Karl Pearson 
99 
Next we find for Mvera cattle strain and the wild Glossina morsitans strain, 
^2 = 40-508, or P = -000,008, 
or only once in 125,000 trials would a pair of samples so divergent arise when 
testing the same material. 
Lastly, testing the resemblances of wild-game strain and wild G. morsitans 
strain, we find 
;^= = 35-41, or P = -000,2, 
not such a gigantic divergency as we have found in many cases, but a difference 
so great that it only occurs once in 5000 trials requires explanation as divergency 
and cannot be used as an argument for " sameness." 
It will thus be quite clear that as far as the measurements of length go, there 
is wide divergence to be accounted for between the trypanosomes found in the 
cattle, the wild-game and the tsetse fly, and that statistically this divergence is the 
remarkable feature. Yet the conclusion of Sir David Bruce and his colleagues, 
arguing very largely from the frequency distributions, is that "The Mvera cattle 
strain, the wild-game strain and the wild G. morsitans strain belong to the same 
species of trypanosome, T. pecorum*." 
It will be seen that actual statistical analysis does not in any way confirm the 
bulk of the conclusions reached by Sir David Bruce and his collaborators. The 
strains may or may not be ultimately of like origin, but what is quite clear from 
the analysis is that, if we are to rely on the measurements, then it is the diver- 
gence, not the sameness of these strains, which should have been emphasised. 
No stronger evidence could be deduced of the danger of appeal to statistics 
when the statistics are not handled by the trained statistician. The mere appeal 
to the resemblance of frequency curves given in the form of percentages, often 
based on widely different totals, is an only too common error of medical investi- 
gations ; it is by no means confined to the Scientific Commission of the Royal 
Society, Nyasaland. But it has recently become so marked a feature of Series B 
of the Proceedings of the Royal Society, that a vigorous protest is really needful. 
Thus in the very last part issued (Vol. 87, B, p. 89) occurs a paper on " The 
Trypanosomes causing Dourine." In this paper there maybe microscopic evidence 
to differentiate the strains A, B and G dealt with ; on that I cannot express an 
* A further conclusion is also reached (Ibid. p. 26) " T. pecorum, Nyasaland, is identical with the 
species found and described in Uganda." Unfortunately the species found in Uganda is dealt with 
in a paper (R. S. Proc. Vol. 82, B, p. 468) which provides no frequency distributions, and does not tell 
us the total number on which the mean length — 13-3 microns — is based. The mean value of the 
T. pecorum, Nyasaland is 13-954 [R. S. Proc. Vol. 87, B, p. 3) and the standard deviation is 1-398 in 
microns, thus the probable error of the mean is -67449 x -0623. Assuming the Uganda trypanosome to 
be the same strain and to have the same variability as the T. pecorum, Nyasaland, the difference of the 
means = -654, with a probable error of -67449 x \/2 x -0623 = -67449 x -088, thus the deviation of the means 
is 7-73 times its standard deviation. A deviation so great would only occur about once in 4 x 10''* trials, 
i.e., would be practically impossible if the two strains were identical. Here again it is excessive 
divergence not sameness which the statistics indicate. 
13—2 
