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).
