Gerd Gigerenzer was giving a seminar to 160 gynecologists with a decade or more of experience. He set out to prove that most doctors do not understand test results. He posed a question that is customary in medical studies, in probabilities:
The probability that a women has breast cancer is 1 percent.
If a women has breast cancer, the probability that she test positive is 90 percent.
If a women does not have breast cancer, the probability that she nevertheless test positive is 9 percent.
A women test positive. She wants to know whether that means that she has breast cancer for sure or what the chances are. What do you tell her?
A) 9 in 10
B) 8 in 10
C) 1 in 10
D) 1 in 100
The best answer is one out of ten. That is, out of test women who test positive in screening, one has cancer. The other nine women receive false alarms. Yet the 160 gynecologists’ answers, monitored by an interactive voting system offering the four choices above, were all over the map. The majority believed that the answer was 8 in 10. Only 21% correctly informed the patient.
If I break it down in simple terms:
1- Ten out of every 1,000 women are expected to have breast cancer.
2- Of these 10 women with breast cancer, 9 test positive.
3-Of the 990 without breast cancer, 89 nevertheless test positive.
4- This means 98 (89+9) are expected too test positive, of whom nine actually have cancer. This is close to one out of 10.
The sloppy thinking by the “experts” was on full display during the COVID-19 pandemic. The proper way to conduct testing was discussed here.