Causal Correlations

This reference to background theory is important, because two sets of phenomena can be correlated to a very high degree, even with no direct causal relationship between them. A favorite example that appears in many statistics texts is the discovered positive correlation in boys between foot size and quality of handwriting. It is hard to imagine a causal relation hold- ing in either direction. Having big feet should not make you write better and, just as obviously, writing well should not give you big feet. The correct explanation is that both foot size and handwriting ability are positively correlated with age. Here a noncausal correlation between two phenomena (foot size and handwriting ability) is explained by a third common correla- tion (maturation) that is causal.

At times, it is possible to get causal correlations backward. For example, a few years ago, sports statisticians discovered a negative correlation between forward passes thrown and winning in football. That is, the more forward passes a team threw, the less chance it had of winning. This suggested that passing is not a good strategy, since the more you do it, the more likely you are to lose. Closer examination showed, however, that the causal relation- ship, in fact, went in the other direction. Toward the end of a game, losing teams tend to throw a great many passes in an effort to catch up. In other words, teams throw a lot of passes because they are losing, rather than the other way around.

Finally, some correlations seem inexplicable. For example, a strong posi- tive correlation reportedly holds between the birth rate in Holland and the number of storks nesting in chimneys. There is, of course, a background the- ory that would explain this—storks bring babies—but that theory is not fa- vored by modern science. For the lack of any better background theory, the phenomenon just seems weird.