We cannot rely on correlation alone. But insisting on absolute proof of causation is too exacting a standard

It is said that there is a correlation between the number of storks’ nests found on Danish houses and the number of children born in those houses. Could the old story about babies being delivered by storks really be true? No. Correlation is not causation. Storks do not deliver children but larger houses have more room both for children and for storks.

This much-loved statistical anecdote seems less amusing when you consider how it was used in a US Senate committee hearing in 1965. The expert witness giving testimony was arguing that while smoking may be correlated with lung cancer, a causal relationship was unproven and implausible. Pressed on the statistical parallels between storks and cigarettes, he replied that they “seem to me the same”.

The witness’s name was Darrell Huff, a freelance journalist beloved by generations of geeks for his wonderful and hugely successful 1954 book How to Lie with Statistics. His reputation today might be rather different had the proposed sequel made it to print. How to Lie with Smoking Statistics used a variety of stork-style arguments to throw doubt on the connection between smoking and cancer, and it was supported by a grant from the Tobacco Institute. It was never published, for reasons that remain unclear. (The story of Huff’s career as a tobacco consultant was brought to the attention of statisticians in articles by Andrew Gelman in Chance in 2012 and by Alex Reinhart in Significance in 2014.)

Indisputably, smoking causes lung cancer and various other deadly conditions. But the problematic relationship between correlation and causation in general remains an active area of debate and confusion. The “spurious correlations” compiled by Harvard law student Tyler Vigen and displayed on his website (tylervigen.com) should be a warning. Did you realise that consumption of margarine is strongly correlated with the divorce rate in Maine?

We cannot rely on correlation alone, then. But insisting on absolute proof of causation is too exacting a standard (arguably, an impossible one). Between those two extremes, where does the right balance lie between trusting correlations and looking for evidence of causation?

Scientists, economists and statisticians have tended to demand causal explanations for the patterns they see. It’s not enough to know that college graduates earn more money — we want to know whether the college education boosted their earnings, or if they were smart people who would have done well anyway. Merely looking for correlations was not the stuff of rigorous science.

But with the advent of “big data” this argument has started to shift. Large data sets can throw up intriguing correlations that may be good enough for some purposes. (Who cares why price cuts are most effective on a Tuesday? If it’s Tuesday, cut the price.) Andy Haldane, chief economist of the Bank of England, recently argued that economists might want to take mere correlations more seriously. He is not the first big-data enthusiast to say so.

This brings us back to smoking and cancer. When the British epidemiologist Richard Doll first began to suspect the link in the late 1940s, his analysis was based on a mere correlation. The causal mechanism was unclear, as most of the carcinogens in tobacco had not been identified; Doll himself suspected that lung cancer was caused by fumes from tarmac roads, or possibly cars themselves.

Doll’s early work on smoking and cancer with Austin Bradford Hill, published in 1950, was duly criticised in its day as nothing more than a correlation. The great statistician Ronald Fisher repeatedly weighed into the argument in the 1950s, pointing out that it was quite possible that cancer caused smoking — after all, precancerous growths irritated the lung. People might smoke to soothe that irritation. Fisher also observed that some genetic predisposition might cause both lung cancer and a tendency to smoke. (Another statistician, Joseph Berkson, observed that people who were tough enough to resist adverts and peer pressure were also tough enough to resist lung cancer.)

Hill and Doll showed us that correlation should not be dismissed too easily. But they also showed that we shouldn’t give up on the search for causal explanations. The pair painstakingly continued their research, and evidence of a causal association soon mounted.

Hill and Doll took a pragmatic approach in the search for causation. For example, is there a dose-response relationship? Yes: heavy smokers are more likely to suffer from lung cancer. Does the timing make sense? Again, yes: smokers develop cancer long after they begin to smoke. This contradicts Fisher’s alternative hypothesis that people self-medicate with cigarettes in the early stages of lung cancer. Do multiple sources of evidence add up to a coherent picture? Yes: when doctors heard about what Hill and Doll were finding, many of them quit smoking, and it became possible to see that the quitters were at lower risk of lung cancer. We should respect correlation but it is a clue to a deeper truth, not the end of our investigations.

It’s not clear why Huff and Fisher were so fixated on the idea that the growing evidence on smoking was a mere correlation. Both of them were paid as consultants by the tobacco industry and some will believe that the consulting fees caused their scepticism. It seems just as likely that their scepticism caused the consulting fees. We may never know.

Written for and first published at ft.com.