(Matthews, 2000) at Teaching Statistics

Another facetious but highly informative paper. Is there a connection between storks and babies? Yes, with a low enough p-value that people might bat an eye.

Most textbook examples of “correlation does not imply causation” make the true cause pretty clear. This one does a good job of obfuscating it.

The author shows that there’s a correlation between stork population and human births. He explains that some might take this as evidence that storks deliver babies. This is then the opportunity to clear up a major misunderstanding about p-values.

…According to its p-value, there is only a 1 in 125 chance of obtaining at least as impressive a value assuming the null hypothesis of no correlation were true. Yet as with any p-value (and contrary to what unwary users of them believe), this does not imply that the probability that mere fluke really is the correct explanation is just 1 in 125; still less does it imply a 124/125 = 99.2% probability that storks really do deliver babies. Such apparent nit-picking distinctions are frequently overlooked by consumers of p-values. In the case of the correlation between storks and human births, however, they no longer seem so pedantic: indeed, they provide the very welcome “escape route” by which to avoid a patently ludicrous inference.

The point to stress is that the p-value is a statement on how extreme of a result to expect given the null hypothesis—in this case, that there’s no correlation.