IV.—PARTIAL ASSOCIATION. 3 
to apply the principle of equation (7). Calculate what would be 
the death-rate for each occupation on the supposition that the 
death-rates for occupied males in general (11-5, 102-3) apply to 
each of its separate age-groups (under 65, over 65), and see 
whether the total death-rate so calculated exceeds or falls short 
of the actual death-rate. If it exceeds the actual rate, the 
occupation must on the whole be healthy; if it falls short, un- 
healthy. Thus we have the following calculated death-rates :— 
Farmers . . .. 115x868 +1023 x '132 = 23-5. 
Textile workers . 115x-966+102'3 x ‘034 =14"6. 
Glass workers . . 115x984 +102:3 x 016 =13-0. 
The calculated rate for farmers largely exceeds the actual rate ; 
farming, then, must on the whole, as one would expect, be 
a healthy occupation. The death-rate for either young farmers 
or old farmers, or both, must be less than for occupied males in 
general (the last is actually the case); the high death-rate 
observed is due solely to the large proportion of the aged. Textile 
working; on the other hand, appears to be unhealthy (14:6 <15°9), 
and glass working still more so (13:0<16°6) ; the actual low total 
death-rates are due merely to low proportions of the aged. 
It is evident that age-distributions vary so largely from one 
occupation to another that total death-rates are liable to be very 
misleading—so misleading, in fact, that they are not tabulated at all 
by the Registrar-General ; only death-rates for narrow limits of age 
(5b or 10 year age-classes) are worked out. Similar fallacies are 
liable to occur in comparisons of local death-rates, owing to 
variations not only in the relative proportions of the old, but also 
in the relative proportions of the two sexes. 
It is hardly necessary to observe that as age is a variable quantity, 
the above procedure for calculating the comparative death-rates 
is extremely rough. The death-rate of those engaged in any occu- 
pation depends not only on the mere proportions over and under 
65, but on the relative numbers at every single year of age. The 
simpler procedure brings out, however, better than a more complex 
one, the nature of the fallacy involved in assuming that crude death- 
rates are measures of healthiness. [See also Chap. XI. §§ 17-19.] 
Lzample iv.—Eye-colour in grandparent, parent and child. 
(The figures are those of Example ii.) 
4, light-eyed child ; B, light-eyed parent ; C, light-eyed grand- 
parent. 
& =5008 (4B) =2524 
2 = 3584 (40) = 2480 
B)=3052 (BC) =2231 
(C)=3178