Lucy Whitaker 
41 
therefore, that the Poisson Law of Small Numbers should be applied in order to 
deal with the errors of random sampling iu any small frequency, and an appeal 
should not be made — as is usually the case — to Sheppard's Tables on the assump- 
tion that the frequency is Gaussian. 
The following Table I illustrates the results obtained (a) from the Binomial, 
(b) from the Poisson-Exponential and (c) from the normal curve on the two 
hypotheses that (i) the frequency is 10 in the 1000 and (6) is 30 in the 1000. 
But here a word must be said as to which Gaussian is to be compared with the 
Binomial or the Poisson-Exponential. The usual method of fitting a Gaussian is 
to give it the same mean and standard-deviation as the material to which we are 
fitting it. For example, we should compare the Poisson exponential with a Gaussian 
at mean m and with standard-deviation \/ni, or the point binomial with mean nq 
TABLE L 
Comparison of Binomial, Poisson- Exp07ien.tial and Gaussian for cellfrequency 
variations in samples for case of 10 and 30 in a total population of 1000 
Percentage Frequency 
O 
S-i 
s 
10 in lUOO 
30 in 1000 
Binomial 
Poisson- 
Exponential 
Gaussian 
Binomial 
Poisson- 
Expouential 
Gaussian 
0 
■00004 
•00005 
■00132 
19 
•00848 
■00894 
•01100 
1 
•00044 
•00045 
•00327 
20 
•01287 
■01341 
•01553 
2 
■00020 
•00227 
■00735 
21 
■01857 
■01916 
•02118 
3 
■00739 
•00757 
•01491 
22 
•02556 
■02613 
•02792 
4 
•01861 
•01892 
•02736 
23 
•03362 
•03408 
•03544 
5 
■03745 
•03783 
•04539 
24 
•04233 
■04260 
•04373 
6 
•06274 
•06306 
■06806 
25 
•05110 
■05112 
•05198 
7 
•08999 
•09080 
•09224 
26 
•05927 
■05898 
•05970 
8 
•11282 
•11260 
•11300 
27 
• ^06613 
■06553 
•06625 
9 
•12561 
■12511 
•12514 
28 
29 
•07107 
■07367 
■07021 
■07263 
•07104 
•07360 
10 
•12574 
■12511 
•12526 
30 
■07375 
■07263 
■07367 
11 
•11431 
■11374 
•11334 
12 
•09516 
■09478 
•09271 
31 
■07137 
•07029 
■07126 
13 
•07305 
■07291 
•06854 
32 
■06684 
•06590 
■06659 
14 
•05202 
■05208 
•04580 
33 
■06064 
•05991 
■06013 
15 
•03454 
■03472 
•02767 
34 
■05334 
■05286 
■05246 
16 
•02148 
•02170 
■01511 
35 
■04553 
■04531 
•04423 
17 
■01256 
•01276 
■00746 
36 
■03775 
■03776 
•03602 
18 
•00693 
•00709 
■00333 
37 
■03042 
■03061 
•02835 
19 
•00362 
■00373 
•00134 
38 
•02384 
•02417 
•02156 
20 
•00179 
•00187 
•00049 
39 
■01819 
•01859 
•01584 
21 
•00085 
•00089 
•00016 
40 
■01351 
•01394 
•01125 
22 
•00038 
•00040 
•00005 
41 
■00979 
•01020 
•00771 
23 
•00016 
•00018 
•00001 
42 
■00691 
•00729 
•00511 
Biometrilia x 
