Probability and statistics
Correlation is not causation
Two things moving together is a fact about the data, not a verdict on what causes what, until the other explanations are ruled out.
An old warning; its modern form was argued out between R. A. Fisher and the epidemiologists over smoking in the 1950s, and Austin Bradford Hill gave the constructive version in 1965.
Doll and Hill reported in 1950 that lung cancer patients in London hospitals were far more often heavy smokers than patients with other diseases. The correlation was strong. It still left three explanations open: smoking causes cancer; something else causes both; or the chain runs the other way. Fisher, the most eminent statistician alive, took the second seriously and wrote to Nature in 1958 that a common cause, the individual's genotype, could make some people both smoke and get cancer with no direct causation at all. He was wrong about smoking, but the structure of his objection is the one that still applies: a correlation is compatible with several causal stories, and the data that produced it cannot choose between them.
Hill's 1965 address to the Royal Society of Medicine turned the argument into a working method. He listed nine viewpoints for judging whether an association is causal: strength, consistency across studies, specificity, the cause preceding the effect, a dose-response gradient, biological plausibility, coherence with other knowledge, experimental evidence, and analogy. He was explicit that none of them gives indisputable proof and that he did not believe in hard-and-fast rules. The strongest in practice is experiment: randomising who gets the treatment breaks the link between the treatment and every hidden cause at once, which is why a randomised trial can overturn decades of observational agreement.
Two mistakes are common. One is to say 'correlation is not causation' and stop, as if the phrase settled anything; Fisher's demand was for better evidence, and better evidence was gathered, through cohorts of British doctors followed for years and dose-response gradients. The other is to assume a confounder must exist because one can be imagined. A confounder has to be named, has to be associated with both variables, and has to be strong enough to produce the observed effect. Hill's point about strength was exactly this: a very large ratio between exposed and unexposed is hard to explain away with a hidden factor, while a small difference is easy.
Example
On 12 July 1958 R. A. Fisher published a letter in Nature arguing that the association between smoking and lung cancer had been read as causal too quickly. He reported twin data from the Institute of Human Genetics in Munster: among pairs of identical twins, 24 percent differed clearly in their smoking habits, against 51 percent of 31 pairs of fraternal twins. Fisher took this as evidence that smoking behaviour is partly inherited, so a genotype that disposes people to smoke could also dispose them to cancer. The genetic explanation did not survive later cohort and dose-response evidence, but the letter is a clear record of what a correlation leaves open.
Where it applies
When a dashboard shows that users who adopt a feature retain better, ask whether the kind of user who adopts it would have stayed anyway, and run the randomised test. In AI evaluation, a model that scores higher on a benchmark correlated with user ratings has not been shown to produce better ratings until you try it on real traffic.
Think about it
Which correlation are you currently acting on as if it were a cause, and what would a randomised test of it cost?
Applied it to something real? Log it.
Test yourselfFisher accepted that smokers got more lung cancer. What alternative did he propose, and what kind of evidence can rule it out?
A common cause: a genotype disposing people both to smoke and to cancer. Randomised experiments break that link; short of those, Hill's viewpoints (strength, dose-response, temporality, consistency) weigh the alternatives.
Related models
- Confirmation biasPeople look for, notice and remember evidence that fits what they already believe, and rarely test what would prove them wrong.
- Selection biasIf the way cases got into your sample is related to what you are measuring, the sample will mislead you however large it is.
- Second-order thinkingKeep asking "and then what?" until you have looked at the consequences of the consequences.
- The map is not the territoryEvery model, metric or plan is a simplification, and the parts it leaves out can matter more than the parts it shows.
Sources and further reading
- R. A. Fisher, Lung Cancer and Cigarettes, Nature 182 (12 July 1958), transcription hosted by the University of York
- Austin Bradford Hill, The Environment and Disease: Association or Causation?, Proceedings of the Royal Society of Medicine 58 (1965)
- Richard Doll and A. Bradford Hill, Smoking and Carcinoma of the Lung, British Medical Journal (30 September 1950)