68 
The Opsonic Index — A Medico- Statistical Enquiry 
of the Arithmetic Mean to be called the best descriptive average. Another 
measure of the phagocytic frequency distribution has been proposed, namely the 
point corresponding to the maximum ordinate or mode. This is in many ways 
much to be preferred to the average as a descriptive constant for a skew distribu- 
tion. For one thing it has a more obvious physical meaning, as it represents the 
state of affairs which most frequently occurs, i.e. is most probable. Moreover the 
mode is not affected to nearly the same extent as the average by extreme numbers, 
which may in some cases be due to extraneous causes. The mode is, however, 
much more difficult to evaluate, and the ultimate test of its utility in ordinary 
practice will be the ease of its determination. Nevertheless it may be questioned 
whether, if we are going to search for the single numerical quantity which will 
best characterise the phagocytic count, either the mean or the mode is the best 
for the purpose. If the variability of the distribution, the extent to which it 
ranges and the frequency with which deviations from the mean or mode occur are 
the essential points of difference between a normal serum effect and an immune 
serum effect, then it is certain that neither the mean nor the mode will be the best 
single measure available. We may look into the point later on but it is one which 
would have to be settled by the statistician. 
The stage then which we have reached in this consideration is this, that the 
Arithmetic Mean of the phagocytic frequency distribution is the most natural if 
not the most accurate single expression for the totality of our count. The state- 
ment, for instance, that the average number of bacteria per leucocyte is 3H is no 
more true than that the Scottish express travels between London and Edinburgh 
at 50 miles an hour : in fact it is less true, if only for the reason that the express 
does at times in the course of every journey travel at this speed. At the same 
time the average does express something which we can perfectly well under- 
stand. It has the great convenience of being readily and rapidly evaluated, and 
also obviates in practice the necessity for deciding, when two or more leucocytes 
are in juxtaposition, whether a bacterium situated on a boundary is to be placed 
in the one or the other. 
But it may be objected that the opsonic index is not simply the average of the 
phagocytic count. Such an average varies, as we know, with thickness of bacterial 
emulsion, age of serum, length of incubation and so on. It was with the idea of 
getting rid of these variations that Wright and Douglas devised the opsonic index 
as a useful gauge of degree of phagocytic activity. The index is defined as the 
ratio of the averages of the counts for test and normal sera, and is a number 
intended to show how much more, or, as the case may be, le^^ctive a test serum 
is than a standard normal serum. Normal serum activity — supposed to be 
more or less constant— supplies the unit, and test serum activity is given in terms 
of this unit. But apart from the possibility of variations in normal sera the unit 
is variable owing to the impossibility of standardising the bacterial emulsions 
used in the test. This difficulty is got over by making a fresh evaluation of the 
unit for each separate group of determinations. The index is, however, at bottom 
