Interactive · Statistics

The correlation number never tells you which story is true

Pick a real-world pair of variables that move together. The correlation stays exactly the same number the whole time — what changes is the causal diagram underneath it. That's the entire point: a strong correlation is compatible with several completely different realities, and the number alone can't choose between them.

1. Pick a pair of correlated variables

r = 0.82
A strong, real, measured correlation. This number does not change below — only the explanation does.

2. Now pick which explanation you think is true

3. Why the number can't settle it

Correlation is symmetric, causation isn't

The correlation between X and Y is mathematically identical to the correlation between Y and X — the formula doesn't know which one happened first, or whether either caused the other. Direction is not contained in the number at all.

A confounder creates correlation without any direct link

If Z drives both X and Y independently, X and Y move together perfectly — with zero causal arrow between them. Ice cream sales and drowning deaths both rise with heat; ice cream doesn't cause drownings.

Big datasets manufacture coincidental correlations

Test enough unrelated variable pairs and some will correlate strongly by chance alone. The larger and more varied the dataset, the more "significant-looking" nonsense correlations you should expect to find.

What actually distinguishes them: intervention

The real test is: if you forcibly change X (not just observe it), does Y change? That's what experiments, randomized trials, and controlled interventions are for — they're the tool that correlation alone can never substitute for.