Correlation vs. Causation

Definition

Correlation means two quantities move together; causation means that changing one would change the other. Observing a correlation cannot by itself tell you which causes which, or whether a third factor drives both, so causal claims need design or assumptions beyond the data.

In plain terms

A correlation coefficient runs from −1 to +1 and measures how closely two series follow a straight-line pattern. It is a fact about the data. Causation is a claim about what would happen if we intervened. Between the two lie at least four possibilities: A causes B; B causes A (items with more reviews sell more, or items that sell more collect more reviews); a third factor causes both (Confounding); or it is coincidence, which is common in small samples and in collections of many series.

Routes towards causal knowledge: randomised experiments, natural experiments where something changed for reasons unrelated to the outcome, and explicit causal models whose assumptions can be examined and challenged.

Example

Twelve months of synthetic data: average temperature, ice-cream sales (hundreds of cones) and sunburn cases.

Ice-cream sales and sunburn are correlated at 0.94. Once temperature is accounted for, the remaining correlation is about zero: sun drives both, and neither causes the other. Banning ice cream would not prevent sunburn.

Common misunderstandings

• “No correlation means no causal link.” A relationship can be curved, hidden by another factor, or present only in some groups.
• “Correlation is useless.” It is valuable for prediction and for finding what to investigate; it just does not establish cause.
• “A very strong correlation settles it.” Strength measures how tightly the data follow a pattern, not why.