Correlation, as we all know so well, does not imply causation. But sometimes it comes damn close.
For example: Parents of daughters are more likely to divorce than parents of sons. When I wrote and then rewrote about this odd fact in Slate, I got hundreds of emails from readers protesting that daughters might not cause divorce. Maybe some third factor causes both divorce and daughters.
There’s even a clear candidate for that factor: Stress. It’s well established that in many species, stressed populations produce unusually many female offspring. If the same is true in humans, then perhaps both daughters and divorce are the products of exogenous stress.
The problem with that theory is that it’s arithmetically implausible. To explain even a small correlation between daughters and divorce, you’d have to make pretty extreme assumptions about the effects of stress.
For example: Suppose half of all parents are stressed, stressed parents have 55% girls and a 50% divorce rate, and unstressed parents have 45% girls and a 25% divorce rate. Those are much stronger effects (especially on the boy/girl ratio) than anyone could actually believe. Nevertheless, even with these strong assumptions, we get a 36.25% divorce rate among parents of girls and a 38.75% divorce rate among parents of boys—not a very big difference. So the stress theory just doesn’t hold water.
The general point is that before you attribute a correlation to some mysterious (or non-mysterious) third factor, it’s worth pulling out an envelope, flipping it over, and jotting down some numbers. If your numbers have to be ridiculous to get the result you want, you probably need a different theory.