Correlation ratio
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).
Correlation ratio. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Correlation_ratio&oldid=46528