Andrew W. Young and Karl Pearson 
229 
(11) Summary of Formulae. 
It will be convenient for purposes of reference to have all the formulae collected 
into one section. 
General Formulae. 
For (fy- defined by 
or 
.^2 = s 
NX. 
•(A), 
where N is the number in a sample, n, is the number in the sth division of that 
sample and is a number connected with the sth division satisfying the condition 
S (As) = S {ris) = A'^, we have proved that for an "infinite" sampled population 
and 
N 
1_ 
IP 
6S (t') + (8 - 4.A^)S(|-) - 12,s(j'£,) + (2-4,l=)<.-33-66.>=-lCV.« 
^^(f') n'^f- ^<»-'-'^(!)-<"-) 
(C), 
where c is the number of divisions or cells and i/jg = Tij — A,, or, with a fair amount 
of approximation. 
N 
...(D). 
Contingency. 
In the case of a contingency-table the sth division may be taken to be the 
{u, v) cell and A, = where «„ and n,,, are the marginal totals of the wth row and 
the vth column. Formulae (A), (B), (C), (D) are then directly applicable. 
Test for zero contingency. 
When there is zero contingency in the total population 
and (B) reduces to 
(B'), 
* As usual the bar over a letter denotes "the mean value of." It is to be noted that usually there 
is only one sample and the value of in that sample has to be taken as 
