xlvi 



Tables for Statisticians and Biometricians [V VII 



The values of S 2 T g (h) and S*T s (h) may be found from the fundamental formulae 



&r s (A) = r s (h + 01) +T.(h- 01) - 2r s (h) 



(iv), 



.(v). 



or they can be ascertained very closely indeed from the formulae 



S 2 T S = i% s T 8+2 + 2 %s T s+4 I 



Here 



8 and 4 % 8 are given in Table V below. 



TABLE V. 



Table of the ^-Coefficients. 



It is convenient to note that 



which gives an easy process for finding the coefficient of the S 4 term from that of the 

 S 2 term. 



We remark that the method of determining S 2 and & 4 by (v) will fail, if 

 any one or more of the functions T s+2 , T s+4 , T s+6 lie outside the table. Hence it 

 cannot be used beyond TIS when it is desired to go to fourth differences, or beyond Ti 5 

 when second differences suffice. It is, however, easy to obtain the values of the 

 tetrachoric functions lying just beyond the borders of the table by aid of the re- 

 currence formula 



r s (h) = hp s T s -i(h)-q s r s -z(h) ........................ (vii), 



supposing s > 20. 



Table VI below gives the values of p s and q a from s= 2 to 25. 



