Implicit population selection biases can lead to all sorts of fun.<p>One that I saw a paper get wrong a while ago was one which claimed to find an inverse correlation between two different traits that individually improved intelligence. The catch? The sample population was chosen from university students at no name school X. But people who did well on <i>both</i> traits would have done well enough to go to a better school and so were underrepresented in the population sample!<p>(I forget the paper, but pay attention and you'll find lots of other examples...)
This reminds me of a thought experiment I read a while ago, I believe on the Atlantic. I'll paraphrase with a bit more math:<p>Suppose that acting ability and attractiveness are independently normally distributed with mean 0 and standard deviation 1. Further suppose that to be a successful movie star, an individual must have an acting ability plus attractiveness of 6.<p>Then among people with the necessary attributes to be movie stars, attractiveness and acting ability will be negatively correlated. In this example, we might expect to see movie stars with (intelligence, attractiveness) around (3,3) or (2,4) or (4,2), but it's much more unlikely that we see many people around (4,4).