Correlation vs Causation: How to Tell the Difference, With Examples

Countries that eat more chocolate win more Nobel prizes. Towns that sell more ice cream have more drownings. Children with bigger feet read better. All of these are true, and none of them means what it first seems to.

The chocolate one is real. In 2012, a cardiologist named Franz Messerli lined up each country’s chocolate consumption per person against its Nobel prizes per person and found a correlation of about 0.79, which is very strong. The paper was half a joke, but the number was genuine. So should Switzerland be proud of its cocoa?

Almost certainly not. And the reason why is one of the most useful ideas in thinking about evidence.

What a correlation is

A correlation is a pattern: when one thing is higher, the other tends to be higher (a positive correlation), or lower (a negative one). It’s measured by a number called r, which runs from −1 to +1. At zero there’s no straight-line pattern. At 1 the two move in perfect step.

A cause is something that, if you changed it, would change the other thing. If you could reach in and make people eat more chocolate, would their country’s Nobel count go up? That’s a causal claim, and it’s a much stronger one.

Correlation is easy to measure. You need two columns of data. Causation is hard, because it makes a claim about what would happen under a change you may never have made.

Four explanations to check before “A causes B”

When A and B move together, there are always several stories that fit. Run through these before accepting the obvious one.

1. A third thing causes both (a confounder)

Ice cream sales and drownings both rise in hot weather, because more people buy ice cream and more people swim. Hot weather drives both, and neither drives the other. If you hold the temperature steady in the toy above, the link fades away.

Children with bigger feet read better because older children have bigger feet and read better. Age is the confounder. In the chocolate example, wealth is the likely one: rich countries buy more chocolate, and they also spend more on universities.

This is the most common trap. When you see a surprising link, the first question is: what third thing could be pushing both up at once?

2. B causes A (reverse causation)

Sometimes the arrow runs the wrong way. People who go to the doctor more often are, on average, sicker. Does seeing a doctor make you ill? Of course not: being ill sends you to the doctor.

Or take a pattern researchers have studied for years: people who are depressed are more likely to be out of work. Does losing a job cause depression, or does depression make it harder to keep a job? The evidence suggests both happen, and untangling the two takes careful work.

3. It’s a coincidence

Look through enough pairs of numbers and some will line up by chance. There are whole websites of charts showing, for example, that the number of films Nicolas Cage appears in tracks the number of people who drown in swimming pools, and the match is surprisingly tight over a decade. Nobody believes it. But with thousands of datasets to compare, a striking chart is guaranteed. The fewer the data points, and the more comparisons made, the more coincidences you’ll find.

4. The sample was selected

Sometimes a correlation is created by who got counted. Suppose a college admits students who are either very academic or very athletic. Among its students, you’ll find the athletes are less academic, because someone who was neither wouldn’t be there at all. The link is real inside the college, and doesn’t exist in the wider world. Statisticians call this collider bias. It’s a close cousin of survivorship bias, and just as easy to fall into.

A real case: the night light

In 1999, the journal Nature published a study that sent a shiver through parents. Children who slept with a night light on in the first two years of life were far more likely to be short-sighted later: 34% of them, against 10% of children who slept in darkness. The conclusion seemed obvious: night lights damage young eyes.

A year later, two other research teams looked again, and added one thing to their questionnaires: whether the parents were short-sighted. They found that short-sighted parents were more likely to leave a light on in the baby’s room, perhaps because they wanted to see the child clearly. And short-sightedness is strongly inherited. Once the parents’ eyesight was taken into account, the night-light effect nearly vanished.

There was a confounder all along, and it was sitting in the family. The data had been telling the truth. The interpretation hadn’t.

How scientists find out what causes what

If correlation can’t show cause, what can? A few tools, in rough order of strength.

Randomised experiments. Randomly assign people to get a treatment or not. Chance spreads every other factor, known and unknown, evenly between the groups, so if the groups end up different, the treatment is the most likely reason. The first famous one was in 1747, when the naval surgeon James Lind gave twelve scurvy-stricken sailors six different remedies. The two who got oranges and lemons recovered fast enough to help nurse the others.

Natural experiments. When you can’t randomise, look for situations where something changed for one group and not a similar one, almost by accident. In the 1850s, John Snow compared cholera deaths among households served by two London water companies, one of which had moved its intake upstream of the city’s sewage, with otherwise similar customers. (He also traced the Broad Street outbreak to a single pump.)

Dose and response. If more of the cause brings more of the effect, a causal link is more plausible. Smokers who smoke more heavily get lung cancer more often.

Timing and mechanism. The cause must come before the effect, and there should be a plausible way it could work. In 1965, the epidemiologist Austin Bradford Hill proposed a checklist of such considerations, including strength, consistency, timing, dose-response and plausibility. It’s still used.

When observation fooled a generation of doctors

The strongest reason to be careful is what happens when we’re not. For decades, large observational studies found that women who took hormone replacement therapy after the menopause had far fewer heart attacks. The effect looked big, and doctors prescribed it as a heart protector.

Then in 2002, the Women’s Health Initiative randomly assigned thousands of women to hormones or a dummy pill. The trial was stopped early because the hormone group had more heart disease, not less. The women who’d chosen HRT in the earlier studies were healthier, wealthier and saw doctors more regularly. They would have had fewer heart attacks anyway. The confounder was the kind of person who takes hormones.

That’s the whole argument in one story. It isn’t that correlation is useless, or that observational studies are always wrong. It’s that without randomisation, you can’t rule out a hidden difference between the people who chose and the people who didn’t.

How to use it

When you meet a claim like “people who do X are healthier, richer or happier”, you can run a short list of questions:

• What else could explain it? Wealth, age, health, personality, effort.
• Could it run the other way? Does the outcome make people do the thing?
• Is it a one-off coincidence? Has it been found more than once, in different groups?
• Who’s missing from the data? Was the sample selected in a way that creates the link?
• Was there an experiment? If not, hold the conclusion loosely.

None of this means you should dismiss every correlation. Smoking and lung cancer began as a correlation, and it was a causal one. The point is to know what a correlation can and can’t show, and to ask for more before acting on it.

If you’d like to test your own instincts, the free statistics test has several of these traps, and the thinking traps test covers the neighbouring mistakes people make about cause and effect.