Concept
Correlation
Overview
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.
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
ρ
{\displaystyle \rho }
or
r
{\displaystyle r}
. 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.
The concept has been generalized to other forms of association between two variables, such as mutual information and distance covariance.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Correlation is discussed.
Correlation is an important subject; for with species, and in a lesser degree with domestic races, we continually find that certain parts have been greatly modified to serve some useful purpose; but we almost invariably find that other parts have likewise been more or less modified, without our being able to discover any advantage in the change. No doubt great caution is necessary with respect to this latter point…
Charles Darwin, The Variation of Animals and Plants under Domestication
names the idea; states what it is; opens on it
Not much attention is paid in this year to reading and writing; but it is obvious that if this were regarded as desirable, the same principle would apply. It is the community and continuity of the subject-matter that organizes, that correlates; correlation is not through devices of instruction which the teacher employs in tying together things in themselves disconnected.
John Dewey, The school and society
states what it is; names the idea; opens on it
All impressions from moment to moment made on our organs of sense, stand in direct correlation with physical forces existing externally. The modes of consciousness called pressure, motion, sound, light, heat, are effects produced in us by agencies which, as otherwise expended, crush or fracture pieces of matter, generate vibrations in surrounding…
Herbert Spencer, First Principles
a chapter is titled for it; names the idea; opens on it
Premising that by rational correlation is not meant one in which we can trace, or think we can trace, a design, but one of which the negation is inconceivable (and this is the species of correlation which Cuvier's principle implies); then we hold that our knowledge of the correlation is of a more certain kind than where it is simply inductive. We think that Professor Huxley, in his anxiety to avoid the error of…
Herbert Spencer, Essays
names the idea; states what it is
Hilaire’s great work on this subject. Breeders believe that long limbs are almost always accompanied by an elongated head. Some instances of correlation are quite whimsical; thus cats with blue eyes are invariably deaf; colour and constitutional peculiarities go together, of which many remarkable cases could be given amongst animals and plants. From the facts collected by Heusinger, it appears that white sheep and…
Charles Darwin, On the Origin of Species By Means of Natural Selection
names the idea; states what it is
Philosophers who discussed Correlation
Related ideas
Opposing perspectives
Place in the tradition
Part of Type physicalism.