I hope someone may know fresh examples of Simpson's paradox for use in my statistics courses. The examples I've been using are fine, but I'd like to have some new ones.
I'm familiar with the ones on the Wikipedia page: the gender bias lawsuit at Berkeley, batting averages, mortality rates among low birth babies, party voting on the Civil Rights Act, and success rates of kidney stone treatments. I'm also familiar with the example of survival rates on the Titanic and the one about delayed flights at America West vs. Alaska Airlines. These are all good ones, but, like I said, I'm looking for more. Does anybody know any others?
For those who aren't familiar with it, Simpson's paradox is essentially a property of unreduced fractions: It's possible to have, simultaneously, $\frac{a_1}{b_1} < \frac{c_1}{d_1} \text{ and } \frac{a_2}{b_2} < \frac{c_2}{d_2}, \text{ but } \frac{a_1 + a_2}{b_1+b_2} > \frac{c_1+c_2}{d_1+d_2}.$
For example, $\frac{1}{3} < \frac{34}{100}$ and $\frac{66}{100} < \frac{2}{3}$, but $\frac{67}{103} > \frac{36}{103}$. It can be hard to spot this happening in a given real-world scenario.