4 
164 Pigmentation Snrvey of School Children in Scotland 
This is Pearson's test of goodness of fit* and is applicable, in the manner above 
stated, to the present data. 
(/S) One can determine the divergency in hair colour or eye colour of any 
locality from the remaining population by measuring how far the local group deviates 
from being a random sample of the general population. This can be done by 
forming a divergency table and evaluating the mean square contingency coefficient 
which measures the degree of departure of the local group from complete resem- 
blance to the general population, or the degree of relative divergency of the local 
group. Such tables -f- have already been formed for the purpose of determining the 
relative divergency of the local insane from the general insane population with 
respect to pigmentation. In a divergency table two groups of the population are 
dealt with, the local group and the remaining population, but of course the number 
of classes is not limited. In this investigation the number of classes is small, five 
for hair colour and four for eye colour. The frequencies for a particular class, 8, 
of the two groups form a column of the table, while the frequencies of all the 
different classes of either group form a row of the table. If -^^^ = the total square 
((tTI ' ~" TIZ 
contingency coefficient and x^ — ^ ] ' \ ] '>^ = number in any local group and 
N 
iV^= total population, then the relation X'" — j^^^X" holds between x. '^ and 
or x^ is a fraction of the total square contingency, being, as seen in the working, 
a partial summation of x'-- T'he mean square contingency coefficient is of course 
Since x," has already been calculated, the above formula need not be used. In 
terras of 
<^^ = Q = \/ + 
and is readily obtained. Since Q measures the divergence of a local group from 
the remaining population, it is called the divergency coefficient. The probable 
errors of Q have not been evaluated, except in one or two instances. It is sufficient 
to note that any value of Q > '008 in the present series is probably significant. 
The values of Q and log P have been calculated for all the forms of local groups, 
namely, divisions, counties and districts, and are given in the following tables 
(Tables XIX., XX., XXI. and XXII.). These two sets of constants have been 
classed, the classification being the same as that previously adopted for the pig- 
mentation of adultsj. As may be seen from the maps, Class O with values of 
log P < 3 and Q < "008 is the non-significant class, the localities belonging to this 
class being similar on the whole to the general population. 
* Phil. Mag. Vol. i. pp. 157—175, July 1900. 
t Tocher: Biometrika, Vol. v. pp. 333, 334. For theory and probable errors see Pearson, Biometrika, 
Vol. V. pp. 198—203. 
J Tocher : Biometrika, Vol. v. pp. 335 — 340. 
