Correlation vs. Causation
Correlation means two variables move together in a measurable pattern — when one rises, the other tends to rise (or fall). Causation is a stronger claim: changing one variable actually produces a change in the other. Every causation is a correlation, but plenty of correlations are not causation.
This is the lesson that keeps you from being fooled by statistics. Ice cream sales and drownings rise together every summer, and buying ice cream still does not cause anyone to drown. Learning to ask what else could explain this pattern is the whole skill.
Why correlation isn't proof of cause
When two variables correlate, there are three possible stories: the first causes the second, the second causes the first, or something else drives both. A scatterplot cannot tell you which story is true — it only shows that the pattern exists.
Direction can even run backward from what you assume. Cities with more firefighters at a fire have more fire damage — not because firefighters cause damage, but because bigger fires draw both more firefighters and more damage.
The scatterplot below shows a real positive correlation: ice cream sales and drownings climb together all summer. The upward pattern is genuine — yet no one believes buying ice cream causes drownings.
Lurking variables
A lurking variable is a hidden third variable that drives both measured variables at once, creating a correlation between them. In the ice cream example, the lurking variable is hot weather: heat pushes people to buy ice cream and to swim, and more swimming means more drownings.
The classic school example: children with larger shoe sizes tend to read at a higher level. The lurking variable is age — older children have both bigger feet and stronger reading skills. Whenever a correlation seems absurd as cause and effect, hunt for the variable lurking behind both.
What actually establishes causation
Observing existing data can never fully rule out lurking variables. To establish cause, researchers run a controlled experiment: randomly assign subjects into two groups, change only the variable being tested in one group, and compare the results. Random assignment spreads the lurking variables evenly across both groups, so any remaining difference must come from the treatment.
That is why headlines that say linked to or associated with are making a correlation claim, not a causation claim. Without a randomized experiment, be skeptical of any leap from moves together to causes.
Worked examples
Example 1: find the lurking variable
Monthly data shows a strong positive correlation between sunscreen sales and air-conditioner use. Does sunscreen cause people to run their air conditioning?
Answer: No — hot weather is a lurking variable that causes both.
Example 2: correlation stated, causation claimed
An ad says: Students who use our flashcard app have GPAs points higher than students who don't. Therefore the app raises GPA. What's wrong with this claim?
Answer: The ad proves correlation only; motivation (or another lurking variable) could explain the GPA gap.
Example 3: design a real test
How could researchers actually test whether the flashcard app causes higher grades?
Answer: Run a randomized controlled experiment.
Try one yourself
Common questions
Can two variables be correlated by pure coincidence?
Yes. With enough data sets, some will line up by chance — there are famous spurious correlations like cheese consumption tracking engineering doctorates. A correlation with no plausible mechanism and no lurking variable may just be noise.
Does a stronger correlation make causation more likely?
No. Strength measures how tightly the variables move together, not why. Shoe size and reading level correlate strongly across children, and the cause is still age, not feet. Strong correlation with a lurking variable is still not causation.
If correlation never proves causation, why measure it at all?
Correlation is still useful for prediction — knowing one variable helps you estimate the other, whatever the reason. And a real correlation is often the first clue that sends scientists looking for a causal mechanism to test properly.
What words signal correlation rather than causation?
Linked to, associated with, related to, and tends to all describe correlation. Causes, produces, raises, and reduces are causal claims — those need experimental evidence to back them up.
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