Causality

Simplest Simpson's Paradox

A beautiful example from here:

Last month I sat down and thought about it, with the idea of coming up with the simplest and most memorable possible example. Here it is. Imagine there is a disease that kills 50% of the people who get it. There is a pill you can take if you get the disease. Of the people who take the pills, 80% die. It looks like the pills are killing people. But they aren't, they are helpful. This is Simpson's paradox. What is really happening is that half the people with the disease have mild cases and half have severe cases. A patient with a mild case will get better on their own. But everyone with a severe case dies unless they receive treatment. People with mild cases don't bother to take the pills, because they are going to get better anyway. Only people with severe cases take the pills. 80% of them die, but without the pills they all would have died.