Miscellanea 
199 
is the frequency of the alternative character y in the sub-group or district i. For example 
a, /3, y ... may be the alternative hair colours in a country of which the diffei-ent districts are 
a, b, c, d ... z. Such tables arise over and over again in anthropometric surveys. If now each 
sub-group or district were a random sample of the general population, then the coefficient of 
contingency of this table — say the coefficient of mean square contingency — should within the 
limits of probable error bo zero. We have thus a table of the contingency between geogra[)hical 
sub-districts and the alternative characteristics. And the greater this contingency the more 
markedly are the sub-groups divergent from random samples of the general population. In 
other words the population is geographically* heterogeneous. Accordingly if we take the 
same or nearly the same set of characters for two populations and about the same number 
of sub-groups or districts, such tables as the above give by their coefficients of contingency 
a reasonable measure of inter-racial comparison. The population or race with the highest 
coefficient of contingency is clearly the most heterogeneous. The relative heterogeneity of 
Prussians, Swedes, Italia.ns, Scottish and, perhaps, English could, I think, be now determined in 
this manner from published data for at least hair and eye colour. 
But we require not only an inter-racial coefficient of heterogeneity, but an intra-racial 
coefficient, which will measure the relative heterogeneity of the various groups. To reach this, 
pick out any district or sub-class b and oppose it to the rest of the population in a table of the 
following kind : 
TABLE II. 
a 
/3 
y 
e 
7 
0) 
Totals 
b 
Rest 
'ha 
n 
e Ce 
n, 
bv 
n —n, 
1 017 
n,. 
11 -n, 
ta btii 
JV-n, 
Totals 
H 
n 
e 
n 
V 
n 
fa) 
iV 
This is also a contingency table, of a very contracted character it is true, but none the less 
absolutely valid, if it be only used for i-elative purposes. Let the coefficient of mean square 
contingency of this table be found and be Cj, then the relative values of (7^, C^, C^, etc. will be 
measures of the class and local differences, or what we may call intra-racial differences. I 
suggest these C's as the coefficients we are seeking. We will now investigate the natui'e of Cy 
Let be the mean square contingency, then : 
1 w 
1 " 
nba- 
71^ 
N 
N 
N 
nba- 
1-t- 
N 
N 
.(i). 
* The sub-groups need not of course be ' geographical ' ; they might be economically, socially, 
or otherwise differentiated. 
