TITLE: More examples of Simpson's Paradox, barring the ones on Wikipedia, Titanic, and delayed flights.
QUESTION [17 upvotes]: 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.

REPLY [2 votes]: I simplify and correct some grammar of the text in Jon Wayland's Quora answer.

Several teachers were itching to know the optimal duration of study for students to score well on tests. So, they  gathered the approximate number of hours students were studying, then compare to the students’ test scores.
Mr. Simpson convinced the faculty that more data means better results, and so all of the teachers integrated their cross-course data for the analysis.
The results were astounding. To everyone’s confusion, the less a student studied, the higher they tend to score on tests.

In fact, the coefficient associated with this correlation was strongly negative: $-0.7981$.
Should they be encouraging their students to study less? How in the world could data be backing such a claim? Surely something was missing.
The teachers decided to consult the school’s statistician, Ms. Paradox. After Mr. Simpson explained their results to her, she suggested they analyze each course’s data individually.
So, they then analyzed only Phys. Ed. and proceeded to have their minds blown.

A correlation of 0.6353! How in the statistical universe was this even possible?
Ms. Paradox then explained this as Simpson’s Paradox, a statistical phenomenon where a seemingly strong relationship reverses or disappears when introduced to a third confounding variable.
She convinced Mr. Simpson to plot all the data again, but then color-code each course separately to distinguish them.

After doing so, Mr. Simpson and his colleagues concluded that the relationship was indeed positive, and that the more hours a student studied, the higher the grade tends to be.
Including the course of study in the analysis completely reversed the relationship.

R Code for this example:
[I don't know how to post the R Code as he did, numbered and all. Can someone add it here? Thx!]