Before you call it causation, three other explanations have to fail

The slogan is not enough

Everyone knows that correlation does not imply causation, and the phrase has become a way of ending discussions rather than advancing them. It is true, but on its own it is unhelpful, because sometimes correlation is caused by causation and the question is which case you are in. What is needed is not the slogan but the list of what else it could be.

The list is short. If two things move together, there are four broad possibilities, and only one of them is the causal story you had in mind. Working through the other three is quick, and it is the difference between scepticism and knowledge.

One: it happened by chance

With enough variables and enough patience, strong correlations appear between things that have nothing to do with each other. This is not a rare curiosity; it is a mathematical certainty once you are comparing many series, because the number of possible pairs grows far faster than the number of series.

The defences are familiar. Was the relationship specified before it was looked for, or found by searching? Does it hold in a different dataset, a different period, a different population? A correlation discovered by inspecting data and reported from the same data has not been tested at all — it is the hypothesis, not the evidence for it. This is the reason a finding that replicates in an independent sample is worth so much more than one that is merely striking.

Two: the causation runs the other way

Reverse causation is embarrassingly easy to miss when the assumed direction is intuitive. If people who exercise are healthier, exercise may be producing health, or health may be producing the capacity to exercise, and the correlation is identical under both. If firms with a certain practice are more profitable, profitability may be what allows the practice to be afforded.

A useful habit is to state the reversed version out loud in the same words as the original, because the reversed sentence is often just as plausible and the plausibility is what does the persuading. When both directions sound equally sensible, the correlation is supplying no information about which one is happening, and any confidence you feel is coming from somewhere other than the data. Sometimes both directions operate at once, reinforcing each other, which is the hardest case of all to untangle from observational records.

Timing helps but does not settle it, since a cause must precede its effect but many things anticipate their own consequences. People change behaviour in expectation of an outcome, which can make the effect appear to precede the cause in the record. The strongest resolution is a design where the direction is fixed by the researcher rather than inferred, which is another way of describing a randomised trial.

Three: something else causes both

This is the big one, and it accounts for most of the false causal claims in circulation. A third factor produces both of the things you are looking at, so they move together with no direct link between them at all. Because the third factor may be anything, including things nobody measured, this possibility can never be fully excluded from observational data.

Researchers control for confounders they can name and measure, which helps and is far from complete. Controlling for a variable measured badly leaves part of its influence in the data. Controlling for a variable that sits on the causal path between the two things removes exactly the effect you were trying to find. And the confounders you did not think of are entirely untouched by any of this, which is the reason randomisation is valued so highly: it is the only method that handles the ones you never named.

Four: it really is causal

This possibility deserves stating, because relentless scepticism can become its own failure. Correlations often do reflect causation, and the way to build confidence without a trial is to accumulate evidence of different kinds that fail in different ways.

What raises confidence: a plausible mechanism that predicts other things which then turn out to be true, a dose-response pattern where more exposure goes with more effect, the relationship appearing in populations with different confounders, the effect changing when the exposure changes for reasons unrelated to the outcome, and natural experiments where circumstance assigned people to conditions arbitrarily. None of these is conclusive alone. Together they can be more persuasive than a single trial, which is how several of the strongest causal conclusions in public health were reached long before anyone could have run an experiment.