Correlation vs Causation
핵심 개념
Correlation measures the strength and direction of a linear relationship between two variables, expressed as the correlation coefficient r. Causation means one variable directly produces a change in another — a far stronger claim that correlation alone can never establish. Lecture notes.md
The Correlation Coefficient *r*
| Value of *r* | Meaning |
|---|---|
| +1 | Perfect positive linear relationship |
| 0 | No linear relationship (nonlinear patterns may still exist) |
| −1 | Perfect negative linear relationship |
Key nuance: r = 0 rules out a *linear* relationship but not a nonlinear one. Lecture notes.md
Why Correlation ≠ Causation
Two variables can move together for reasons that have nothing to do with one causing the other:
- Confounding variable (lurking variable): A hidden third variable drives both. Classic example: ice-cream sales and drowning rates both rise in summer — the confounder is *warm weather*, not ice cream. Lecture notes.md
- Reverse causation: A causes B, or B causes A — correlation alone cannot tell you the direction.
- Coincidence: Random patterns in data can produce spurious correlations with no underlying mechanism.
Relationship to Other Topics
Understanding correlation ties closely to Spread (Variance & Standard Deviation) — variability in both variables affects the strength of r. It also complements Normal Distribution, where many correlation-based methods assume normality. For context on *describing* data before testing relationships, see Central Tendency.
큐 질문 (능동적 회상)
Use these questions for active recall. Check answers in Review & Spaced Repetition.
- 1.**What is the range of the correlation coefficient *r*, and what does each extreme mean?**
- 2.If r = 0, does that guarantee no relationship between two variables? Why or why not?
- 3.Describe the ice-cream / drowning example. What is the confounding variable, and why does it produce a misleading correlation?
- 4.What is reverse causation? Give an example of how it could fool a researcher.
- 5.List two reasons why a strong correlation between variables A and B does NOT prove A causes B.
요약
A correlation tells you *how closely* two things move together in a straight line (−1 to +1), but it can never tell you *why* — hidden confounders or reverse causation are always possible explanations. Lecture notes.md