“Correlation is not causation” is the most repeated sentence in statistics and one of the least useful, because of where people stop saying it. It arrives at the end of an argument, as a verdict. It belongs at the beginning, as a question: if these two things move together and one does not cause the other, then what does explain it?
Answering that question is a skill. Reciting the slogan is not. Someone who can name the specific alternative explanation for a specific correlation — and say what evidence would rule it out — is doing causal inference. Someone who only recites the slogan has a way to dismiss any finding they dislike, which is worse than useless, because it works equally well on findings that are true.
Smoking and lung cancer is the standard reminder. Nobody ever ran a randomised trial assigning people to smoke. The case was built entirely from observational data, and it is now about as settled as anything in medicine. “Correlation is not causation” was the tobacco industry’s argument, and it was, in the narrow logical sense, correct.
Three explanations, plus two nuisances
When X and Y move together, there are exactly three causal structures that can produce it.
| Explanation | Shape | Example |
|---|---|---|
| Causation | X → Y | Price rises, units sold fall. |
| Reverse causation | Y → X | Firms with rising sales hire more salespeople, and it looks like hiring drives sales. |
| Common cause | Z → X and Z → Y | People who take vitamins are healthier. Being health-conscious causes both. |
Drawn out, with the data you would actually have underneath each one:
Three different worlds, one scatter. Nothing in the numbers picks between them, which is why the slogan is a question rather than a verdict: which of these three, and what would rule the other two out? Two more things produce correlations without any of the three being true:
- Coincidence. Test enough pairs of variables and some will correlate strongly by chance. This is why a correlation found by scanning a hundred columns is worth far less than one predicted in advance.
- Selection. Conditioning on a shared consequence creates a correlation out of nothing. Among hospital inpatients, two unrelated diseases can appear negatively correlated, because having either one is enough to get you admitted. The same thing happens whenever your data is a filtered slice: paying customers, surviving firms, users who completed onboarding.
Selection is the one most people have never been taught, and it is everywhere in company data, because company data is almost always a filtered slice of something.
Confounding is the default, not the exception
The common-cause case deserves more weight than it usually gets, because in observational data almost nothing is randomly assigned. People choose their treatments. Firms choose their strategies. Users choose which features to open. Whatever drives that choice usually also drives the outcome.
The pattern shows up sharply when a relationship reverses once you split the data by a third variable — the effect described in Simpson’s paradox in dashboards. That reversal is not a curiosity. It is confounding made visible, and the only reason you saw it is that you happened to split by the right column. Most of the time the confounder is a column you do not have.
So the practitioner’s move is not “is this correlation real?” — it usually is. The move is: name the confounder out loud. Say which specific third thing could produce both. If you can name it, you can look for it, adjust for it, or admit the estimate is contaminated. If you cannot name any, that is weak evidence for causation, and worth saying too.
What actually settles it
Randomisation. Assign the treatment by coin flip and every confounder, known or unknown, is balanced on average between the groups. Nothing else does this. It is the reason A/B tests earn the trust they get, and the reason the trust evaporates the moment assignment is not really random — see A/B test pitfalls for the ways an experiment leaks its own randomisation.
When you cannot randomise, the strategy is to find something in the world that randomised for you, and then argue for it explicitly:
- Natural experiments. A policy that changed on a date, a threshold that cuts eligibility, a rollout that happened region by region. The claim is that units just above and just below the line are otherwise alike.
- Difference-in-differences. Compare the change in a treated group with the change in an untreated one. The claim is that both groups would have moved in parallel without the treatment. That claim is an assumption about a world you never observe.
- Instrumental variables. Find something that affects the treatment and affects the outcome only through it. The claim is that the instrument has no other path to the outcome, which the data cannot confirm.
- Adjustment. Control for the confounders. The claim is that you measured all of them, and controlling for the wrong variable — one that sits on the causal path, or a shared consequence — makes the estimate worse, not better.
Every one of these methods works by importing an assumption that the data itself cannot check. That is not a flaw to hide. It is the actual content of the analysis, and it is what a careful reader wants to argue with. A causal estimate presented without its assumption is a number with its reasoning removed.
For a clean introduction to the distinction, Khan Academy’s Correlation and causality walks through the basic structures without the jargon.
The useful upgrade to the slogan is short: correlation is evidence about causation whose strength depends entirely on what else could explain it. Your job is to list those alternatives and knock them down one at a time. That is harder than saying the sentence, and it is the only version of the idea that ever changes a decision.