310 Prohahle Error of a Correlation Coe^cient 
(5) To sum up: — If i/ = 4> '0 be the equation, it must satisfy the following 
requirements. If J2 = 1, 1 is the only value of x which gives the value of y other 
than zero. If n = 2, ±1 are the only values of x to do so. If R = 0 the equation 
H-t 
probably reduces to ?/ = y„(l - x") . 
Conclusions. 
It has been shown that when there is no correlation between two normally 
distributed variables y = y^{l — x") 2 gives fairly closely the distribution of r found 
from samples of n. 
Next, the general problem has been stated and three distributions of r have 
been given which show the sort of vai'iation which occurs. I hope they may serve 
as illustrations for the successful solver of the problem. 
