May 5, 2016


Math Stumps Your Doctor, Too (Faye Flam, 5/05/16, Bloomberg)

Studies going back to psychologist Daniel Kahneman's work in the 1970s and 80s show that even doctors tend to misunderstand probabilities, especially as they apply to risk. That's a problem but not an insoluble one. Intuition can be retrained. People can learn to look at uncertainty in a different way.

Take the famous hypothetical example of a test that is 95 percent accurate for a disease that affects 0.1 percent of the population. Imagine you're a doctor and your patient tests positive. What is the chance that she has the disease? Most people's intuitive answer is a rather dire 95 percent. This is wrong in a big way. Despite the ominous test result, the patient is unlikely to be sick. 

"Even doctors and medical students are prone to this error," wrote Aron Barbey, a cognitive neuroscientist at the University of Illinois, in a paper on risk literacy published last month in the journal Science.

Some people do get the right answer: that the patient has about a 2 percent chance of having the disease.

Those few with math training can get help from a formula called Bayes' Theorem.

But there's also an intuitive approach that requires no formula at all. Imagine 1,000 people getting the test. On average, one will have the disease. The 5 percent error rate means that about 50 of the 999 healthy people will test positive. Now it's easy to see that the group of false positives is about 50 times bigger than the group of real positives. In other words, just 2 percent of the people testing positive are likely to be sick.

Posted by at May 5, 2016 7:37 PM