Correlation does not imply causation

An observed association between variables, by itself, does not establish that changes in one variable cause changes in the other.

Confounding: A distortion of an association caused by a third variable related to both variables being studied. A common cause can make two variables move together without either causing the other.
Correlation: A statistical measure of the direction and strength of association between variables. Correlation quantifies association, but does not identify its causal source.
Bradford Hill criteria: A set of considerations proposed for assessing whether an observed association may be causal. The criteria organize evidence beyond the presence of an association.
Stork and baby births correlation: A reported correlation between stork populations and human birth rates in parts of Europe. It illustrates how shared geographic and social factors can explain a striking association.
Reverse causation: A mistaken causal interpretation in which the proposed effect actually influences the proposed cause. An association may run in the opposite causal direction from the one assumed.
Causality: A relationship in which changes to one event, variable, or condition bring about changes in another. Causation is the stronger claim that an association alone cannot establish.
Instrumental variable: A variable used to estimate a causal effect when treatment assignment is confounded, under specific assumptions. Instrumental-variable analysis can address confounding when randomization is unavailable.
Ice cream and drowning correlation: An association between ice cream sales and drownings that can arise because both increase in warm weather. Temperature is a common cause of the two seasonal trends.
Directed acyclic graph: A directed graph with no directed cycles, used to represent relationships among variables. Its arrows make competing causal explanations for one association explicit.
Counterfactual: A description of what would have happened under an alternative condition that did not occur. Causal effects compare an outcome with the unobserved alternative for the same unit.

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