But Pearson's language on the matter was inconsistent and confusing. The father of correlation did worry about its overuse, says Theodore Porter, a historian of science at UCLA and a Pearson specialist. A footnote to the second edition of The Grammar of Science, published in 1900, lays out a critique of spurious relationships in terms that would not look out of place on an Internet message board:
All causation as we have defined it is correlation, but the converse is not necessarily true, i.e. where we find correlation we cannot always predict causation. In a mixed African population of Kaffirs and Europeans, the former may be more subject to smallpox, yet it would be useless to assert darkness of skin (and not absence of vaccination) as a cause.
Pearson's critics expressed the same concern. That year in Science, a reviewer called out the book's "transition of correlation into causation" as one that is "scarcely allowable" and went on to note (emphasis mine) that, "correlation does not imply causation, though the converse is no doubt true enough."
So it seems the fear of correlations was formalized—made into a turn of phrase, I mean—at around the time that correlations came into formal being. One might say (citing another correlation) that Pearson's work marks the transition from an age of causal links to one of mere relationships—from anecdotal science to applied statistics. As correlations split and multiplied, we needed to remind ourselves of what they meant and what they didn't. The graph below, again from Google Books, shows the shift in language that marked this change in spirit: Up until the early 1900s, causation showed up more often than correlation in the corpus; then the concepts flip. (I'll let someone else explain why correlations have been trending downward since 1976.)
In the decades to come, the phrase correlation does not imply causation made its way into textbooks and academic journals, while the social sciences were made over with newfangled statistics. By the 1940s, economists had devised a name for the insufficiency of correlations: They called it the "identification problem." A flood of numbers in the postwar years may have made the anxiety more acute until its apotheosis in the present day, when Google, Amazon, and the other data juggernauts belch smoggy clouds of information and spit out correlations by the ton. "That may be as deep a sense of causation as they care about," Porter says. "To them, perhaps, automated number-crunching stands for the highest form of knowledge that civilization has ever produced." In that sense, the admonitory slogan about correlation and causation isn't so much a comment posted on the Internet as a comment posted about the Internet. It's a tiny fist raised in protest against Big Data.
But there's still another puzzle in the phrase. To say that correlation does not imply causation makes an important point about the limits of statistics, but there are other limits, too, and ones that scientists ignore with far more frequency. In The Cult of Statistical Significance, the economists Deirdre McCloskey and Stephen Ziliak cite one of these and make an impassioned, book-length argument against the arbitrary cutoff that decides which experimental findings count and which ones don't. By convention, we call an effect "significant" if the chances of its deriving from a twist of fate—as opposed to some more genuine relationship—are less than 5 percent. But as McCloskey and Ziliak (and many others) point out, there's nothing special about that number and no reason to invest it with our faith.
It's easy to imagine how this point might be infused into the wisdom of the Web: "Facepalm. How many times do I have to remind you? Don't confuse statistical and substantive significance!" That comment-ready slogan would be just as much a conversation-stopper as correlation does not imply causation, yet people rarely say it. The spurious correlation stands apart from all the other foibles of statistics. It's the only one that's gone mainstream. Why?
I wonder if it has to do with what the foible represents. When we mistake correlation for causation, we find a cause that isn't there. Once upon a time, perhaps, these sorts of errors—false positives—were not so bad at all. If you ate a berry and got sick, you'd have been wise to imbue your data with some meaning. (Better safe than sorry.) Same goes for a red-hot coal: one touch and you've got all the correlations that you need. When the world is strange and scary, when nature bullies and confounds us, it's far worse to miss a link than it is to make one up. A false negative yields the greatest risk.
Now conditions are reversed. We're the bullies over nature and less afraid of poison berries. When we make a claim about causation, it's not so we can hide out from the world but so we can intervene in it. A false positive means approving drugs that have no effect, or imposing regulations that make no difference, or wasting money in schemes to limit unemployment. As science grows more powerful and government more technocratic, the stakes of correlation—of counterfeit relationships and bogus findings—grow ever larger. The false positive is now more onerous than it's ever been. And all we have to fight it is a catchphrase.
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