IV.—PARTIAL ASSOCIATION. 45
absence of J as suggested, nor to the presence and absence of
C and D conjointly. If it be then argued that the presence
and absence of Z is the source of association, the process may
be repeated as before, the association of 4 and B being tested
for the universe C'DZ, and so on as far as practicable.
Partial associations thus form the basis of discussion for any
case, however complicated. The two following examples will
serve as illustrations for the case of three attributes.
Example i.—(Material from ref. 5 of Chap. 1.)
The following are the proportions per 10,000 of boys observed
with certain classes of defects, amongst a number of school
children. (4) denotes the number with development defects, (B)
with nerve-signs, (2) the number of the “dull.”
rl 10,000 (4B) 338
(4) 8717 (4D) 338
(B) 1,086 (BD) 455
(D) 789 (ABD) 153
The Report from which the figures are drawn concludes that “the
connecting link between defects of body and mental dulness is
the coincident defect of brain which may be known by observation
of abnormal nerve-signs.” Discuss this conclusion.
The phrase “connecting link ” is a little vague, but it may
mean that the mental defects indicated by nerve-signs B may
give rise to development-defects 4, and also to mental-dul-
ness 0; A and D being thus common effects of the same cause
B (or another attribute necessarily indicated by B), and not
directly influencing each other. The case is thus similar to that
of the first illustration of § 2 (liability to small-pox and to. non-
vaccination being held to be common effects of the same circum-
stances), and may be similarly treated by investigation of the
partial associations between 4 and D for the universes B and f.
As the ratios (4)/N, (B)/N, (D)/N are small, comparisons of the
form (4) (5) of Chap. III. (p. 31), or (2) (a) (0) above, may very
well be used (¢f. the remarks in § 10 of the same chapter,
p. 31).
The following figures illustrate, then, the association between
4 and D for the whole universe, the B-universe and the B-
universe :—
For the entire material :—
Proportion of the dull=(D)/N . . == 7°9 per cent.
yy defectively develo h
were dull =(4D)/(4) + ped ¥ °Y= 8 ans "
ge
