Two things can move together without one causing the other, and confusing the two is one of the most common errors in reading statistics. The difference is simple once you see it. You can check your work with the free tools on Calc Solver.
What Correlation Means
Correlation means two variables tend to move together. When ice cream sales rise, drowning incidents also rise, so the two are strongly correlated. Correlation only describes the pattern; it never explains why the pattern exists.
What Causation Means
Causation means changing one variable directly changes the other. Turning up a heater causes room temperature to rise, because the heater produces the heat. Causation is a much stronger claim than correlation, and it needs stronger evidence.
Why Correlated Things May Not Cause Each Other
Three explanations compete whenever a correlation appears. First, one variable may cause the other. Second, the direction may run the other way. Third, a hidden third variable may cause both, as summer heat causes both ice cream sales and swimming, which explains the ice cream and drowning link. Without ruling out the third explanation, causation cannot be claimed.
How Researchers Test for Causation
The strongest test is a controlled experiment: split subjects randomly into two groups, change one variable for one group only, and compare results. Random assignment balances hidden factors, so any difference can be credited to the changed variable. Observational studies without random assignment can suggest causation but cannot prove it alone.
Common Mistakes to Avoid
First, reading a headline correlation as proof of cause. Second, ignoring a plausible third variable. Third, forgetting that even real causation can be small: a cause can be genuine yet weak, so effect size matters as much as existence.
Practice Problems to Try
For each pair, state whether the link is correlation only or plausibly causal, and name a possible third variable: umbrella sales and traffic accidents; hours studied and exam scores; shoe size and reading ability in children.