Correlation

Correlation is a statistical relationship between two variables in which variation in one is associated with variation in the other. It is measured by correlation coefficients — Pearson's r for linear relationships, Spearman's rho for monotonic relationships, Kendall's tau for ordinal associations — each quantifying the strength and direction of the relationship on a scale from -1 to +1.

Correlation is not causation. Two variables may be correlated because one causes the other, because both are caused by a third variable (confounding), because the correlation is spurious (random noise in small samples), or because the variables are connected by a complex feedback loop in which each partially causes the other. The discipline of causal reasoning exists precisely because correlation alone cannot distinguish these cases.

In complex systems, correlation becomes an especially weak guide to structure. Variables may be strongly correlated at short timescales and uncorrelated at long timescales; correlations may reverse sign during phase transitions; and high-dimensional systems may exhibit correlations that are statistically significant but mechanistically meaningless. The discovery that most correlations in high-dimensional biological datasets do not replicate is one of the central findings of modern genomics — and a warning against treating correlation as evidence of mechanism.