Why does a strong correlation between two things not prove that one causes the other?
A correlation only says X and Y move together; it leaves the causal direction — and whether a hidden third factor drives both — completely open.
A real study once found a striking correlation (r = 0.79, highly significant) between a country's chocolate consumption and its number of Nobel laureates. Eating chocolate obviously doesn't win Nobel Prizes — so what's going on? Behind any correlation X ~ Y, several different causal stories are possible:
- X → Y — X really causes Y.
- Y → X — the arrow runs the other way.
- X ↔ Y — they cause each other (feedback).
- Z → X and Z → Y — a confounder Z drives both (here: national wealth raises both chocolate-buying and research funding).
- Coincidence — pure chance, especially when you mine many variables.
So a high correlation coefficient, even with a tiny p-value, establishes only association, never direction or mechanism. A small p-value just means the pattern is unlikely to be pure chance — it says nothing about why the pattern exists.
Tip: Ask three questions of any correlation: Could it run backwards? Could a third factor cause both? Could it just be coincidence among many comparisons?