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Psychology · Chapter 2

Correlation Is Not Causation

A correlation just says two measurements move together. Psychologists capture that with one number — the coefficient r, from −1 to +1. Drag the dots to reshape the cloud and watch r change, then see why even a perfect r never proves that one thing causes the other.

Scatterplot

Drag any dot ↕ to reshape the cloud and watch r move. The line is the best fit; the tighter the dots hug it, the closer r is to ±1.
−1
+1
Correlation coefficientdrag a dot or pick a pattern

Correlation ≠ Causation

A strong r — even r = ±1 — never proves that X causes Y. Whenever two things move together, three rival explanations must be ruled out first:
  • ⇆Reverse causation. Maybe Y drives X, not the other way around. Happier people may exercise more, rather than exercise creating the mood.
  • 🔍A third variable. A hidden factor drives both. Ice-cream sales and drowning deaths rise together every summer — but hot weather causes both; neither causes the other.
  • 🎲Coincidence. With enough measurements, some pairs line up by pure chance and mean nothing at all.
Only a controlled experiment — randomly assigning people to conditions — can establish that X causes Y. A correlation can only hint at where to look.