Correlation Ratio

Let there be  observations of the th phenomenon, where , ...,  and

			(1)
			(2)
			(3)

Then the sample correlation ratio is defined by

(4)

Let  be the population correlation ratio. If  for , then

(5)

where

			(6)
			(7)
			(8)

and  is the confluent hypergeometric limit function. If , then

(9)

(Kenney and Keeping 1951, pp. 323-324).

REFERENCES:

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, 1951.