Do You Think Rationally?

Keith Stanovich’s new book What Intelligence Tests Miss: The psychology of rational thought convincingly argues that IQ tests are severely incomplete as measures of cognitive functioning, since they fail to assess important abilities such as the ability to make decisions that further one’s personal goals or form beliefs that correspond with reality. It is unfortunate that our society emphasizes IQ far more than rational thought, since the latter can be taught to a significant extent. The following excerpt (pp. 145-146) allows you to test your own ability to deal with probabilistic information.

“Imagine that the XYZ virus causes a serious disease that occurs in 1 in every 1000 people. Imagine also that there is a test to diagnose the disease that always indicates correctly that a person who has the XYZ virus actually has it. Finally, imagine that the test has a false-positive rate of 5 percent. This means that the test wrongly indicates that the XYZ virus is present in 5 percent of the cases where the person does not have the virus. Imagine that we choose a person randomly and administer the test, and that it yields a positive result (indicates that the person is XYZ-positive). What is the probability (expressed as a percentage ranging from 0 to 100) that the individual actually has the XYZ virus, assuming that we know nothing else about the individual’s personal or medical history?

“Don’t read on until you have taken a stab at the problem. Do not feel that you must calculate the answer precisely (although if you think you can, go ahead). Just give your best guesstimate. The point is not to get the precise answer so much as to see whether you are in the right ballpark. The answers of many people are not. They show a tendency to overweight concrete and vivid single-case information when it must be combined with more abstract probabilistic information.

“The most common answer is 95 percent. The correct answer is approximately 2 percent! People vastly overestimated the probability that a positive result truly indicates the XYZ virus. Although the correct answer to this problem can again be calculated by means of Bayes’ rule, a little logical reasoning can help to illustrate the profound effect that base rates have on probabilities. We were given the information that, of 1000 people, just one will actually be XYZ-positive. If the other 999 (who do not have the disease) are tested, the test will indicate incorrectly that approximately 50 of them have the virus (.05 multiplied by 999) because of the 5 percent false-positive rate. Thus, of the 51 patients testing positive, only 1 (approximately 2 percent) will actually be XYZ-positive. In short, the base rate is such that the vast majority of people do not have the virus. This fact, combined with a substantial false-positive rate, ensures that, in absolute numbers, the majority of positive tests will be of people who do not have the virus.”

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