44 
PROFESSOR K. PEARSON ON MATHEMATICAL CONTRIBUTIONS 
We see accordingly that there is quite a large correlation between recovery and the 
presence of the cicatrix. The two things are about as closely related as a child to its 
“ mid-parent.” While the correlation is very substantial and indicates the protective 
character of vaccination, even after small-pox is incurred, it is, perhaps, smaller than 
some over-ardent supporters of vaccination would have led us to believe. 
Illustration VII. Effectiveness of Antitoxin Treatment. —To measure quanti¬ 
tatively the effect of antitoxin in diphtheria cases. 
In like manner we may find the correlation between recovery and the administration 
of antitoxin in diphtheria cases. The statistics here are, however, somewhat difficult 
to obtain in a form suited to our purpose. The treatment by antitoxin began in the 
Metropolitan Asylums Board hospitals in 1895, but the serum was then administered 
only in those cases which gave rise to anxiety. Hence we cannot correlate recovery 
and death with the cases treated or not treated in that year, for those who were likely 
to recover were not dosed. In the year 1896 the majority of the cases were, on the 
contrary, treated with antitoxin, and those not treated were the slight cases of very 
small risk ; hence, again, we are in great difficulties in drawing up a table .* Further, 
if we compare an antitoxin year with a non-antitoxin year, we ought to compare the 
cases treated with antitoxin in the former year with those which would probably have 
been treated with it in the latter year. Lastly, the dosage, nature of cases treated, 
and time of treatment have been modified by the experience gained, so that it seems 
impossible to club a number of years together, and so obtain a satisfactorily wide 
range of statistics. In 1897, practically all the laryngeal cases were treated with 
antitoxin. Hence the best we can do is to compare the laryngeal cases in two years, 
one before and one after tbe introduction of antitoxin. The numbers available are 
thus rather few, but will help us to form some idea of the correlation. I take the 
following data from p. 8 of the Metropolitan Asylums Board ‘ Report upon the Use of 
Antitoxic Serum for 1896 ’:— 
Laryngeal cases. 
Recoveries. 
Deaths. 
Totals. 
With antitoxin, 1896 .... 
319 
143 
462 
Without antitoxin, 1894 . . . 
177 
289 
466 
Totals. 
496 
432 
928 
* When a new drug or process is introduced the medical profession are naturally anxious to give every 
patient the possible benefit of it, and patients of course rush to those who first adopt it. But if the real 
efficiency of the process or drug is to be measured this is very undesirable. No definite data by which to 
measure the effectiveness of the novelty are thus available. 
