Algebra
Data and statistics
Correlation vs causation
20 practice questions
2 video lessons
Theory + worked examples
Theory
Correlation means two variables move together; causation means one actually causes the other.
Correlation does NOT prove causation. A hidden lurking variable may cause both.
Correlation is not causation.
Why they differ.
The key caution:
\[\text{correlation}\ \neq\ \text{causation}\]
Only a controlled experiment can establish causation.
How to interpret a correlation
- Note the correlation and its strength.
- Ask whether a lurking variable could explain it.
- Do not assume one causes the other.
- Look for an experiment to test causation.
Example 1 — A spurious link
Ice cream sales and drownings both rise in summer. Does ice cream cause drownings?
Solution
No — hot weather (a lurking variable) drives both.
Example 2 — Lurking variable
What is a lurking variable?
Solution
A hidden variable that influences both measured variables.
Example 3 — Proving causation
What kind of study can establish causation?
Solution
A controlled, randomized experiment.
Example 4 — Interpret a correlation
A study finds coffee drinkers live longer. Can you conclude coffee causes long life?
Solution
No — it is correlation; other factors may explain it.
Common pitfalls
Never conclude causation from correlation alone.
Watch for lurking variables.
Only experiments establish cause and effect.
Frequently asked questions
What is the difference between correlation and causation?
Correlation is moving together; causation is one causing the other.
Does correlation prove causation?
No.
What is a lurking variable?
A hidden factor that influences both variables.
What establishes causation?
A controlled, randomized experiment.
← Previous subtopic
Correlation coefficient
Next subtopic →
Interpreting slope and intercept of a linear model
More in Data and statistics