MATHEMATICAL SECTION. 95 
of the “unfavorable ;” and the “ratio of verification (the favorable 
cases divided by the sum of the favorable and unfavorable,” becomes 
Sip On ae —_ 
8 
v= 
And this is Mr, Frnuey’s method of computation. 
Mr. GrLBERT then employs a process to which he gives no name, 
but which may be called the elimination of hypothetical chance. 
: ) Pa ie ae sa . 
He estimates that e verifications of positive predictions might 
have been expected if the same number of positive predictions had 
been made at random, and sets these cases aside as ot neither 
discrimination nor want of it. In effect, he subtracts 22 © from each 
of the quantities 0, p, and ¢, and proceeds with the wees This 
portion of his reasoning is regarded as sound, and the process may 
be applied with great bn to properly formed ratios. 
The ratio v is 
c ay vay e+ c 
a  ?p ra pr 
To eliminate hypothetical chance, “E should be subtracted from 
each of the quantities ¢ and p, ¢ and ©? Cage é and p’. Denoting 
the result by @, 
ee ie a OD. 
4 2 (es — op) 
~ p(s—0) +0(s—p) 
When 
p= 100, o= 51, c= 28, s = 2808; 
then 
p = 27038, = 2752, é= 2680 ; 
and 
__ 26°18 + 26:18 355. 
~ 98:18 + 49° Ag 
The above formula, like many others, successfully passes all the 
tests which Mr. Gilbert devised for his own formula, but it fails 
Ss 
