem, may be calculated as the prevalence or base rate(1/1000) times the test's sensitivity or hit rate (proportion of sick peoplewho test positive, presumably 1), divided by the overall incidence of positivetest results (the percentage of the time the test comes out positive,collapsing over sick and healthy people—that is, the sum of the sick peoplewho test positive, 1/1000 X 1, and the healthy people who test positive,999/1000 X .05). One bugaboo in the problem is that many peoplemisinterpret "false positive rate" as the proportion of positive results thatcome from healthy people, instead of interpreting it as the proportion ofhealthy people who test positive. But the biggest problem is that peopleignore the base rate (1/1000), which ought to have reminded them thatthe disease is rare and hence improbable for a given patient even if thetest comes out positive. (They apparently commit the fallacy thatbecause zebras make hoofbeats, hoofbeats imply zebras.) Surveys haveshown that many doctors needlessly terrify their patients who test positivefor a rare disease.• Try this: "Linda is 31 years old, single, outspoken, and very bright.She majored in philosophy. As a student, she was deeply concerned withissues of discrimination and social justice, and also participated in antinucleardemonstrations. What is the probability that Linda is a bankteller?What is the probability that Linda is a bankteller and is active inthe feminist movement?" People sometimes give a higher estimate to theprobability that she is a feminist bankteller than to the probability thatshe is a bankteller. But it's impossible for "A and B" to be more likelythan "A" alone.When I presented these findings in class, a student cried out, "I'mashamed for my species!" Many others feel the disgrace, if not aboutthemselves, then about the person in the street. Tversky, Kahneman,Gould, Piattelli-Palmarini, and many social psychologists have concludedthat the mind is not designed to grasp the laws of probability,even though the laws rule the universe. The brain can process limitedamounts of information, so instead of computing theorems it uses crude