Karl Pearson 
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(iii) The probability that the strains are alike after allowance has been made 
for the host. 
(iv) The nature of the heterogeneity which is statistically demonstrable in 
the bulk of trypanosome measurements. 
I should like before considering the material to indicate one or two very 
important points. I am not concerned here with the truth or error of the con- 
clusions drawn by Sir David Bruce and his collaborators. I am only concerned 
with the nature of the process by which they have drawn their inferences. That 
process consists in a measurement of the individual trypanosomes and an appeal 
to the statistics of these measurements — in short to what I should term biometric 
reasoning. There may well be other means of discussing the resemblances of the 
different strains of trypanosome, — either by microscopic examinations of diver- 
gencies in the life history of the different strains or by differentiation in their 
action on different hosts, or otherwise. But in the present case the appeal to statistics 
of measurement has been made. Drs Stephens and Fantham in their paper on 
T. rhodesiense (R. S. Proc. Vol. 85, B. p. 227) actually term their work a "biometric 
study," and the later papers of Sir David Bruce and others are no less " biometric." 
Now if an appeal be made to statistics, then by a statistical method alone can the 
answer be given. Further, that method must be the analysis of the modern fully 
equipped and highly trained statistician. Such a statistician, and he alone, can 
assert or deny on the basis of statistics the probability of any of these strains 
of trypanosomes being samples of the same population ; he alone is in a position 
to judge the value of the evidence provided by the frequency distributions. If he 
finds substantial " divergence " where Sir David Bruce and his collaborators 
assert " sameness," then either statistical theory is wrong, or Sir David Bruce 
understands by "sameness" something quite different from the "sameness" of the 
statistician, and something which cannot be judged by the methods of statistics, to 
which accordingly no appeal should have been made, or only an appeal after a long 
series of control experiments. The " sameness " postulated by Sir David Bruce is 
something quite incompatible with the "sameness" found by the statistician when 
he investigates two samples of 100 crania of the same race or two samples of 1000 
blood corpuscles of two series of frogs of the same race. It is what the statistician 
calls marked divergence and not sameness. If it be asserted that the extreme 
divergence actually existing between the strains of trypanosomes statistically dis- 
cussed is due to difference of individual host and not to difference of strain, it will 
be clear that the divergence and not the sameness ought to have come out of the 
statistical investigation, and then control investigations ought to have been made to 
explain that divergence by environmental or other differences. But this is d priori 
to assume the identity of the strains and a posteriori to seek an explanation of 
marked divergence deduced statistically, whereas in the actual papers this great 
divergence is assumed to be statistical sameness and this sameness used as an 
argument for identity of strains. The statistician coming to the data critically 
Biometrika x 12 
