You've heard the phrase: correlation does not imply causation. It's the most repeated warning in statistics — and the most ignored. A correlation tells you two variables move together; it says nothing, by itself, about whether one causes the other.
Why two things can correlate without one causing the other
- A confounder (lurking variable). Ice-cream sales correlate with drowning deaths. Neither causes the other — hot weather drives both. The confounder creates the link.
- Reverse causation. You find that people who exercise are healthier. Does exercise cause health, or do healthier people find it easier to exercise? The arrow might point the other way.
- Coincidence. With enough variables, some will correlate by pure chance. The number of films Nicolas Cage appears in has correlated with pool drownings. Nobody thinks that's real — it's a spurious correlation.
- Selection / sampling effects. How the data was collected can manufacture a correlation that doesn't exist in the wider population.
The rule of thumb: a correlation is a clue, not a conclusion. It tells you a relationship is worth investigating — it doesn't tell you which way the arrow points, or whether there's an arrow at all.
What it actually takes to show causation
- A randomized controlled experiment. Randomly assigning who gets the treatment breaks the link with confounders — this is the gold standard for causal claims.
- Ruling out confounders statistically (e.g. controlling for them in a regression) when an experiment isn't possible.
- A plausible mechanism — a reason why A would cause B.
- Consistency, dose-response, and temporal order — the cause comes before the effect, and more of it produces more effect.
How this connects to your analysis
When you run a correlation or regression and get a significant result (small p-value), you've shown the relationship is unlikely to be pure chance — but "not chance" is not the same as "causal." Significance rules out coincidence; it does not rule out confounders or reverse causation. Always ask what else could explain this? before claiming cause.
Quick example. A study finds a strong positive correlation (r = 0.7) between hours of sleep and exam scores. Tempting headline: "sleep boosts grades." But conscientious students might both sleep more and study more — conscientiousness is the confounder. Without an experiment, you can't separate them.
Measure the correlation first
Correlation Calculator →Get Pearson/Spearman r with a p-value and scatter plot — then reason carefully about cause.Related reading: Interpreting p-values · Effect size explained · Choosing a statistical test