AP® Statistics · Unit 5 · Topic 5.2
Correlation, Causation, and Lurking Variables
A strong correlation between two variables never proves one causes the other, because a hidden third variable — a lurking variable — can drive both at once. Only a well-designed experiment with random assignment can support a causal claim.
Correlation measures how two variables move together, nothing more. When you see a strong correlation in observational data — data collected by just watching and recording, with no one controlling anything — your first move should be suspicion, not excitement. The world is full of lurking variables: unmeasured factors sitting backstage, quietly pulling the strings on both variables you did measure. A lurking variable manufactures a correlation by causing both things at once, so they rise and fall together even though neither one touches the other.
Shoe size and reading ability among elementary schoolers is the classic case. Bigger feet don't make you read better. Age does both jobs: older kids have grown bigger feet and spent more years learning to read. Erase age from the picture and the correlation between feet and reading would likely vanish. This is why a correlation of 0.95 — even one that looks almost perfect — still proves nothing about cause. A strong number tells you the pattern is real and consistent; it tells you nothing about why the pattern exists. Any observational correlation, no matter how tight, can always be explained away by some lurking variable you didn't measure.
For a correlation to support a causal claim, the study has to rule out lurking variables directly, and the only reliable way to do that is random assignment. When subjects are randomly assigned to groups, any lurking variables get spread out roughly evenly across those groups by chance, so they can no longer explain a difference in outcomes. That is the bridge from this topic into experimental design: correlation describes, random assignment lets you believe in cause.
Key terms
- Lurking variable
- An unmeasured variable that influences both variables being studied, creating a correlation without any direct causal link.
- Correlation
- A numerical measure of how strongly two quantitative variables move together, ranging from -1 to 1.
- Observational data
- Data collected by recording what naturally happens, without the researcher controlling or assigning any variable.
- Random assignment
- Randomly placing subjects into groups so lurking variables are spread evenly across groups, allowing causal conclusions.
- Confounding
- When the effects of two variables on an outcome cannot be separated because they are entangled in the data.
Watch it explained
- How it worksHow does a lurking variable manufacture a correlation between two unrelated things?
- Common mistakeWhy isn't a correlation of 0.95 enough to justify a causal headline?
- Going furtherWhat has to be true about a study before a correlation can support a causal claim?
- Ties togetherHow does random assignment rescue the causal claim that correlation alone cannot make?
Check yourself
End of topic.