Correlation measures how two variables move together. It doesn't tell you whether one causes the other.
Why Correlation Misleads
- Confounding: a third factor drives both. Ice-cream sales and drownings both rise in summer; heat causes both.
- Reverse causation: the direction is the opposite of what you assume. People with more illness visit doctors more, not the other way round.
- Selection effects: the data only includes certain cases. Studying only successful startups hides the failures that did the same things.
- Coincidence: with enough variables, some will correlate by chance.
Measuring Correlation
- Pearson correlation measures linear relationships.
- Spearman correlation measures monotonic relationships and is robust to outliers.
Always plot the data; very different patterns can share the same correlation.
Getting Closer to Causation
- Randomised experiments (A/B tests) are the gold standard: randomisation balances confounders.
- Natural experiments: use situations where something happened to some groups but not others for reasons unrelated to the outcome.
- Difference-in-differences: compare changes over time between affected and unaffected groups.
- Regression with controls, with care: you can only control for confounders you've measured.
In Machine Learning
Predictive models find correlations. A feature that predicts well isn't necessarily something you can change to alter the outcome. Keep prediction and intervention questions separate.