J. F. Tocher 
163 
In the previous section the difference between each local group and the general 
population, i.e. the {RLD)'s for each colour class, were detected and discussed. In 
doing so, the significance or non-significance of these differences for each local 
group (division, county or district) was determined for each colour class or category. 
It has been noted that for each class of hair colour or of eye colour, many localities 
exhibit significant differences from the general population. In others the dif- 
ferences may be insignificant, while in a few localities the differences may be 
considerable although not quite significant. But it is possible that a locality may 
exhibit a difference or differences almost or just significant for one or more colour 
classes and yet, when the differences of all the classes constituting the character 
(either hair colour or eye colour) in any one locality are considered collectively, 
these differences as a whole may quite conceivably occur even if the locality in 
question were a fair sample of the general population. A comparison between the 
entire pigmentation of each local group and the entire pigmentation of the general 
population is therefore necessary, in order to detect what local groups really 
diverge and what local groups do not diverge significantly from the general popu- 
lation, for the two characters under consideration, namely, hair colour and eye 
colour. In other words, the degree of general resemblance of local populations 
(firstly in hair colour and secondly in eye colour) to the general population is to be 
determined. Such a determination can be made at least in two ways, and has 
already been made in the pigmentation of one fairly long series, namely, the 
Scottish Insane. 
(a) One can observe for each locality how closely the observed frequencies of 
the various classes of hair colour or eye colour as a group correspond to their 
respective theoretical frequencies — the theoretical frequencies meaning of course, as 
ah'eady noted, those which would be got if, for each locality, the frequencies of the 
various classes constituting the character were proportionally the same as the 
frequencies found in the general population The probability that differences in 
the class frequencies would arise at random in any locality as great as, or greater 
than, the observed set of differences in class frequencies, can be found by evaluating 
VttJ/ "X + Vtt U l.-'i.5^ ^1.3.5...(H'-3)y 
if n be even, and 
p = g-hx^ ( 1 + ^ ' + -I ^ — -I- H ^ ' ^ 
V 2 2.4^2.4.6 2.4.6. ..(n'-3)/ 
if n be odd, 
where n' = n + 1 classes in the series constituting the character, 771^ = theoretical 
frequency of any class, m/ = observed frequency of any class and 
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