Primary
Correlation ○｜Definition｜1st｜20251119205401-00-⌔
Correlation
In statistics, correlation is a type of statistical relationship between two random variables or bivariate data. It usually refers to the extent to which a pair of quantities are linearly related. More generally, an arbitrary relationship between variables is called an association, meaning the degree to which the variability in one can be accounted for by the other.12
The presence of a correlation is not sufficient to infer the presence of a causal relationship, and this is often stated as “correlation does not imply causation”. Furthermore, the concept of correlation is not the same as dependence: if two variables are independent, then they are uncorrelated, but the opposite is not necessarily true – even if two variables are uncorrelated, they might be dependent on each other.
Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling.
There are several correlation coefficients that may be used to measure correlation, often denoted or . The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which in turn may be present even when one variable is a nonlinear function of the other). Other correlation coefficients, such as Spearman’s rank correlation coefficient, have been developed to be more robust than Pearson’s and to detect less structured relationships between variables.345
The concept has been generalized to other forms of association between two variables, such as mutual information and distance covariance.
Printed 2026-06-28.
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Link to original Footnotes
Upton, G., Cook, I. (2006) Oxford Dictionary of Statistics, 2nd Edition, OUP. ISBN 978-0-19-954145-4 ↩
“Glossary of Statistical Terms”. SticiGui. 2019-09-02. Retrieved 2025-12-18. ↩
Croxton, Frederick Emory; Cowden, Dudley Johnstone; Klein, Sidney (1968) Applied General Statistics, Pitman. ISBN 9780273403159 (page 625) ↩
Dietrich, Cornelius Frank (1991) Uncertainty, Calibration and Probability: The Statistics of Scientific and Industrial Measurement 2nd Edition, A. Higler. ISBN 9780750300605 (Page 331) ↩
Aitken, Alexander Craig (1957) Statistical Mathematics 8th Edition. Oliver & Boyd. ISBN 9780050013007 (Page 95) ↩
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