Correlation vs causation, explained with charts

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Two lines rise together on a chart and the conclusion seems obvious: one must be causing the other. Often it is not. Correlation means two things move together. Causation means one actually makes the other happen. Mixing them up is one of the most common mistakes in reading data, and charts make it particularly tempting.

What correlation means

Positive correlation: when one goes up, the other tends to go up. On a scatter plot, the dots slope upwards.
Negative correlation: when one goes up, the other tends to go down. The dots slope downwards.
No correlation: the dots form a shapeless cloud.
Strength: a correlation coefficient runs from minus 1 to plus 1. Values near 0 mean little linear relationship, and values near plus or minus 1 mean a strong one.

A correlation coefficient only measures a straight-line relationship. Two things can be strongly related in a curved way and still show a coefficient near zero. Always look at the scatter plot, not just the number.

Why correlation is not causation

There are several ways two things can move together without one causing the other.

1. A third factor drives both

This is called a confounder.

Ice cream sales and drowning incidents rise and fall together. Ice cream does not cause drowning. Hot weather increases both.
Fires attended by more firefighters tend to cause more damage. The firefighters are not causing it: bigger fires bring more crews and do more damage.
How to spot it: ask what else changes along with both variables. Season, population, age and income are common hidden drivers.

2. The causation runs the other way

This is reverse causation.

People who use walking sticks tend to have worse mobility. The stick is not making their mobility worse. Poor mobility leads people to use one.
How to spot it: ask whether B could just as plausibly cause A.

3. Coincidence

With enough datasets, some will move together by pure chance. Collections of so-called spurious correlations online pair things like cheese consumption with unrelated causes of death, and the lines match closely.
Time series are especially prone to this. Anything that has steadily grown over twenty years, such as population, prices or internet use, will correlate with anything else that has grown over the same period.
How to spot it: ask if there is a plausible mechanism. Check whether the relationship holds in other places or periods.

4. Selection effects

If the data only includes certain people or cases, a pattern can appear that does not exist in the wider population.
For example, studying only successful companies can make risky strategies look like a recipe for success, because the companies that tried them and failed are not in the data.

How charts make it worse

Two lines on one chart, especially with dual axes scaled to overlap, look as if they are linked.
Trend lines on scatter plots suggest a rule even when the dots are scattered widely.
Headlines on charts often state a causal conclusion that the data cannot support.

How causation is actually established

Randomised controlled trials assign people at random to groups. Random assignment balances out hidden factors, so differences in outcome can be attributed to the treatment.
Natural experiments use events that split people into groups almost at random, such as a policy that changed at a border or a cut-off date.
Careful observational studies control for known confounders and test whether the pattern holds across different groups. They can strengthen a case, but cannot rule out every hidden factor.
Evidence from several angles, such as a plausible mechanism, a dose-response pattern and consistent results across studies, makes a causal claim more convincing.

A checklist for any correlation chart

Could a third factor drive both?
Could the causation run the other way?
Is this two trends that both just grow over time?
Who is included in the data, and who is missing?
Is there a plausible mechanism?
Does the headline claim more than the data shows?

What is the most convincing spurious correlation you have come across? Share it in the comments.