Correlation vs causation: why moving together is not proof

Correlation says two things move together. Causation says one changes the other. A hidden third factor can make correlation look causal.

Correlation is a pattern. Causation is a claim about mechanism. To move from one to the other, you need timing, a fair comparison, and alternative explanations ruled out.

By the Math Says Yes editorial team

Human-reviewed under our source and correction standards.

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THE TRAP

Seeing two lines move together and instantly choosing the neatest cause-and-effect story.

Two gears that never touch, both turned by a third gear below them through belts.

The short difference

means two variables tend to change together. Causation means changing one variable would change the other, all else held equal. The gap between those statements is large. A correlation can be a clue, but it does not identify direction, rule out shared causes, or prove what would happen under an intervention. Causation needs a comparison that makes the alternative explanations less plausible.

Quick Comparison

Correlation

Causation

What it answers

Do two variables tend to move together?

Would changing one variable change the other?

Common mistake

Reading a pattern as proof of a mechanism.

Claiming cause without timing, mechanism, or a fair comparison.

Use when

You need a clue, warning sign, or prediction.

You need an explanation or intervention decision.

What the Numbers Show

ice cream sales

drownings

over the year →

Illustrative seasonal pattern. The two lines move together because both follow summer heat, not because ice cream causes drowning.

Worked example

Ice cream sales and drownings can rise together across warm months. The simple is real in the stylized data: both lines climb in summer and fall in winter. But the causal story is not that ice cream causes drowning. Warm weather increases swimming and also increases ice cream buying. Temperature is a , a third factor that pushes both variables in the same direction.

What people get wrong

Most readers stop at the chart. A strong-looking or pair of matching trend lines can still be explained in several ways. Reverse causality is possible when the supposed effect actually influences the supposed cause. Confounding is possible when a moves both. Selection can also manufacture a relationship. The chart starts the investigation; it does not finish it.

When it applies

Use the warning whenever a headline says one thing raises, lowers, causes, prevents, or predicts another. Ask whether the cause came before the effect, whether comparable groups were used, and what third variables could move both measures. Randomized experiments answer these questions most cleanly. When experiments are not possible, careful causal inference tries to approximate a fair comparison.

Source note

Hernan and Robins provide the causal-inference framing: causal claims depend on comparisons that approximate what would have happened under alternative actions. Tyler Vigen's editorial catalogue of spurious correlations illustrates how visually persuasive non-causal relationships can look. The page uses ice cream and drowning as a teaching example, not as a live safety estimate.

Try It

Hidden confounder

Slide the temperature and watch both rise together.

Hidden common cause

20°C

temperature

360

ice cream sales

drownings

Ice cream ≠ cause of drownings

Temperature

20°C

The fork is the causal claim: temperature pushes both outcomes upward independently.

At 20°C, ice cream sales sit at 360 and drownings at 5 — both pushed up by the heat, not by each other. Slide toward cooler days and the two fall together; the ice cream never touched the water.