Karl Pearson 
213 
Now it will be obvious at once from these results that the uegative correlation 
between successive means for the one slide is not of essential significance ; there is, 
as we had anticipated, a slight positive correlation, which is not again, however, of 
very real importance. Whether Dr Fleming would also have reached this, had he 
counted 400 means of 50, instead of 20 such means, it is impossible to say. 
But what is quite obvious is that while Greenwood and White's count extended 
to more than 20 slides and Fleming's to only one, yet the variability of their 
400 means is not greater but rather less than that of Fleming's 20 means. 
But it is precisely on this variation of means that the variability of the opsonic 
index as found for one individual tested against himself depends. It is therefore 
clear that if these "enormous working errors" are due to the "functional error" 
of observers, and not to the variations of random sampling, they occur equally 
easily inside and outside Sir Almroth Wright's Laboratory. But if three separate 
sets of observers working on different material by different methods* reach prac- 
tically like variations in the values of the means, have we not reasonable ground 
for assuming that we are not dealing with " enormous functional errors," but 
that the large working errors, to which attention has been drawn by those trained 
in statistical theory, are for the most part variations of random sampling, i.e. what 
Sir Almroth Wright terms " errors of method," errors which he lightly brushes 
on one side, — without providing the least quantitative evidence — merely saying 
that he has satisfied himself that "the 'mathematical limit of error ' of the opsonic 
index is such as need not seriously be taken into account." He has yet to satisfy 
the biometrician that his " fellow-workers," the " increasing number of bacterio- 
logical workers all over the world" and he himself have the knowledge requisite 
to test critically this insignificance of the " mathematical limit of errorf ." 
(6) Taking the actual means of sets of 50 as given in the footnote for 
Fleming and for Greenwood and White, we have formed the 380 actual opsonic 
indices which would arise in each series from these means tested against them- 
selves: see Table III. It will be seen from an examination of Diagrams IV and V 
that while Greenwood and White's Slide B distribution is somewhat more variable 
than Fleming's!, there is absolutely nothing which would enable one to make 
a substantial differentiation on the ground of the presence and absence of 
" enormous working errors." 
* In one, if not in two of the series attempt was made to count the bacilli for every leucocyte. 
+ As we have seen the variability on Greenwood and White's Slide B is in excess of their average 
variability for the whole series, i.e. -31 against "25 ; Fleming's variability is - 28. It is interesting to 
look at the whole series of 20 means of 50 due to the two investigations : 
Fleming ... ... — 3-16, 324, 3-28, — 3-46, 3-52, 3-56, 3-60 
Greenwood and White 3-02, 3-16, 3-22, 3 26, 3-32, 3-40, 3-40, 3'46, 3-54 
Fleming 3-62, 3-78, 3-82, 3-84, 3-84, 3 84, 3-88, 3-90, 3-90, 3-98, 4-02, 4 06, 4-14 
Greenwood and White 3-60, — 3-62, 3-64, 3 70, 3-82, 3-84, — 3 92, 4-00, 4-02, 4-02, 4-14 
Thus Greenwood and*White have only one mean outside Fleming's range and the parallelism is 
striking ! 
X We have already seen that Slide B of Greenwood and White was 20°/ o more variable than their 
average data ; accordingly others of their slides reverse their relative variability as compared with 
Fleming's Slide T. A. i. 
