Is Simpson’s Paradox just a mathematical curiosity, or does it happen in real life? And if it happens, what does it mean? To answer these questi

In Search Of: Simpson’s Paradox

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2021-05-26 07:00:10

Is Simpson’s Paradox just a mathematical curiosity, or does it happen in real life? And if it happens, what does it mean? To answer these questions, I’ve been searching for natural examples in data from the General Social Survey (GSS).

At this point I have tried a few thousand combinations and found about ten clear-cut instances of Simpson’s paradox. So I’ve decided to make a more systematic search. From the GSS data I selected 119 opinion questions that were asked repeatedly over more than a decade, and 12 demographic questions I could sensibly use to group respondents.

With 119 possible variables on the x-axis, the same 119 possibilities on the y-axis, and 12 groupings, there are a 84,118 sensible combinations. When I tested them, 594 produced computational errors of some kind, in most cases because some variables have logical dependencies on others. Among the remaining combinations, I found 19 instances of Simpson’s paradox.

So one conclusion we can reach immediately is that Simpson’s paradox is rare in the wild, at least with data of this kind. But let’s look more closely at the 19 examples.