Absence of correlation does not imply absence of causation

By way of Andrew Sullivan we have this attempt by Philip N. Cohen to apply statistics to answer the question: does texting while driving cause accidents? Or rather, he marshals data to ridicule the new book by Matt Richtel on a supposed epidemic of traffic fatalities, particularly among teens, caused by texting while driving. He has some good points about the complexity of the evidence, and a good general point that people like to fixate on some supposed problem with current cars or driving practices, to distract their attention from the fact that automobiles are inherently dangerous, so that the main thing that causes more fatalities is more driving. But then he has this weird scatterplot, that is supposed to be a visual knock-down argument:

We need about two phones per person to eliminate traffic fatalities...
We need about two phones per person to eliminate traffic fatalities…

So, basically no correlation between the number of of phone subscriptions in a state and the number of traffic fatalities. So, what does that prove? Pretty much nothing, I would say. It’s notable that there is really very little variation in the number of mobile phones among the states, and at the lowest level there’s still almost one per person. (Furthermore, I would guess that most of the adults with no mobile phone are poor, and likely don’t have an automobile either.) Once you have one mobile phone, there’s no reason to think that a second one will substantially

Whether X causes Y is a separate question from whether variation in X is linked to variation in Y. You’d like to think that a sociologist like Cohen would know this. A well-known example: No one would doubt that human intelligence is a product of the human brain (most directly). But variations in intelligence are uncorrelated with variations in brain size. (Which doesn’t rule out the possibility that more subtle measurements could find a physical correlate.) This is particularly true with causes that are saturated, as with the one phone per person level.

You might imagine a Cohen-like war-crimes investigator deciding that the victims were not killed by bullets, because we find no correlation between the number of bullets in a gun and the fate of the corresponding victim.

Just to be clear: I’m not claiming that evidence like this could never be relevant. But when you’re clearly in the saturation region, with a covariate that is only loosely connected to the factor in question, it’s obviously just misleading.

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