THEORY OF STATISTICS. 
read similarly to the last. Taking the first row, it tells us that 
there were 2811 men with blue eyes noted, of whom 1768 had 
fair hair, 807 brown hair, 189 black hair, and 47 red hair. 
Similarly, from the first column, there were 2829 men with fair 
hair, of whom 1768 had blue eyes, 946 grey or green eyes, and 
115 brown eyes. The tables are a generalised form of the four- 
fold (2 x 2-fold) tables in § 13, Chap. IIL 
4. For the purpose of discussing the nature of the relation 
between the A’s and the B’s, any such table may be treated on 
the principles of the preceding chapters by reducing it in different 
ways to 2 X 2-fold form. It then becomes possible to trace the 
association between any one or morc of the A’s and any one or 
more of the B’s, either in the universe at large or in universes 
limited by the omission of one or more of the 4’s, of the B’s, or 
of both. Taking Table I., for example, trace the association 
between the erection of houses and the urban character of a 
district. Adding together the first two rows—z.e. pooling London 
and the other urban districts together—and similarly adding the 
first two columns, so as to make no distinction between inhabited 
and uninhabited houses as long as they are completed, we find— 
Proportion of all houses which 
are in course of erection in {s0soto-— 10 per thousand. 
urban districts . . : 
Proportion of all houses which 
are in course of erection ot 12/1761= 7 ir 
rural districts . : HN 
There is therefore, as might be expected, a distinct positive 
association, a larger proportion of houses being in course of 
erection in urban than in rural districts. 
If, as another illustration, it be desired to trace the association 
between the ¢ uninhabitedness ” of houses and the urban character 
of the district, the procedure will be rather different. Rows 1 
and 2 may be added together as before, but column 3 may be 
omitted altogether, as the houses which are only in course of 
erection do not enter into the question. We then have— 
Proportion of all houses which 
are uninhabited in urban [faze 66 per thousand. 
districts : 
Proportion of all houses which} 
are uninhabited in rural  124/1749=171 7° 
districts ( 
The association is therefore negative, the proportion of houses 
uninhabited being greater in rural than in urban districts. 
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