Sometime ago I tried to come up with the simplest possible explanation for Simpson's paradox. This was the result: 1) Imagine that most women with a certain di

Sometime ago I tried to come up with the simplest possible explanation for Simpson's paradox. This was the result: 1) Imagine that most women with a certain disease survive, while most men die. 2) Imagine that most women with the disease take a certain medicine, while most men don't. 3) Imagine that the medicine has absolutely no effect. Women just happen to have better innate resistance to the disease, and also just happen to buy the medicine more because it's marketed to women. Now if you do a statistical analysis without counting men and women separately, you will conclude that the medicine is very correlated with survival! Note that there's no way to know in advance that you should slice the population along such-and-such variables, which can be a lot more subtle than just gender. Also note that the example works even if the medicine has a slight negative effect, i.e. you can reverse the direction of correlations by choosing to slice or not to slice. I think such results make it clear that you can't easily trust conclusions from statistics. One minute you're thinking that cholesterol causes heart disease, and the next minute you're asking yourself, what if cholesterol is part of the body's response to heart disease? That's why we need randomized controlled studies, and theories of causality.