About 80 percent of us believe that our driving skills are better than average.I used to think this was a clear example of cognitive bias. Now I’m not so sure. The idea is that only 50 percent of us can really be better-than-average drivers, so at least 30 percent of people are wrong. The buried assumption here is that driving skill is symmetrically distributed, so that the mean and median are the same. That’s not necessarily true; the distribution might be skewed by the existence of small numbers of very bad drivers. To take a very simple case, suppose that 80% of drivers have no accidents at all, while the other 20% have 5 accidents per year. Then the average (mean) is 1 accident per year, and fully 80% of drivers are better than average! Obviously this example is unrealistic because it includes only two driver types, but it’s illustrative of what I think might be going on.
I couldn’t find any figures online stating the distribution of drivers by accident frequency, so I really don’t know if the distribution is sufficiently skewed to justify 80% of us thinking we’re better than average drivers. (If anyone knows of such statistics, please point me to them.) But it’s certainly not unknown for distributions to be that skewed. To take one example I’m fond of presenting to my students, the average (mean) time to conception for women trying to get pregnant is about 7 months. But 50% of such women will be pregnant within 4 months, and 75% will be pregnant within 6 months. That means at least 75% of women are doing “better than average” in the conception race. The result is driven, of course, by the fact that some couples have fertility problems that delay conception for many months or even years. These couples are analogous to the bad drivers who might be skewing overall accident rates.