What Is the Difference Between Correlation and Causation? And How to Tell

When two variables move together, several arrangements can produce it and only one is direct causation:

• •A causes B, which is the conclusion people jump to
• •B causes A, the reverse direction, which is frequently as plausible and is why studies finding that exercise correlates with better mood have to consider that feeling better makes people exercise
• •A third variable causes both, called confounding, which is the ice cream and drowning case and by far the commonest explanation
• •Selection effects, where the way the sample was assembled creates the association, as when studying only hospitalised patients produces correlations between conditions that do not exist in the general population
• •Reverse selection, where the outcome determines who is in the data at all
• •Coincidence, which with enough variables is guaranteed, and which produces the spurious correlation collections showing cheese consumption tracking deaths by bedsheet entanglement

A randomised experiment settles the question by construction: allocating the treatment by chance means that the treated and untreated groups differ, on average, in nothing except the treatment, so any difference in outcome must be caused by it. That is why the randomised trial is the standard in medicine, and its power comes entirely from the randomisation rather than from any sophistication in the analysis. The problem is that a great many important questions cannot be randomised, for ethical reasons, since nobody will assign people to smoke, for practical reasons, since a researcher cannot randomise which country adopts a policy, or because the exposure has already happened. Most of the interesting causal questions in economics, epidemiology, education and social policy fall into that category, and the field of causal inference exists to answer them from data that was not generated by an experiment.

Several designs extract causal claims from observational data by finding something that behaves like a randomisation. A natural experiment uses an external event that assigned treatment in an effectively arbitrary way, such as a lottery, a policy change at an arbitrary date or a boundary. Difference in differences compares the change over time in a group affected by something against the change in a similar unaffected group, which removes fixed differences between them and any common trend. Regression discontinuity exploits a threshold, comparing people just above and just below a cutoff for a scholarship, a benefit or a diagnosis, who differ essentially at random in everything except being on one side of the line. Instrumental variables use a factor that affects the treatment and has no other route to the outcome, which is difficult to find and easy to misuse. Causal diagrams, developed by Judea Pearl, provide a formal way to reason about which variables must be controlled for and, importantly, which must not, since controlling for a variable on the causal path or for a common effect of two variables introduces bias rather than removing it.

The clearest demonstration that causation can be established without experiment is the link between smoking and lung cancer, argued through the 1950s against opposition including from Ronald Fisher, who suggested a genetic predisposition might cause both. Austin Bradford Hill set out nine considerations in 1965 that are still used: the strength of the association, its consistency across different populations and methods, its specificity, the temporal sequence with cause preceding effect, a dose-response relationship, biological plausibility, coherence with what else is known, experimental evidence where available, and analogy with similar established relationships. None is individually sufficient and Hill was explicit that they are not a checklist. The smoking evidence satisfied nearly all of them: the association was very large, appeared in every population studied, rose with the number of cigarettes, fell after quitting, had a plausible mechanism and was reproduced in animals. That combination is what closed the argument, and it is the model for how causal claims are established when the experiment cannot be run.

A correlation can arise from A causing B, B causing A, a third variable causing both, selection in how the data was assembled, or coincidence, and confounding is the commonest. Randomisation settles causation by making the groups comparable in everything else, which is why it is the standard where it is possible. Where it is not, natural experiments, difference in differences, regression discontinuity and instrumental variables recover causal claims by finding something that assigned treatment arbitrarily, and Hill's nine considerations, applied to smoking, show how a case is built without an experiment.