Representation of information is important. In the case of many so-called cognitive illusions, the problem results from difficulties that arise from getting along with probabilities. The problem largely disappears the moment you give the person the information in natural frequencies. You basically put the mind back in a situation where it's much easier to understand these probabilities. We can prove that natural frequencies can facilitate actual computations, and have known for a long time that representations whether they be probabilities, frequencies or odds have an impact on the human mind. There are very few theories about how this works.
give you a couple examples relating to medical care. In the U.S. and
many European countries, women who are 40 years old are told to participate
in mammography screening. Say that a woman takes her first mammogram
and it comes out positive. She might ask the physician, "What does
that mean? Do I have breast cancer? Or are my chances of having it
99%, 95%, or 90% or only 50%? What do we know at this point?"
I have put the same question to radiologists who have done mammography
screening for 20 or 25 years, including chiefs of departments. A third
said they would tell this woman that, given a positive mammogram,
her chance of having breast cancer is 90%.
What we do is to teach these physicians tools that change the representation so that they can see through the problem. We don't send them to a statistics course, since they wouldn't have the time to go in the first place, and most likely they wouldn't understand it because they would be taught probabilities again. But how can we help them to understand the situation?
Let's change the representation using natural frequencies, as if the physician would have observed these patients him- or herself. One can communicate the same information in the following, much more simple way. Think about 100 women. One of them has breast cancer. This was the 1%. She likely tests positive; that's the 90%. Out of 99 who do not have breast cancer another 9 or 10 will test positive. So we have one in 9 or 10 who tests positive. How many of them actually has cancer? One out of ten. That's not 90%, that's not 50%, that's one out of ten.
Here we have a method that enables physicians to see through the fog just by changing the representation, turning their innumeracy into insight. Many of these physicians have carried this innumeracy around for decades and have tried to hide it. When we interview them, they obviously admit it, saying, "I don't know what to do with these numbers. I always confuse these things." Here we have a chance to use very simple tools to help those patients and physicians to understand what the risks are and which enable them to have a reasonable reaction to what to do. If you take the perspective of a patient that this test means that there is a 90% chance you have cancer you can imagine what emotions set in, emotions that do not help her to reason the right way. But informing her that only one out of ten women who tests positive actually has cancer would help her to have a cooler attitude and to make more reasonable decisions.