78 The Opsonic Index - A Medico- Statutiml Enquiry 
Number of Bacteria 
0 
1 
2 
3 
k 
5 
6 
8 
9 
10 
11 
i5 
n 
15 
16 
i7 
18 
No. of Leucocytes : 
1. Normal Serum 
2. Test Serum 
13 
3 
13 
5 
12 
8 
10 
5 
15 
9 
13 
10 
10 
16 
10 
1 
10 
3 
4 
1 
5 
3 
1 
5 

3 
1 
1 
1 
1 
Mean 1=3-36 ±-16. S. D. 1 = 2-36. 
Mean 2 = 6-66 ±-27. S. D. 2 = 3-96. Index =2-00. 
We note here the much larger standard deviation which we get in the case 
of the glanders bacillus as compared with the tubercle bacillus, both as regards 
normal and test sera. In this case, although the bacillus is used killed, it is not 
old nor dried. The divergence in this instance between test and normal sera, as 
judged by standard deviations, is much greater than in the instances chosen for 
the tubercle bacillus. As regards the order of the probabilities in favour of 
significant difference between the distributions, we are unable here to consider the 
case of the test serum distribution arising as a random sample from the normal 
serum distribution, because the normal serum range for the small numbers here 
recorded does not extend so far as that of the test serum. We can, however, 
reverse the problem and ask what are the probabilities against the test serum giving 
a distribution like that of the normal serum. When we do so, we find that the 
probability against such being the case is .so enormous that the tables provided for 
the purposes of its evaluation {Biometrika, Vol. I. p. 159) do not go far enough to 
enable us to obtain it. All we can say is that the chances against our normal serum 
representing merely one random sample of the test serum, are something greater 
than 999,999 to 1. 
If these probabilities give us an indication of the degree of correctness and 
incorrectness of our inferences regarding opsonic activity, and if we can regard 
them as representing those for correctness of diagnosis, we should be in a position 
to compare them with our impressions of the degree of correctness of the usual 
clinical diagnosis in which some element of doubt exists. Let us take a concrete 
example. It would, I think, be satisfactory to know that our expressed opinion as 
to whether a chronically swollen joint represented a gonorrheal or a tubercular 
infection would be wrong only once in 200, or once in 100, or once in 50, nay even 
once in 10 times. Now these are just the sort of cases in which an estimation of 
an opsonic index or, as the case may be, a phagocytic distribution gives us the 
greatest help. 
There are also confirmatory tests which may be, and in fact usually are, applied. 
One of these is the method of multiple testing. When an important diagnosis has 
to be made, it is seldom given on merely a single index. The index is determined 
on several occasions, and if, as usually happens, the indices show characteristic 
divergences from the normal, the evidence is considered as greatly strengthened 
for a positive statement. Or again, special methods are applied in order to 
