Let there be N_i observations of the ith phenomenon, where i = 1, ..., p and N | congruent | sum N_i y^__i | congruent | 1/N_i sum_α y_(i α) y^_ | congruent | 1/N sum_i sum_α y_(i α). Then the sample correlation ratio is defined by E_(y x)^2 congruent ( sum_i N_i (y^__i - y^_)^2)/( sum_i sum_α (y_(i α) - y^_)^2). Let η_(y x) be the population correlation ratio.

correlation coefficient | regression coefficient