To The Opsonic Index — A Medico-Statktical Enqmry 
inner of the two curves. This signifies that for this index the odds in favour 
of abnormality are not more than those in favour of normality, i.e. the odds are 
even. In the case of an index unity the probabilities that we are dealing with 
an abnormal index are seen to be very small, while for indices of '7 or 1-3 they 
are very considerable. Fig. 3 sliows to scale the actual probabilities for all indices 
ranging between '7 and 1"3. In the neighbourhood of the index 1 we see that 
probabilit}^ is practically zero. As we proceed outwards in either direction we find 
the chances of abnormality are becoming greater and greater. The values are as 
follows : — 
Chances in Favour of Ahnormality. 
Index 
Probability 
Index 
Probability 
■70 
•990 
1-05 
•081 
•965 
I^IO 
•428 
■80 
•914 
V15 
•750 
■85 
•801 
1 ■w 
•907 
■90 
•614 
1 -^5 
•976 
■95 
•303 
V30 
•991 
VOO 
•018 
Within the limits "8 and 1"2 the probability curve slopes rapidly to zero. If 
then we postulate that for a definite statement on a single examination a 
probability of at least '9 is required — and this signifies that our statement would at 
the worst be wrong once in ten times — we fix our limits of normality at approxi- 
mately '8 to 1"2. Outside these we can be reasonably certain that we are dealing 
with abnormal sera. 
These being the facts and the analysis of the facts, it seems reasonable to 
conclude that even in the admittedly difficult case of the tubercle bacillus we have 
a means of differentiating within certain limits a hyperopsonic or subopsonic 
serum from a normal one. 
Before proceeding to consider our second point as to the comparability of 
indices, we may look at the question of simple diffei'entiation from another point of 
view. We shall leave aside for a moment the index altogether, and fall back upon 
the frequency distributions from which the averages which enter into the index 
are calculated. Take the following tuberculo-opsonic distributions, the names 
attached to which sufficiently explain them. 
Number of Bacteria 
ingested 
0 
1 
3 
5 
6 
7 
8 
Mean 
Index 
Number of leucocytes: 
1. Normal Serum 
10 
29 
28 
18 
9 
2 
2 
1 
1 
2-12 + •OB 
2. Test Serum I 
12 
16 
24 
30 
8 
6 
1 
1 
2 
2-45 + -11 
1-16 
3. Test Serum II 
14 
18 
26 
18 
9 
6 
6 
2 
1 
2-48 + •IS 
ri7 
Standard Deviation (S. D.) Normal = 1-53. 
„ „ 1 = 1-65. 
„ 11 = 1-85. 
