Correlation ratio

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A characteristic of dependence between random variables. The correlation ratio of a random variable relative to a random variable is the expression

where is the variance of , is the conditional variance of given , which characterizes the spread of about its conditional mathematical expectation for a given value of . Invariably, . The equality corresponds to non-correlated random variables; if and only if there is an exact functional relationship between and ; if is linearly dependent on , the correlation ratio coincides with the squared correlation coefficient. The correlation ratio is non-symmetric in and , and so, together with , one considers (the correlation ratio of relative to , defined analogously). There is no simple relationship between and . See also Correlation (in statistics).

How to Cite This Entry:
Correlation ratio. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article