Ixviii 



Tables for Statisticians and Biometricians [VIII IX 



Hence, interpolating for d/N= '130,8562 we find r= '0379, the correct value. 

 We accordingly conclude that the correct value in a finial panel will usually be 

 obtained by the central difference formula (7 bis), although this value fails to be 

 given exactly by the forward difference formula (e). At the same time we note 

 that a unit error in the fourth decimal place of r will rarely be of any importance 

 in statistical inquiries. 



Illustration (viii). Intelligence and General Nutrition, (Girls.) 



Intelligence 



In this case (1 - a h ) = '329,915, |(1 - a k ) = -447,863, 



leading by aid of Table XXIX of Part I to 



h = '44015, k = '13107, 



while 



Clearly 



Ql 



^-= '155,5556. 



5o5 



= 4015, < = 



= '3107, -^ = -6893. 



Between the values h = *4 and *5 and k = 1 and "2, our value for d/N occurs 

 in the r tables for values '00, '05, 10 and 15 but the h and k values are nearer 

 to '4 and '1 than '5 and '2. This excludes r = 15, as clearly d/N='155... lies 

 more than half-way from "4 to '5 and "1 to '2, i.e. the diagonal right top to left 

 bottom corner is from 163... to '166 Accordingly we start with interpolating 

 into the r = '05 table. We have 



djN-=z 6 ,x = "6893 x '5985) (-165,835) + f'6893 x -4015) (148,979) 

 4125,4605 1(173,234] ('2767,5395 ] (156,008] 



+ -3107 x -5985) (-159,512) + ('3107 x -4015) (-136,717) 

 1859,5395 ] (159,456] (1247,4605 ] (143,667] ' 



The upper numbers in the right-facing curled brackets give d/N= -155,0218. 

 This is not large enough, and we accordingly choose the r = 10 table for our 

 second interpolation and this gives d/N= 162,2162. Finally, interpolating linearly 

 for d/N = -155,5556, we have 



The true value of r is '0542. 



71944 



