Thursday, January 04, 2007

More than 50% can be above average

Glen Whitman at Agoraphilia points out how the common example of cognitive bias that "80% of us believe that our driving skills are better than average" can be a correct description of reality, when the median is greater than the mean. By example, the mean time to conception for women trying to get pregnant is 7 months, but 50% of such women are pregnant within 4 months and 75% pregnant within 6 months, so 75% of such women do "better than average."


Unknown said...

I don't think is a particularly good example. When respondents to the question "Are you a better driver than average?" answer in the affirmative, they almost certainly mean that, in a group of 100 random drivers, they'd be in the top 50 (and not that their driving skill is greater than M, the mean driving skill of the group). So, I think it remains as a good example of cognitive bias.


SB said...

A few bad drivers - say 20% - can result in the average loss being very high. So, the 80% may have a
"better than average" loss ratio.

In fact, that is the case for motor insurance claims. For the statistically minded, loss ratios follow a Poisson-distribution, hence the average loss is higher than the average person's loss.