78 
On Errors of Random Sampling 
For the benefit of those who wish to extend my small tables, it may be worth 
indicating the arithmetical arrangement which I have found most convenient. 
I use the following scheme : 
1 
m, p, q, 
q + m 
Term 
1 
00 
Multiplier 
m (p + 1) 
(q + m) 1 
(a) 
m (p + 1) 
(q + m) 
08) 
(m- l)(p + 2) 
(q + m - 1) 2 
(6) 
/3b 
(7) 
(m-2) (jt) + 3) 
(7 + m - 2) 3 
00 
(S) 
(d) 
The values of », m, p, q and q + m are written at the top of the sheet, -~ aQ d 
100 G 0 are calculated ami written in the right-hand top corner. 
Two columns are next formed ; the entries in the right-hand column having 
been made, any given term of the left-hand column is the product of the entries 
in the columns immediately above it. The entries in the left-hand column are 
added up and the sum checked by comparing it with ^ . Finally each term is 
converted into a percentage by multiplying with 100 G 0 . 
In this way, provided one has a mechanical calculator, a series having only 
a moderately lai'ge number of arithmetically significant terms is rapidly evaluated. 
Still, when all is said, the calculation of a table for values of m and n ranging from 
say five to a hundred and p from 0 to '1 would need an heroic amount of patience. 
Even the present admittedly imperfect results have involved the expenditure of 
some little time and effort* and it was necessary to consider how best to utilise 
our limited resources. 
Having chiefly before my eyes the needs of laboratory workers, I felt sure that 
the cases of m and n not greater than 25 were of the most importance. Probably 
in the type of problem alluded to on p. 73 the "control" should be regarded as 
our n and it is usually possible to arrange the experiments in such a fashion that 
animals at least equal in number to those specially tested serve as the control. 
When it is possible to plan a large control, it is usually practicable to fix the 
* I desire heartily to thank my assistant, Mr J. W. Brown of the Lister Institute Statistical 
Department, to whose zealous co-operation in the arithmetical work I am greatly indebted. 
