In the observation and collection, therefore, of the individual phenomena or events which are to serve as materials for our average re sults, the first precaution to be observed is, that those phenomena or events should be strictly comparable as regards the combination of causes by which they are brought about ; or, as the French statists express it, we must ensure " de l'ensemble des causes possibles." The frequent omission of this most necessary precaution has given birth to the dogma of Morgagni — Non num erandese sed pendenclee cunt observationes — and to the most valid objections urged against the tion of the numerical method in medicine.
For the collection, arrangement, and classifi cation of the facts which are to form the ma terials of our averages, no concise rules can be laid down. The tabular forms must adapt themselves to the exigencies of each individual inquiry ; and must be more or less compli• cated as the subjects of investigation con sist of few or many particulars. In reporting cases, for instance, and in collecting and analyzing those recorded by others, tabular forms embracing many particulars are re quired ; and the preparation of' such forms demands unusual skill and care.* The same remarks apply to the collection and classifi cation of recorded experiences and opinions bearing on particular subjects of inquiry t ; a numerical summary of authorities favourable and adverse to particular doctrines, consti tuting what may be not inaptly termed the statistics of opinion.
2. Of the average and extreme results de duced from observation.—The observer having exercised all due care in the observation of his facts, having grouped together only those events which owned the same combination of antecedents or causes ; and having further correctly performed the work of enumeration, has thus obtained certain average and extreme results, which are to constitute standards of comparison and data for reasoning ; the question naturally arises—are these average and extreme results sound and trustworthy standards and data, or not ; and what are the circumstances which render them the one or the other ? Common sense and experience combine to give an authoritative answer to this question. Our average and extreme re sults are more or less sound and trustworthy, as the individual facts from which they have been calculated are more or less numerous. Where the facts upon which it is attempted to found a general principle, or to establish a standard of comparison, are very few, we are at once conscious of their insufficiency ; and the more readily when an attempt is made to apply the principle or standard in question to some important practical purpose. A better illus
tration of the futility of such an attempt can scarcely be found than the well-known test of Ploucquet. That author proposed to deter mine whether or not a child was still-born by referring every doubtful case to a standard of comparison, founded upon three observ ations of the relative weight of the lungs and body ; of which three observations, one was made upon the body of an immature infant, so that the subjects of the observations were not strictly comparable. Though Ploucquet, in this procedure, offended against two of the most obvious statistical rules, his test con tinued to be treated with undeserved respect, till comparatively recent investigations on a larger scale had demonstrated the little re liance to be placed upon it.
The most common attention to the ordinary daily occurrences of life would suffice to caution us against such errors as that into which Ploucquet fell. Coincidences of the most startling character are constantly happening to put us on our guard against them. One which occurred to the writer of this article deserves to be put on record. Two cases of congenital absence of the larger pectoral muscle on the same side of the body, oc curred, on the same day, among the out patients of the King's College Hospital. This defect he has never happened to observe within the wards of that Hospital or else where, either before or since. A similar coincidence, though of a less striking cha racter, presented itself in the same institution while the writer was noticing with some care and interest the complexion and physiognomy of patients suffering from pulmonary consump tion. his own previous experience, in con formity with the general opinion, had pointed out the fair complexion as that of the great majority of phthisical patients ; but the almost exclusive occurrence for several days together of the olive complexion, among patients labouring under that disease, had almost led him to discard his former opinion and that of the best authorities, and to embrace one which, as farther observation convinced him, would have been erroneous.