CORRELATED VARIABILITY. 51 



n I , and taking the positive root. Substi- 



tute this value in the whole equation to the 4th power for 

 /(r), and in the first derivative of the same equation for /'(r) 

 (remembering that the first derivative of /(#) is obtained by 

 multiplying each term in /(x) by the exponent of x in that 

 term and diminishing the exponent of x by 1). The correc- 

 tion 7774 should be added to the value of r used in substi- 

 f (r) 



tuting. Repeat this process as often as the correction affects 

 the fourth place of decimals, and go to r 5 if necessary. 

 The probable error of r as thus determined is 



found as follows: First calculate the relations &= '- 



fr rh 



and /? 2 = ^=. Also find 

 V 1 r 2 



7= f l e 

 2^ /0 



and ^ 2 = 7= 



from Table IV. Moreover, 



l 



2(1 -r)' 



7T V l_ r 



Then, 



A744Q 

 Prob. error of r=,?te(a 



which can be easily solved by substitution. In using the 

 foregoing formula, it must be noted that "a is the quadrant 

 in which the mean falls, so that h and k are both positive." 

 In other words, a + c > b + d and a + b > c + d. (Pearson, J 00 C .) 



Example. The eye-colors of a certain set of people (see Bio- 

 metrika, II, 2, pp. 237-240) and of their great -grandparents were 

 found to be distributed as follows. 



