Nate Silver wrote a really excellent article yesterday on confidence intervals, and it really describes very well a pet issue of mine: probabilities and our brains. Probabilities play a very large role in our decision making processes and are specifically very important when performing risk assessments, but I think, as humans, we are naturally ill-equipped to handle probabilities in a meaningful and precise way.
With due respect to our reader, Skeptical Sam, I’m not sure that people’s intuitions are all that good when it comes to estimating confidence intervals. Most people probably know, almost to the minute, how long their commutes to work take them on average. But if I asked you to tell me how often your commute takes 10 minutes longer than average — something that requires some version of a confidence interval — you’d have to think about that a little bit, and you might wind up being pretty far off. Calculating the average amount you expect your family to spend on groceries in a month, likewise, is easier than estimating the risk of some catastrophic event that will cause you to go bankrupt.
Finally, there’s some evidence from behavioral economics that human beings are bad at estimating probabilities out at the tail ends of the bell curve. We’re pretty decent at telling a favorite from an underdog, but we’re not so good at telling an 8:1 underdog from an 80:1 underdog or an 8,000:1 underdog, even though those are huge differences statistically.
All of these are good reasons not to trust your gut.
This also reminds me of an excellent Radiolab episode on a similar topic: Stochasticity.
I think the only real way to combat the counter-intuitive nature of these concepts is more education, and I think there’s some very real opportunities to beef up high school math curricula when it comes to probabilities. I remember spending a very short amount of time on the subject, and it being particularly uninteresting (red and blue marbles…). I think a larger amount of time spent on particularly the larger concepts of what probabilities actually mean would make for a more informed populace.Read More