MATHEMATICAL SECTION. 
95 
of the “ unfavorable; ” and the “ ratio of verification (the favorable 
cases divided by the sura of the favorable and unfavorable/’ becomes 
s — 0 ~ p 4-2 g c-\- c 
V =-^--- 
s s 
And this is Mr. Finley’s method of computation. 
Mr. Gilbert then employs a process to which he gives no name, 
but which may be called the elimination of hypothetical chance. 
07) 
He estimates that — verifications of positive predictions might 
s 
have been expected if the same number of positive predictions had 
been made at random, and sets these cases aside as proving neither 
discrimination nor want of it. In effect, he subtracts — from each 
s 
of the quantities o, p, and c, and proceeds with the residuals. This 
portion of his reasoning is regarded as sound, and the process may 
be applied with great utility to properly formed ratios. 
The ratio v is 
c + c' ^ c4-c' . 
s p + p' 
ow 
To eliminate hypothetical chance, — should be subtracted from 
S 
o^p' 
each of the quantities c and p, and — from c' and p'. Denoting 
s 
the result by %, 
S 8 
2 (cs — op') 
op 
8 
p {8 — o') 4- 0 {8— p) 
When 
p = 
100, 0 = 
: 51, C = 
28, s = 2803 ; 
then 
- 
p' = 
2703, o' 
= 2752, 
c' = 2680; 
and 
i — 
26T8 4- 
2618 
0.355. 
9818 + 
4918 
The above formula, like many others, successfully passes all the 
tests which Mr. Gilbert devised for his own formula, but it fails 
