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
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
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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