You see a correlation between two variables, for example clever people wear fancy clothes. Then you assume that one variable must cause the other, in our case: a higher intellect gives people also a better sense of aesthetic taste, or good taste in clothing somehow also makes people smarter. In fact, you may be overlooking a third variable which explains the other two, as well as their correlation. In our case: clever people earn more money, which makes it easier to buy your clothes in shops which help you with your aesthetics.
Here’s an example from Nate Silver’s blog:
Gallup has some interesting data out on the percentage of Americans who pay a lot of attention to political news. Although the share of Americans following politics has increased substantially among partisans of all sides, it is considerably higher among Republicans than among Democrats:
The omitted variable here is age, and the data should be corrected for it in order to properly compare these two populations.
News tends to be consumed by people who are older and wealthier, which is more characteristic of Republicans than Democrats.
People don’t read more or less news because they are Republicans or Democrats. And here’s another one from Matthew Yglesias’ blog:
It’s true that surveys indicate that gay marriage is wildly popular among DC whites and moderately unpopular among DC blacks, but I think it’s a bit misleading to really see this as a “racial divide”. Nobody would be surprised to learn about a community where college educated people had substantially more left-wing views on gay rights than did working class people. And it just happens to be the case that there are hardly any working class white people living in DC. Meanwhile, with a 34-48 pro-con split it’s hardly as if black Washington stands uniformly in opposition—there’s a division of views reflecting the diverse nature of the city’s black population.