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What real life examples of Simpson's paradox exist?
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Simpson's paradox is characterized by the inconsistency between the conditional and marginal interpretations of data. In other words Simpson's paradox occurs when groups of data show one trend, but the trend is reversed when the groups are combined together.

There are so many examples that cut across the spectrum of fields of study. According to Brilliant.org, imagine you and a friend do problems on Brilliant, and your friend answers a higher proportion correctly than you on each of two days. Does that mean your friend has answered a higher proportion correctly than you when the two days are combined? Not necessarily!

This seemingly unintuitive possibility is referred to as Simpson's paradox.

Let's see how this can occur.

• On Saturday, you solved $7$ out of $8$ attempted problems, but your friend solved $2$ out of $2$. You had solved more problems, but your friend pointed out that he was more accurate, since $\dfrac{7}{8} < \dfrac{2}{2}​$​. Fair enough.
• On Sunday, you only attempted 22 problems and got 11 correct. Your friend got 55 out of 88 problems correct. Your friend gloated once again, since $\dfrac{1}{2} < \dfrac{5}{8}$​.

However, the competition is about the one who solved more accurately over the weekend, not on individual days. Overall, you have solved 88 out of 1010 problems whereas your friend has solved $7$ out of $10$ problems. Thus, despite your friend solving a higher proportion of problems on each day, you actually won the challenge by solving the higher proportion for the entire weekend! While your friend got furious, you calmly pointed him to this page: you had just shown an instance of Simpson's paradox.

by Wooden (936 points)