80 
On Errors of Random Sampling 
found in the first sample are likely to fall. As remarked above, it was thought 
that when the first sample exceeded fifty its numerical composition would often be 
at the choice of the worker. I think, therefore, that these tables are likely to 
serve most of the objects I had in mind when the work was undertaken, although 
it is much to be desired that someone will have leisure considerably to extend 
them. I do not see any immediate prospect of being that person. 
The class of problem in which this species of investigation seems desirable has 
already been described and the reader is perhaps not anxious to see any more 
arithmetical examples. I may, however, give a single concrete instance of the 
kind of research in which, I hope, the tables will be of value. 
Tests of the Accuracy of Simple Interpolation. 
[The True Values are given in brackets,] 
Example I. ?i = 22, p = i, m — 16. 
0 — 3 Successes 1 — 3 Successes 3 Successes 
57-38(57-49) 51-27 (51-65) 18-70(19-14) 
Example II. «=37, p = 4, w=22. 
0 — 3 Successes 1 — 2 Successes 3 Successes 
62-85 (67-89) 36-47 (39-83) 16-64 (18-88) 
Example III. a = 71, p = 4, m = 43. 
0 — 2 Successes 1 — 3 Successes 3 Successes 
46-43(47-53) 50-60(56-66) 15-21 (18-25) 
Example IV. « = 100, p = 4, m = 39. 
0 — 3 Successes 1 — 2 Successes 3 Successes 
83-84 (84-93) 48-59(50-78) 13-78 (15-15) 
In a paper by Rous*, several experiments of the following kind are detailed. 
15 micef were injected intraperitoneally with a suspension of mouse embryo in 
normal saline and 11 days later reinjected with the same substance. Ten days 
after the second injection they were inoculated subcutaneously with a mass made 
from mouse embryos 1*5 cm. long, and 17 previously untreated mice were inoculated 
at the same time to serve as a control. 
In only one of the 17 control mice was no graft found at the autopsy, but 8 of 
the treated mice did not " take." If we wish to know whether this difference 
be an effect of the intraperitoneal inoculations, we may put n = l7, p = l, and 
ascertain the chance that in m = 15 there would be 8 or more successes. 
From the tables, with interpolation, I find the odds against such a result to be 
about 260 to 1. In other words it is very likely that the treatment has led to the 
* "An Experimental Comparison of Transplanted Tumour and a Transplanted Normal Tissue 
Capable of Growth," by Peyton Rous, M.D., Joum. Experimental Medicine, 1910, Vol. xn. p. 344. 
t I take the number stated in the text but can only identify 14 in the corresponding table. 
