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PHILOSOPHICAL SOCIETY OF WASHINGTON. 
imperfect. I assume that the extent of association is a quantity 
capable of numerical expression, and further assume it = -j. 
This is tantamount to the assumption that whenever either of the 
c c 
ratios or - 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 — h times. The 
following table will hardly need further explanation: 
Phenomena. 
A and B 
A and Not-B 
Not-A and B 
Not-A and Not-B 
Both occur. Neither occurs. Extent of association. 
c s — a — h-\-c 
a — c 
b-c 
s — a — 6 + c 
h — G 
a — c 
6 “ 
ab 
a { s — b ) 
( b - c ? 
( s — a ) b 
(g — n — 6 -h cy 
(s — a) (g — 6) ' 
For illustration, let blindness and deafness be the phenomena 
denoted respectively by A and B. Then the extent of association 
between blindness and deafness = that between sight and 
u c (b — G ? j . 
dealness = 7 -r, Ac. 
(g — a ) b 
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 
