84 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
imperfect. I assume that the extent of association is a quantity 
2 
capable of numerical expression, and further assume it = one 
This is tantamount to the assumption that whenever either of the 
; Oo, aor! 5 ae 
ratios ; or iF is constant, the extent of association varies directly as 
the other ratio, and = 1 when they each = 1. 
Not-A and Not-B may also be regarded as phenomena whose 
presence is equivalent to the absence of A and B and vice versa, 
Not-A, therefore, occurs s — a times; and Not-B s— 6 times. The 
following table will hardly need further explanation: 
Phenomena. Both oceur, Neither occurs. Extent of association. 
2 
A and B c s—a—b+e LD 
ab 
pe vat (a—c)? 
A and Not-B a—c hee veo 
As pis (b—c/) 
Not-A and B b—c hee en 
mae ee 2 
Not-A and Not-B s—a—b+e c (s—a—b+¢e) 
(s—a)(s—b)° 
For illustration, let blindness and deafness be the phenomena 
denoted respectively by A and B. Then the extent of association 
2 
between blindness and deafness = 3 that between sight and 
_ (b—c) 
deafness = (s—a)d’ Xe. 
I call the above expressions for extent of association indiscrimi- 
nate association ratios. It is important now to understand that the 
magnitude of each is determined both by general and special causes. 
In an ordinary community the indiscriminate association ratio be- 
tween sight and hearing is very large, nearly =1, for the general 
reason that most people can see whether they can hear or not, and 
most people can hear whether they can see or not. If there is a 
special reason why a larger proportion of men able to see than of 
blind men shall be able to hear, this special reason will tend to in- 
crease the indiscriminate association ratio, and a contrary special 
reason will tend to diminish it. 
I now seek to obtain a discriminate association ‘ratio, whose 
magnitude shall be affected by special causes only, and which may 
