STATISTICS, MEDICAL. — The Sta tistical Method; the Numerical Method. La 117elbode Numbique.— It is to be regretted that the use of numbers in any branch of scientific inquiry should have seemed to need a special name ; for the name has given rise to prejudices and misconceptions which could never have attached to the thing signified. There is no science which has not sooner or later discovered the absolute necessity of re sorting to figures as measures and standards of comparison ; nor is there any sufficient reason why physiology and medicine -should claim an exemption denied to every other branch of human knowledge. On the con trary, they belong in an especial manner to the class of sciences which may hope to de rive the greatest benefit from the use of num hers ; p:Ereonl iho, are most given to expregs Of the necessity or expediency of resorting to them, find them selves constrained to sanction by their own practice what they condemn in theory. This is an all-sufficient answer to those who con tent themselves with objecting in general terms to the employment of numbers in me dical investigations. As to more minute and detailed objections, these will be found to be anticipated and disarmed by the simple con sideration that they apply in reality not to the use, but to the abuse of numbers. The time has long gone by, when the absolute dependence of all science on observation and experiment could admit of question or dis pute ; and, as no one in the present day claims for physiology and medicine any im munity from the severe conditions which the very nature of things imposes, we are spared those appeals to authority which might for merly have been required at our hands. The absolute necessity of observation and experi ment towards the improvement of the science and art of medicine, in the widest acceptation of those terms, may, therefore, be safely taken for granted. The only points upon which any serious difference of opinion or divergence of practice exists, are the degree of care and accuracy which should be brought to bear on individual observations and experiments, the properties which fit single facts to he thrown into groups or classes ; the language which ought to be employed in expressing the ge neral results of such classifications ; and the numb& of facts which, being so grouped or classified, may be required to establish a ge neral proposition, or to furnish an accurate test or trustworthy standard of comparison.
The human mind is so constituted, that it looks forward to an occurrence with a con fidence proportioned to the number of times that it has been previously known to happen. Hence, the universal belief that all living beings will die, and that the sun will rise and set to-morrow ; hence, the somewhat less sanguine expectation that quinine will cure ague, and that vaccination will either pre vent or modify small-pox ; hence, the little hope we have that a severe attack of Asiatic cholera will terminate favourably, and our absolute despair of the recovery of a patient seized with hydrophobia. In these, and other analogous cases, we have either the expe rience of all mankind in all times and places, or that of large numbers of men in addition to our own. We do not require that the in dividual occurrences which have created our confidence, our misgiving, or our despair, should be committed to paper, arranged in columns, and embodied in sums or averages. For practical purposes we are satisfied with our own impressions. But should a doubt be expressed, and supported by a show of reason or experience, whether vaccination possess the virtue generally attributed to it ; should some new preventive measure or mode of treatment be recommended in cholera, as su perior to other plans previously adopted ; we ask for the specific facts which have seemed to warrant the doubts of the one party, and the recommendation of the other. If these facts are few, we naturally view them with mistrust, and are disposed to attribute them, at the best, to some coincidence ; or if, being more in number, their actual amount is stated in vague and general terms, we as naturally demand the precise figures. We feel instinc tively, that common and familiar words are altogether wanting in precision ; that they take their meaning from the character of those who use them ; that, in a word, " the sometimes of the cautious is the often of the sanguine, the always of the empiric, and the never of the sceptic ; while the numbers, 1, 10, 100, 1000, have but one meaning for all mankind."
But this mistrust of vague generalities of expression, is not the only form in which the more cautious and logical spirit of modern times embodies itself. The same misgivings are felt and expressed as to the propriety of committing the facts which are to serve as the materials of our theories to the uncertain keep ing of the memory. We feel that a science built up of such materials, bears to true science the same sort of relation which tradition bears to history. It may not be destitute of valu able truths and sound principles, but it must fail in that precision and delicacy of discrimi nation which forms the peculiar attribute of true science as of true history. The history of medicine abounds with examples of impor tant principles of treatment, and valuable re medies discovered solely by the light of experience, based upon the mere recollection of a number of individual occurrences. In this way the efficacy of bark and arsenic in ague, of mercury in syphilis, and of iodide of potassium in certain forms of secondary disease was discovered. Indeed, it may be confidently affirmed that all our knowledge of remedies is traceable to this source ; and it is probable that we shall continue to be indebted to it for all future discoveries of importance. It is the natural method of discovery, and, as such, will necessarily maintain its ground. But a very little reflection will convince us of the utter inadequacy of this method to meet the strict requirements of the science, and the ever-vary ing exigencies of the art of medicine. We may be able by its aid to sketch the broad out lines, and mark the salient points of a science, but we cannot hope to fill in the details with all the lights and shadows which go to make up the perfect landscape. Still less can we satisfy ourselves or others as to the real merits of disputed questions by an appeal to un written or loosely recorded experience. We all feel that there is no solution for our doubts short of an appeal to observations carefully and faithfully recorded, and summed up in the clear and simple language of figures. The use of mercury in syphilis, supplies us with an apt illustration of this truth. An experience, founded upon unrecorded and unnumbered occurrences, first recommended this remedy for the treatment of that disease ; but it would were applied healed much sooner than the others, and next to them the sores that were dressed with mercurial ointment. But of the ten patients to whom caustic was applied, no less than eight had buboes, whilst only one bubo occurred in all the others; and it happened in one of the patients whose chancres had been dressed with mercury. I thought also that buboes appeared to be less frequent from the application of caustic, where mercury had been previously given. This fell within my ob servation from time to time, with patients who had taken mercury, either of their or by the advice of others ; and appearing to be of importance, I was resolved to bring it like wise to the test of experiment, and the result was as follows : of forty-eight patients with chancres in an incipient state, and exactly as they occurred in practice, one half was treated in the manner I have mentioned, by destroy ing the chancres with caustic immediately on may being desired to see them, while all the others were put under mercury for eight or ten days before the application of caustic. In every other circumstance the method of treat ment was the same. The difference, however, surprised me exceedingly. Of the twenty-four treated with the immediate application of caustic, twenty were seized with buboes; while only three buboes occurred in an equal number to whom mercury had been previously admin istered." The subject of the treatment of syphilis has been selected for illustration on account of the large use which has been made of figures in discussing the relative value of the two modes of treatment; and the extract from the works of Benjamin Bell as a proof that, long anterior to any discussions among me dical men as to the value of the numerical method and the extent to which it might be applied in the solution of medical questions, men of shrewd common sense were driven to the use of numbers, as the natural and only means of solving difficult questions, and set ting doubtful or disputed points at rest. Thus much, by way of introduction, the difference of opinion which prevails as to the value of the numerical method seemed to demand.