Sat, 02 Oct 2021
Simplest example of Simpson's paradox
I had read many times about Simpson's paradox but it never quite clicked for me. I saw many examples, but I couldn't quite get what was really going on. And I could never remember the numbers in the examples, so I couldn't ponder it while waiting for the bus or whatever.
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.
Now I understand Simpson's paradox.
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