Ixxii 



Tables/or Statisticians and Biometridans [VIII IX 



The answer is correct to three figures. To get a better approximation we must 

 proceed to second differences. 



Let us try forward differences in this case using formula (e). We have 



[081,519] 



[-086,679] 



- -1075,5288 



544 '" 88 



- -006,662) 

 000,051) 



~f- '010,199 

 010,692 





-' 



000,961) 

 000,991) 



000,758) 



(-000,756) 

 = '075,709, for r = '35, 

 = -080,745, for r = -40. 

 Hence, by linear interpolation for d/N= '077,241, we have 



<- = -35 + -05x||f=-3652. 



The result could scarcely agree better with the actual value r = '3653 found 

 from the tetrachoric equation had we proceeded by the central difference instead 

 of by a forward difference formula. For a table of this type the latter formula gives 

 very fair results and can be applied to any panel whatever*. 



Illustration (xi). Cleanliness of Home and Mothers Health. 



Health of Mother 



Here 



Hence 

 We have 



$ (1 - a h ) = -284,788, (1 - a k ) = '308,373, 



d/N= '146,81 60. 

 h = -56868, k = '50047. 

 = '6868, A = -3132, y = '004-7, ^ = -9953. 



The value of d/N occurs in the tables for h and k between '5 and '6 for r = '40, 

 45, '50 and '55. The last clearly need not be considered as k is only slightly over 

 '5 and a value such as '146... could not occur in this region. We may also 

 discard the first (r = '40), for when k is close to '50 the value d/N='l4iQ ... 



* It is clearly less exact than the central difference formula in that it neglects third differences, hut 

 these reach practical importance in very few of the cases tested in this Introduction. 



