V.—MANIFOLD CLASSIFICATION. ’ 
The eye- and hair-colour data of Table II. may be treated in a 
precisely similar fashion. If, e.g., we desire to trace the associa- 
tion between a lack of pigmentation in eyes and in hair, rows 1 
and 2 may be pooled together as representing the least pigmenta- 
tion of the eyes, and columns 2, 3, and 4 may be pooled together 
as representing hair with a more or less marked degree of 
pigmentation. We then have— 
Proportion of light-eyed with ) 2714/5943 = 46 per cent. 
fair hair . J 
Proportion of brown-eyed with 115/857 =13 
fair hair . : 
The association is therefore well-marked. For comparison we 
may trace the corresponding association between the most marked 
degree of pigmentation in eyes and hair, 7.e. brown eyes and 
black hair. Here we must add together rows 1 and 2 as before, 
and columns 1, 2, and 4—the column for red being really mis- 
placed, as red represents a comparatively slight degree of pigmenta- 
tion. The figures are— 
roportion rown- v 
p Spt of % ge ged Mth } 288/857 = 34 per cent. 
Proportion of light-eyed with 
mip pd }935/5943=16 
The association is again positive and well-marked, but the 
difference between the two percentages is rather less than in the 
last case. 
5. The mode of treatment adopted in the preceding section rests 
on first principles, and, if fully carried out, it gives the most detailed 
information possible with regard to the relations of the two attri- 
butes. At the same time a distinct need is felt in practical work for 
some more summary method—a method which will enable a single 
and definite answer to be given to such a question as—Are the 
4’s on the whole distinctly dependent on the B’s; and if so, is this 
dependence very close, or the reverse? The subject of coefficients 
of association, which affords the answer to this question in the 
case of a dichotomous classification, was only dealt with briefly 
and incidentally, for it is still the subject of some controversy : 
further, where there are only four classes of the second order 
to be considered the matter is not nearly so complex as where 
the number is, say, twenty-five or more, and the need for 
any summary coefficient is not so often nor so keenly felt. The 
ideas on which Professor Pearson’s general measure of de- 
pendence, the “coefficient of contingency,” is based, are, more- 
over, quite simple and fundamental, and the mode of calculation 
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