Hi 



Tables for Statisticians and Biometridans [VIII IX 



TABLES VIII AND IX. 



Tables for determining the volume of any quadrant or of any cell of a Bivariate 

 Normal Frequency Distribution. (Biometrika, Vol. XL pp. 284 291, Vol. xix. 

 pp. 354 404, Vol. xxn. pp. 1 35. Alice Lee, Margaret Moul, Ethel M. 

 Elderton, A. E. R. Church, E. C. Fieller and J. Pretorius, with introductions 

 by K. Pearson.) 



These tables give the complete series of values needful for determining the 

 theoretical contents of any cell of a correlation table provided we can assume the 

 distribution to be of the normal type. They also provide a ready means of deter- 

 mining the correlation coefficient from a tetrachoric table, i.e. r t . A table 

 (Table XXX) was given in Part I of this work for the range r = O80 to TOO to 

 four decimal places only. That table was adequate for the purpose then in view, 

 that of finding the correlation from a fourfold table, when the correlation took a 

 high positive value, and it can still be used advantageously. 



We start with the fundamental tetrachoric table 



and assume the frequency distribution to be normal ; we suppose 



(i), 



and we take as our standard case h and k both positive. We can always arrange 

 our table so that this shall be so. But having done this the correlation coefficient r 

 will sometimes be positive and sometimes negative according to whether ad be is 

 positive or negative. The equation for r is known to be 



d/N = T (h)T (k) + T 1 (h)T 1 (k)r+T 2 (h)T 2 (k)r 2 +...+T n (h)r n (k)r n +... (ii), 



where T O (h) = (1 a h ), T O (k) = |(1 a k ) and r n is the tetrachoric function of the 

 nth order. 



Our tables supply the values of djN for h = O'O to 2'6, yfc = 0'0 to 2'6 and 

 r = - 1-0 to +1-0. 



The general method of interpolating into tables of double entry has been dis- 

 cussed on pp. xvii-xxi of the present part. An occasionally useful formula going, 

 however, merely to second differences, but involving only table entries is 



