----- . . . that something can be true of every subset but not of the whole set. ----- That's not quite how Simpson's paradox is usually stated. The Wikipedia article at https://en.wikipedia.org/wiki/Simpson's_paradox has some nice examples. —Dan -----Original Message-----
From: "Keith F. Lynch" <kfl@KeithLynch.net>
My favorite probability paradox is Simpson's paradox, i.e. that something can be true of every subset but not of the whole set. A surprising real-world example is that until recently US life expectancy was going up, but that there were two groups for which it was going down: Smokers and non-smokers.
The explanation is that, roughly speaking, life expectancy was only increasing because of people quitting smoking, and that all else was a net loss, presumably because improvements in medical care were more than offset by the increasing unaffordability of that care.
Of course it's not really a paradox, just an example of how mathematical intuition is often wrong.