STATISTICS. 



805 



multitude of causes, has been urged as an ob- 

 jection to the introduction of the numerical 

 method into the service of those sciences. 

 It is admitted, that the use of numbers and 

 averages by the astronomer who deals with 

 the more simple relations of matter, such as 

 magnitude and relative position, and by the 

 engineer who avails himself of its more simple 

 properties, such as its hardness, tenacity and 

 elasticity, have contributed to make the science 

 of the one perfect, and the art of the other 

 safe ; but it is contended that the use of num- 

 bers cannot be extended beyond such narrow 

 limits with safety or advantage, and that medi- 

 cine and political economy lie beyond these 

 limits. The actual practice of mankind, founded 

 upon an instinctive perception of the necessity 

 of employing figures in the service of the phy- 

 sician and statesman, may be fairly alleged as 

 a sufficient answer to this objection ; but a 

 little consideration will serve to show its 

 futility. 



In the first place, it is self-evident that the 

 exclusion of figures from the service of medi- 

 cine, does not bring about the disuse of those 

 very facts and events which are objected to as 

 unfit to be employed as statistical or numerical 

 elements. The physician will still persist in 

 stating and recording the results of his expe- 

 rience. He will still assert that he has sometimes 

 observed this symptom in a certain disease, 

 that he has often found that remedy beneficial, 

 that he has almost never known such and such 

 a mode of treatment to fail. Those who con- 

 tend for the use of numbers in medicine, 

 merely insist on the necessity of reducing the 

 sometimes, the oflen, and the almost never to a 

 more correct and intelligible form of expres- 

 sion ; and they argue that it is utterly incon- 

 sistent to object to the use of facts as mate- 

 rials or elements of numerical propositions, 

 and yet not to censure the use of these same 

 facts as foundations for loose and inaccurate 

 verbal statements. From this dilemma there 

 is obviously no escape. But, though the ob- 

 jection itself is futile, the misgiving of which 

 it is the exaggerated expression is natural and 

 well founded. It cannot excite surprise that 

 the individual facts or events which own so 

 many concurrent causes should be regarded 

 as requiring, on the part of the observer, a 

 greater degree of care in verifying, recording, 

 collecting, and arranging them than would be 

 necessary in the more simple cases already 

 adduced ; and that both the facts themselves, 

 and the numerical expressions in which they 

 are embodied, should be viewed with a pro- 

 portionate degree of distrust. From this mo- 

 derate and reasonable view of the case, no 

 advocate of the numerical method will be 

 found to dissent. On the contrary, he will 

 seek to strengthen it by giving due promi- 

 nence to each separate ground of misgiving, 

 and by laying down stringent rules for the 

 guidance and governance of the observer. 

 Before proceeding to detail some of these 

 rules, it may be well to advert to a probable, 

 and, indeed, obvious cause, of the distrust with 

 which numerical data are sometimes regarded. 



Indiscreet advocates of the numerical method 

 have sought to apply the general results of 

 collections of cases expressed in the language 

 of figures to the treatment of individual cases 

 of the same disease, without making allowance 

 for those differences between case and case 

 which confessedly existed in the collections 

 themselves. They have used a general prin- 

 ciple, as if it had been a rigid and unbending 

 rule of action; forgetting that though, as the 

 experience of assurance offices abundantly tes- 

 tifies, the general results obtained from a large 

 number of individual facts may be safely re- 

 applied to an aggregate of facts of the same 

 nature, they cannot be brought to bear on a 

 single case, or on a small number of cases, 

 without the greatest danger. Each case must 

 be viewed in practice, first as a generality 

 governed by some large law of prognosis, 

 diagnosis, and treatment ; and secondly, as a 

 specialty demanding a careful consideration of 

 all its peculiarities. 



Among the rules which ought to govern the 

 observe/in the collection of facts destined to 

 form the elements of averages, there are some 

 of so simple and obvious a nature as to re- 

 quire no discussion. Such are, the previous 

 preparation of some simple and available form 

 of register, by means of which the several facts 

 may be committed to paper at the very time 

 of observation, so that nothing may be trusted 

 to the memory ; the careful selection of the 

 facts themselves ; the shaping of the inquiries 

 which may be necessary to elucidate those 

 facts as nearly as may be in the same terms ; 

 the avoidance as much as possible of such 

 leading questions as would be likely to bias the 

 respondent, when the facts in question, like 

 most of the particulars which make up the 

 history of diseases, are dependent upon testi- 

 mony ; and especially the purging of the ob- 

 server's own mind of prejudices and precon- 

 ceptions in respect of the subject of inquiry. 



The careful selection of the facts which are 

 to form the materials of our averages is by 

 far the most important of these rules, and 

 one which demands a little further consider- 

 ation. If we consider the facts we are ob- 

 serving in the light of phenomena, or events 

 brought about by a multitude of concurrent 

 causes, it will be obvious that care will re- 

 quire to be exercised, not so much in verify- 

 ing each phenomenon or event as that of 

 which we are in search, as in ascertaining that 

 all the concurrent causes or conditions are, 

 or have been, in operation to bring about that 

 phenomenon or event. The absence of a 

 single cause or condition will vitiate the in- 

 dividual fact, and impair or destroy the value 

 of our average results. A few illustrations 

 will suffice to show what is here intended. 

 We are anxious to determine the true average 

 frequency of the pulse in adult males, in a 

 state of rest, and as free as possible from the 

 influence of all disturbing causes ; but, either 

 from ignorance or oversight, we count it in- 

 differently in every position of the body, and 

 at all times of the day. In this case, our facts 

 cease to be comparable facts ; for it is well 

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