440 Tetrachoric Fioictions for Fourfold Correlation Tables 
The tetrachoric functions of higher order than the sixth (easily found by 
means of the auxiliary table) will be chiefly required when r is large and the series 
consequently converges less rapidly. In connection with such cases, it is well to 
recollect that in the series on the right-hand side of the equation successive 
terms need not necessarily converge but that alternate terms are absolutely 
convergent*. 
Another Use for the Tables. 
The tables can also be used with advantage in the work of connputing the 
frequencies iu the divisions of any frequency table, when the correlation coefficient 
r is known and the frequency is normal. Such problems can be classifled into 
three cases according to the fineness of the grouping and a brief outline of tlie 
methods to be employed is given. 
Case I. Fourfold table. According to 
dividing planes are fixed either by h and k 
the value of d is then calculated from 
the purpose 
or b -j-d and 
to be served, the 
c + d being known ; 
b+d c+d 
N N ' N 
when d is known, b, c and a are also known from the total column and row. 
Case II. Ninefold table. It is required to divide a normal frequency surface 
into nine parts A, B,...Las shown in the diagram. Then it will always be 
A 
B 
G 
D 
E 
F 
G 
I 
L 
N 
to consider one or more of A, C, G, L in turn as the of a standard fourfold 
table and find its value from the equation given in Case I. The column and 
row totals are either known or obtained directly from values of h and k. From 
the known divisions and the column and row totals the values of other divisions 
and groups of divisions are next obtained; the table is then divided afresh, if 
necessary, according to the particular circumstances of the case, the values of 
other groups of divisions obtained, and so ultimately the value of each 
division not already known may be found by differences. 
* Pearson, loc. cit. p. 10. 
