Some ideas on communicating risks to the general public
Via Dan Goldstein @ Decision Science News
In addition, when risks are described as probabilities, people tend to overweight small probabilities and underweight large probabilities. This observation shows up in the “probability weighting function” of Tversky & Kahneman’s Prospect Theory, the dominant behavioral model of gamble evaluations. A representation that leads to misperceptions of underlying probabilities is undesirable.
It seems as if people given conditional probabilities, such as the sensitivity or the false-positive rate, confuse them with the posterior probability they are being asked for. This likely happens because each numerical representation lend themselves to computations that are easy or difficult for that representation. The thing to do with the conditional probabilities listed above is to plug them into Bayes Theorem, which most people do not know. Even if they know the theorem, they have little intuition for it and cannot make good mental estimates.
Consider the colorectal cancer example given previously. Only 1 in 24 doctors tested could give the correct answer. The following, mathematically-equivalent, representation of the problem was given to doctors:
Out of every 10,000 people, 30 have colorectal cancer. Of these 30, 15 will have a positive haemoccult test. Out of the remaining 9,970 people without colorectal cancer, 300 will still test positive. How many of those who test positive actually have colorectal cancer?
Without any training whatsoever, 16 out 24 physicians obtained the correct answer to this version. That is quite a jump from 1 in 24.