liv 



Tables for Statisticians and Biometricians [VIII IX 



will be known. Thus either n v> n u , n v ', n u ' form the d's of four tetrachoric tables 

 and are known, or, if they be o/s, 6's or c's, the corresponding d's can be obtained 

 from the equations (iv) above and the marginal totals of the fourfold tables. 



Thus we deduce the "normal value" of n sf . We propose in the first place to 

 illustrate this process. 



(a) The applications of Tables VIII IX are so wide and so important that 

 we shall illustrate them somewhat at length, beginning with fairly simple illustra- 

 tions of the methods of applying higher interpolation formulae. 



Illustration (i). In a table for the correlation of Father and Son for stature we 

 find, for the heights of Fathers 68"'875 69"'875, twelve Sons of the heights 

 66"'87o 67"'875. This is a perfectly arbitrary cell taken out of a table of 

 20 x 17 cells*. The correlation coefficient of this table worked by the product- 

 moment method is "5189. The problem we put before ourselves is this : Supposing 

 the table corresponds to a normal surface, is a frequency of twelve individuals 

 reasonable for this cell ? As much of the table as concerns our present purpose can 

 be written as follows : 



and 



Clearly n tt = 19, n u ' = 10, w v = 43, n v ' = 22, 



n st = 12 = n v -n u - n v ' + n u f = 43 - 19 - 22 + 10. 



We can now examine the requisite four tables which have to be solved to obtain 

 n st for the normal surface. They are : 



* See Biometrika, Vol. xiv. p. 151, Table XV. 



