If we now take a quick look at all of the considerations we have developed in the course of this work and endeavour to summarize them in as few words as possible, we are led to put forth the following propositions as having been absolutely demonstrated.
The rules of logic are inadequate for judging the influence of a given medication in an equally given disease and for classifying the medications recommended for this same disease according to their influences.
The principles of the law of large numbers are strictly applicable to therapeutic research and they alone can furnish the solution of these two important problems.
Average mortality, as provided by statistics, is never the exact and strict translation of the influence of the test medication but approaches it all the more as the number of observations increases.
A therapeutic law ensuing from the comparison of a small number of observations may be so far from the truth that it merits no degree of confidence in any case whatsoever.
A therapeutic law can never be absolute; its applications can always oscillate between certain limits which are all the narrower, the more the collected observations are multiplied, and which can be determined with the aid of the numbers constituting the statistics that have provided the law.
To be able to decide in favour of one treatment method over another, it is not enough for the method to yield better results; the difference found must also exceed a certain limit, the extent of which is a function of the number of observations.
Any difference in the results obtained that is below this limit, while this limit decreases as the number of observations increases, must be disregarded and deemed void.
The same principles and the same inferences strictly apply to the solution of the basic difficulties arising from the doctrine of the medical constitutions
By applying the same rules, one must endeavour to ascertain whether the mortality rate of a disease changes according to age, sex, regions, etc., etc.
Whenever aetiology is uncertain, the principles of the law of large numbers can only serve to prove the existence or non-existence of a suspected specific cause, regardless of any hypothesis as to its nature. One must try to determine the cause itself [on the basis of] considerations of another kind; this last concern is outside the domain of statistics.