Numbers · 3 min read
Correlation vs Causation: How to Tell the Difference, With Examples
Two things rising together doesn't mean one causes the other. The four other explanations to check, real examples, and how researchers actually establish cause.
By the Cognosc team ·
Towns that sell more ice cream have more drownings. Countries that eat more chocolate win more Nobel prizes. Children with bigger feet read better. All true, and none of them means what it first seems to.
Try it
Ice cream and swimming
Each dot is a summer day. Then hold the temperature steady and look again.
Across all days, more ice cream goes with more swimmers: r = 0.86, a strong correlation. Neither causes the other.
What a correlation is
A correlation means two things tend to move together: when one is higher, the other tends to be higher (or lower). It’s a pattern in data. It says nothing on its own about why the pattern exists.
A cause is something that, if you changed it, would change the other thing. Correlation is easy to measure. Causation is much harder to establish.
Four explanations to check before “A causes B”
When A and B move together, there are always several possibilities.
1. Something else causes both (a confounder)
Ice cream and drownings both rise on hot days, because more people buy ice cream and more people swim. Neither causes the other; the weather causes both.
Children with bigger feet read better because older children have bigger feet and read better. Age is the confounder.
This is the most common trap. When you see a surprising link, ask: what third thing could push both up at once?
2. B causes A (reverse causation)
People who use a lot of sunscreen get more skin cancer. Does sunscreen cause cancer? More likely, people who spend lots of time in strong sun use more sunscreen, and also get more sun damage. Or consider: hospitals are full of sick people, but hospitals don’t make people sick. The arrow can point the other way.
3. It’s a coincidence
Look at enough pairs of numbers and some will line up by chance. There are websites full of charts showing, for example, that the number of films an actor appears in tracks drownings in swimming pools for a decade. With thousands of possible pairs, some will match beautifully by luck alone.
4. The sample was selected
Sometimes the correlation is created by who got counted. If a college admits students who are either very academic or very athletic, it may find that, among its students, the athletic ones are less academic, even if the two are unrelated in the population at large.
How researchers establish cause
Randomised experiments. Randomly assign people to get a treatment or not. Randomness spreads every other factor, known and unknown, evenly between the groups, so if the groups end up different, the treatment is the likeliest reason. This is why drug trials are randomised.
Natural experiments. When an experiment is impossible or unethical, researchers look for situations where something changed for one group and not a similar one, almost by chance, like a policy that applied in one town but not the next.
Building the case. For smoking and lung cancer, experiments on people were impossible. The case was built from strong, consistent correlations, a dose-response pattern (more smoking, more cancer), the right timing, a plausible mechanism, and animal studies. Together they left no reasonable alternative.
Reading headlines
When a headline says “X linked to Y”, ask:
- Was this an experiment or an observation?
- What else differs between the people who do X and those who don’t?
- Could Y be causing X instead?
- How big is the effect, and how many things did they test before finding it?
“Linked to” and “associated with” usually mean a correlation. “Causes” should mean someone has done the harder work.
Test yourself
The free statistics test opens with the ice cream question, and the thinking traps test covers the related trap of assuming that what came first caused what came next.