Ixvi Tables for Statisticians and Biometricians [VIII IX 



corresponding to our h and k lies in the triangle of which the z's are 150... , '139... 

 and '133..., all greater than d/N='130 It is safest, however, to start inter- 

 polating from the mid-table r = "05. 



We have = '5469, < = '4531, % = '3312, -f = -6688 and the scheme : 



h=0'Q h = 0-l 



k = 0-6 143,775 Oo,o) -132,829 (* 1|0 ) 



We can then arrange our work thus, using formula (a): 



d/N= -6688 x -4531) (-143,775) + '6688 x -5469) (-132,829 

 3030,3228 j (137,127] -3657,6672 j (126,204 



+ -3312 x -4531) (-127,212) + '3312 x -5469) (117,555 

 1500,6672 j 1-120,984] -1811,3328 j (111,845 



The lower number in the single curled brackets facing left is the product of the 

 6, <, % ^ pairs standing above them. Taking the upper numbers in the double 

 curled brackets and multiplying them continuously on the machine by the lower 

 numbers in the single curled brackets facing left, we find 



d/^= 132,5363. 



This value is too high; we must therefore reduce the correlation by taking the table 

 for r = '00. The corresponding values for the z's are those in the lower line of the 

 double curled brackets, and repeating the continuous multiplication process on 

 the machine we have d/N= 126,0388. Interpolating linearly for dfN= -130,8562 

 we find 



r .. 00 + -05x^1 = 0371. 



This result would be close enough for the great majority of practical investigations, 

 but the true value of r is -0379. It is of interest to determine how the above result 

 may be brought into accord with the actual value of r. Our d/N is in a finial panel 

 of the table; we cannot get the central difference for z 0tQ and z Q>1 as we are on the 

 border of the table h = O'O. Accordingly, let us try the forward difference formula 

 (e): see p. liii. 



Here 6= '5469 and % = -3312 as before, and we have for the two tables r = -00 



and r = '05 : 



_ (137,1271 (--010,923) (--016,145 



Ze ' x ~ (143,775) 4 1- -010,946] 4 (--016,563 



- 1239 0019 I' 000 ' 108 ! _ -H07 5328 I' 001 ' 091 ! 

 J 1-000,043] J7 ' 5 ' 8 1-001,0581 



,.i 811 q 228 (-001,286 

 l1 ' 3228 1-001,289 



= "125.905, from upper line, 

 = -132,414, from lower line. 



