54 
On the Poisson Laiv of Small Numbers 
will be surprised to see how closely the single negative binomial determined by 
tiuo constants gives the same result as the sum of the eleven Poisson-Exponentials 
determined by eleven constants, no one of which is really of any significance for its 
own exponential*. If we apply the condition for "goodness of fit," ;\;^=5'83 for 
the single binomial and = 5'88 for the sum of the eleven Poisson exponentials, 
leading to P='950 and P="951 respectively, or the fit with a single negative 
binomial is slightly better than that with eleven exponentials. The two constants 
are significant, the eleven constants have no real significance for their individual 
series, as is demonstrated by the fact that the binomials for these series do not 
approximate to the Poisson-Exponential type. 
We may now consider the previous case of suicides of women from the same 
standpointf. The following are the data as given by Bortkewitsch : 
TABLE IX. 
Suicides of Women in Eight German States. 
Nunilier of Suicides 
0 
1 
> 
4 
5 
G 
V 
8 
9 
10 & over 
Totals 
Ob.served Frequencies 
Sum of 8 E.\ponential« 
'.) 
8-0 
19 
16-9 
17 
20-3 
20 
18-7 
15 
15-1 
11 
11-4 
8 
8-3 
2 
5-6 
3 
3-6 
5 
2-1 
3 
2-0 
112 
112 
Single Binomial 
12-6 
18-4 
18-8 
16-4 
13-2 
9-9 
7-2 
5-1 
3-5 
2-4 
4-5 
112 
leading to 
For the single binomial we have : 
3-4732, 0-^= 8-2312, 
112(2-3699- 1-3699)- 2-5=*, 
where q=- 13699 ± -1490, n = - 2-.5354 + -3076. 
If q were very small its probable error would be + '0901. The values of q and n 
are quite significant, q is large and negative and n is small and negative. The 
resulting frequencies are given in the last line of the table as " Single Binomial." 
Turning now to the test of " goodness of fit," we have for the sum of the 8 ex- 
ponentials ^-= 7-957, and for the single binomial ;^2= 7-740, leading to P=-633 
If the reader will turn to the first footnote on p. 53 he will note that for nine cases, the standard 
deviations of the means {aj^U) are roughly about -7 or errors of ± 1 to ±1-5 may easily occur in the 
means. Hence with the possible exception of (13) and (27) the m's have not significant differences, and 
are not typical of the individual societies. 
t The values of the means and standard deviations are : 
Lippe 
Schwarzburg-Eudolstadt ... 
Mecklenburg-Strelitz 
Schwarzburg-Sonderhausen 
The standard deviation of the mean is here ajju, or, say, -5. Thus errors of 1 might easily occur 
in the values of m. There are probably significant differences between the first five and the last three 
states, but not between the first five among themselves or the last three among themselves. Thus the 
Poisson-Exponentials, if correct in theory, are not significant for the individual states. 
m 
a 
Schaumburg-Lippe 
1-429 
1-178 
Waldeck 
2-214 
1-378 
Liibeck 
2-571 
1-223 
Eeuss a. L. 
2-643 
1-631 
[ m 
ff 
' 2-857 
1-995 
5-143 
1-767 
5-286 
2-889 
5-642 
3-061 
