Correlation Ratio
Let there be N_i observations of the ith phenomenon, where i=1, ..., p and
N = sumN_i
(1)
y^__i = [画像:1/(N_i)sum_(alpha)y_(ialpha)]
(2)
y^_ = [画像:1/Nsum_(i)sum_(alpha)y_(ialpha).]
(3)
Then the sample correlation ratio is defined by
Let eta_(yx) be the population correlation ratio. If N_i=N_j for i!=j, then
where
and _1F_1(a,b;z) is the confluent hypergeometric limit function. If lambda=0, then
| f(E^2)=beta(a,b) |
(9)
|
(Kenney and Keeping 1951, pp. 323-324).
See also
Correlation Coefficient, Regression CoefficientExplore with Wolfram|Alpha
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References
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, 1951.Referenced on Wolfram|Alpha
Correlation RatioCite this as:
Weisstein, Eric W. "Correlation Ratio." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CorrelationRatio.html