Fallacy of composition and life expectancy
Matthew Martin 1/08/2015 10:19:00 AM
Gardner's post mentioned studies of female mortality, which had reported that women's life expectancy was lower in some US counties than 20 years earlier, and concludes that life expectancy has fallen for women in these counties. Because of the fallacy of composition, this conclusion does not logically follow. To drive that point home, here's a numerical example. Suppose there are two counties: Healthypeopleshire and Unhealthypeopleshire. We perform surveys over two periods to calculate life expectancy in each county each period. In the first survey, there is one resident of Healthypeopleshire with a life expectancy of 90 years, and two residents of Unhealthypeopleshire with life expectancies of 70 and 56 years respectively.After a vigorous public health campaign, life expectancy rises dramatically for all individuals in period 2:Incidentally, one effect of our public health campaign is that Brad left Unhealthypeopleshire to go live the ways of the healthy people in Healthypeopleshire. Because Brad has a lower expectancy than the other residents of Healthypeopleshire, but a higher expectancy of the other residents of Unhealthypeopleshire, our survey actually shows that life expectancy dropped in both counties, by 5 and 3 years respectively, even though it increased dramatically overall!