THE SCIENTIFIC TREATMENT OF STATISTICS.* ON the subject of statistics
Mr. Galion writes with an en- thusiasm well warranted by the results of his long and costly investigations in a field of inquiry that has hitherto possessed but little attraction for the scientific mind. He speaks of their " beauty and interest," and asserts that' " whenever they are not brutalised but delicately handled, and are warily inter- preted, their power of dealing with complicated phenomena is extraordinary." " They are the only tools," he adds, " by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the science of man."
There can be no doubt that the claim is a just one. Deduc- tion from biological or psychological principles—to confine our remarks, as Mr. Galton does his book, to human statistics —will afford but scanty aid towards solving the problems presented by human society, or ascertaining the laws that govern it, static or dynamic. Inquiries of this kind must be conducted on the inductive method, and the translation of the infinitely varied and countless 'details of observation into manageable generalisations is a task of extreme and novel difficulty, the execution of which Mr. Galton has not only facilitated in a degree -far beyond what statisticians a decade or two ago conceived as possible, but has practically thought out methods that constitute, in fact, a new science.
In the present volume, in which, even more amply than in his previous works, Mr. Galton has displayed a curiously unique originality, combined with a singular keenness of intellectual vision and a marvellous power of dealing with wide areas of minute details, the inheritance of ordinary qualities by multi- tudes rather than by individuals is considered. The principal questions the inquiry raises relate to the statistical regularity of great populations during a long tract of time, the degree in which the descendant resumes in himself the characteristics of his ancestry, and the precise meaning or numerical value of kinship. To none of these questions can definite or:detailed. answers yet be given, nor does Mr. Galton attempt to give such; he rather contents himself with showing upon what.
• Natural Inheritance. By Francis Galton, F.R.S. London : Macmillan and CO. methods alone the investigation can be successfully conducted. It is with natural as distinguished from acquired qualities that he deals,—that is, qualities not due to, though often more or less brought out through, education and circumstances. His theory of heredity is that of " particulate" inheritance, which means the building-up of the individual out of " particular" elements or groups of elements derived from his ancestry. Not that the individual is wholly composed of such elements, for the family likeness is more or less modified by individual variation, and is further diversified through the occurrence of " sports," often of a stable character. And the aim of human statistics may be said to be the determination in the first place of how much of the individual is due to his ancestry, how much to his parentage, and how much to the incidents, intrinsic and extrinsic, of his existence ab ovo ; in the second place, of the derivation of the characteristics of populations, groups, fraternities, or collections of brothers and sisters, and co- fraternities, or groups formed of fraternities born of parents having a common mean characteristic (or group of charac- teristics). The method is mainly a graphical representation of the elements of statistical tables drawn up in a suitable manner, the inconvenience caused by the difference of sex (where present) being first got rid of in a most ingenious way by transmuting all female measures into male measures by a very simple operation. Thus, in relation to stature, it is known that women are to men as 100 to 108, and female statures are con- sequently transmitted into male by multiplying them by 108, or, what is sufficiently exact, by adding an inch for each foot (one-twelfth) to the female statures. From the tables thus freed (where necessary) from the disturbance of sex-difference, schemes of distribution—i.e., of the quality (or faculty) in- vestigated among the cases examined—are constructed, of which the essential feature is a curve connecting the points of intersection of abscissae and ordinates drawn from stations on the axes representing successive tens of cases on the one, and successive tens of units of the quality (or faculty) on the other,—or cases and units of faculty in any prearranged relation to each other. The height of the curve above the horizontal normal, and the general slope of the curve, • give a strikingly effective diagrammatic picture of the distribution as a whole, while the perpendiculars from any point of the curve to the axes perform a like office for the details. From such schemes, with the help of geometrical construction, combined with the application of algebraic and differential processes, a wealth of new knowledge is obtained. In the chapter discussing the data of stature, and in the appendices at the end of the volume, especially in appendices B and F, where some of the more important mathematical problems presented by the subject have been worked out by Mr. J. D. Hamilton Dickson and the Rev. H. W. Watson,
• the mathematical methods used in the inquiry are well illus- trated. In the same chapter, the nature of Mr. Galton's method is fully exemplified, and it is to be regretted that the language is much too abstract, condensed, and mathematical to be comprehended by those who are neither acquainted with the principles of the calculus nor familiar with Mr. Galton's statistical writings. It would be quite out of place to attempt any further exposition of the method in its higher aspects here. Suffice it to say that by the operations above indicated, the number of the units of a quality which answers to a median (mean) grade of the subjects thereof, that is, which is as often exceeded as fallen short of, and the degree of variability of a quality may always be found. These are two principal quterenda in statistics, from which many important propositions follow.
In the chapter on stature, a quality peculiarly susceptible of statistical treatment, the accuracy of Mr. Galton's method is proved by its yielding the same results (barring small errors) as a purely mathematical treatment of the tables. Like eye-colour, artistic tastes, and many other qualities, stature appears to have no influence on marriage selection. Therefore, parents are as often unlike as like in stature. If dealing with unlike parents, we transmute the wife's stature into male stature, and then create a personage half-way as to stature between the husband's and (transmuted) wife's stature .(mid-parent), the manipulation of the tables shows that filial variation in stature has relation not to either parent, but to the mid-parent. If P denote the mid-stature of the general population, it will be found that the members of a fraternity tend to approach P, and, indeed, to approach it nearer than their parents. In other words, the more mediocre the parents are, the more their children resemble them. Probably the converse is also true. This " regression," as it is termed, is a remarkable fact, and explains the great preponderance of mediocre individuals, so great that even " an exceptional man," says Mr. Galton, " is more frequently found to be the excep- tional son of mediocre parents than the average son of very ex-, ceptional parents." In fact, regression tells heavily, to use Mr. Galton's language, against the full hereditary transmission of any gift, and the ablest of all the children of a few gifted pairs is not likely to be as gifted as the ablest of all the children of a very great many mediocre pairs. In fact, the great tendency of man is constantly to approach P, whether in stature or in any other quality; hence, notwithstanding individual varia- tion, the proportions having particular qualities tend to be constant, individual peculiarities being blotted out by the flood making for mediocrity. It is further clear that the variations shown by human statistics of different qualities tend to assume a normal character,—that is, such a character as they would have were they subjected wholly to the chance accidents of circumstance. Indeed, so great is this tendency that, in respect of the qualities forming the subjects of the statistical inquiries undertaken by Mr. Grafton, the mathematical calculations applicable to error and pro- bability—that is, purely " accidental " variability—were found suitable, and on being employed to bring out results closely approximative to those derived from observations.
In fine, we are to a very large extent, if Mr. Galton's con- clusions be accepted, the creatures of what is called " chance," through the accidents of circumstance daring which our ancestors and ourselves have lived. Not, ib must be added to avoid misconceptions, of the circumstances of our own life only, but of the life of the whole stock whence we derive. However, there is a residue of individual "peculiarity," which perhaps may be regarded as a quasi-chemical product of the "particulate" elements that in each individual come, more or less, into new combinations. Among these "particulate " elements must be many which were ancestral " peculiarities ;" so that, after all, so far as we are chance complexes, we are complexes of elements not themselves wholly of an accidental character.
Here we must take leave of this volume. Fascinating as it will be found by those competent to understand it, even at their hands it will require careful and concentrated study. But the book is well worth the time and trouble needed to master it. It lays the foundations of what one day will be a great science, one that will not merely satisfy scientific curiosity, but will be eminently useful to society. No class or category of facts will be excluded from its field, and the great and fruitful truths that lie hid in the masses of statistical tables extant and to come will be brought into the light. For the present its utility is most visible in relation to human statistics, and by the methods indicated by Mr. Galion, if we only get together the requisite data, laws of individual, groupal, and even national history may be estab- lished, and forecasts rendered possible of the greatest interest and value. Thus, it is already clear that the equalisation of conditions, to which we are evidently tending, increases the amount but raises the level of mediocrity. How far this is, on the whole, a gain, cannot be determined until the degree in which P the mean of mediocrity itself is capable of elevation, is approximately known. For this purpose, suitable statistics must be collected for some generations. The time is near at hand when the methodical tabulation of social facts and their manipulation according to scientific processes which, like those employed by Mr. Galton, give real knowledge instead of meagre averages that are little more, at the best, than aids to memory, and are often directly injurious by their misleading character, must be undertaken by the State.
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