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