Correlation and Causation

Correlation means that two measured variables vary together, positively or negatively, in a dataset. Causal inference goes further by assessing whether changing an exposure would change the probability or distribution of an outcome, compared with what would otherwise have occurred.

What correlation establishes

A correlation coefficient describes the direction and strength of a statistical relationship; for Pearson's coefficient, values range from -1 to +1. Correlation alone neither identifies the mechanism nor proves that one variable produces the other.

• An observed correlation may arise from chance, bias or confounding, where a third factor influences both variables.
• Reverse causation is possible: the outcome may influence the apparent exposure rather than the exposure causing the outcome.
• A coefficient near zero rules out neither a non-linear relationship nor causation operating only within particular population groups.

How causal inference is made

Causal inference combines an appropriate study design, valid measurement and analysis with substantive knowledge. Temporality, meaning that exposure precedes outcome, is indispensable.

• Random allocation, where ethical and feasible, strengthens inference by balancing known and unknown confounders on average.
• Observational studies require careful comparison groups and methods to address confounding, selection bias and information bias.
• Consistency across studies, strength of association, dose-response pattern, biological plausibility and experimental evidence can support causality, but no single consideration automatically proves it.
• Researchers must assess whether alternative explanations, including chance and reverse causation, adequately account for the association.

Why the distinction matters in public health

Treating association as causation can produce ineffective or harmful interventions. Epidemiological evidence should therefore distinguish prediction, which may rely on correlation, from causal claims used to justify prevention, treatment or public policy.