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Psychology · Chapter 2

Correlation Is Not Causation

A correlation just says two measurements move together. Psychologists sum it up with one number, the coefficient r. It runs 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. On a keyboard, tab to a dot and use the arrow keys.
−1
+1
Correlation coefficientdrag a dot or pick a pattern

Correlation is not causation

A strong r, even r = ±1, never proves that X causes Y. When two things move together, three other explanations must be ruled out first:
  • ⇆Reverse causation. Maybe Y drives X, not the other way around. Happier people may exercise more, instead of exercise creating the good 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. If you measure enough things, some pairs will line up by pure chance and mean nothing at all.
Only a controlled experiment, with people randomly assigned to groups, can show that X causes Y. A correlation can only hint at where to look.