STATISTICS. From the numerous definitions of statistics which have been given since Achenwall, the learned professor of Göttingen, established this science and gave it a name, we might think that it is very difficult to define its nature and the extent of its domain. Such is not the case, however. The most different definitions have served as introduction to the most similar works, and the ordinarily informed person is no more ignorant than the adept, that, without figures, without "numerical terms", there is no statistics. The quantity of explanations, developments and deductions which can be added without encroaching upon some neighboring domain, is all there can be any discussion about.
—The question whether statistics is a method or a science, as if it could not be both, will also be discussed. As a method, it is an instrument of observation; instead of saying that the use of such and such a remedy succeeds often or sometimes in such and such a disease, the professor of medicine should say to his pupils: According to the experiments made up to the present time, the remedy has produced its effect in 63 cases out of 100, or in such and such a settled proportion. As a method of observation, it is applied only to large numbers. To speak of 33 per cent. or of 25 per cent. when only three or four experiments have been made, is to abuse scientific forms, and sometimes knowingly to deceive the public.
—As a science statistics embraces all social and political facts presented in their numerical relations to one another, as well as to space and time. As there is no political or social fact without men, we need not add, as certain authors have done, that all statistical facts must have relation to men.
—It seems that there are here well-determined limits, and that there is no need of so many definitions. If no author has been satisfied with the definition of his predecessors, it is not because he wished to see his own figure in the introduction to treatises on statistics; it is because statistics, since its origin, has followed a two-fold tendency. The one gave rise to descriptive statistics, as Achenwall defines it: the thorough knowledge of the respective and comparative situation (status) of each state; or of which Schlözer said that it was history at rest, while history is statistics in motion (in other words, statistics is the situation of a people taken at a given moment); finally, what Napoleon I. called the budget of things. Statistics thus understood is a more or less reasoned inventory. The other tendency which statistics has followed would prove relations, discover laws; it is what, in the last century, was called political arithmetic. It was probably from this point of view that Goethe viewed it when he said: "If figures do not govern the world, they show at least how it is governed." For this purpose the inventory is not sufficient; it is necessary to go to the bottom of "numerical terms", to scrutinize them, compare them, draw deductions from them; according to some, averages, and according to others, laws. Here is M. Guerry's definition: "General statistics * * excludes descriptions, and consists essentially in the methodical enumeration of variable elements, whose average it determines". And M. Dufour's: Statistics is "the science which teaches how to deduce from analogous numerical terms the laws of the succession of social facts".
—Thus, some make of statistics a descriptive science more or less allied to geography; others, a science of deduction, employing mathematical processes, and notably the calculation of probabilities. We believe that it is very easy to combine these two points of view. People always commence by describing the present; this is one of the forms of established statistics. When many descriptions have succeeded one another, it is possible to compare the present situation with previous situations; this is done for the whole of the facts as well as for one of the details; from this comparison is drawn a theory, averages, laws; and this is how the form of statistics, once called political arithmetic, is developed.
—This term leads us to the consideration of another subject of discussion. Are "numerical terms" applicable to political facts or to social facts? William Playfair says of statistics, that it consists of investigations into the political material of states. The definitions of Penchet, Gioja, Schubert, Quétélet, Villermé and many others, insist chiefly upon the political application, while, with M. Dufour, M. Moreau de Jonnès applies statistics only to social facts. He says: "Statistics is the science of social facts, expressed in numerical terms. Its object is the thorough knowledge of society, considered in its elements, its economy, its situation and its movements". Nevertheless, the discussions maintained as to the distinctions between the political domain and the social domain, are so trifling that perhaps none of the authors whom we have cited have had the least scruple to pass from "political facts" to "social facts", and vice versa. Moreover, are not these two categories of facts most frequently confounded? We will not stop, therefore, at these useless distinctions.
—Let us limit ourselves to a few words upon another point, which has been very much debated. M. Moreau de Jonnès maintains that "statistics without figures, or whose figures do not enumerate social facts, does not merit the title which it borrows". Statistics without figures is like a river without water, but a statistics consisting only of figures is not the ideal one; in this shoreless sea, where can the ship land? A text is therefore necessary. But there is no general rule as to the amount of explanations which must accompany the "numerical terms". In addressing specialists, accustomed to study political and social questions, few should be given; they should be given more amply when it is intended to enlighten or convince that portion of the public whom figures repel, and who find "numerical terms" very dry, and, to speak plainly, perfectly wearisome. It is therefore only a matter of judgment, of tact.
—This settled (and we have commenced by clearing the ground of obstacles easily removed), we approach a much more delicate point. Let us again quote an author: we are so fond of leaning upon something, even upon a cane which bends under our hand. M. Moreau de Jonnès says: "It [statistics] proceeds constantly by numbers, which gives it the character of the precision and certainty of the exact sciences". This is a quality which people do not tire of denying to statistics. Rightly or wrongly? Rightly and wrongly. In fact, numbers are always precise, but they are not always exact. It is not difficult, however, to know what figures are exact and what are not; we have only to find out how they were obtained. That is the whole secret. If the verification has been made in a positive and material manner, by counting, measuring and weighing, the exactness is absolute, and no one has the right to attack such figures, unless because of false entries in the public accounts. A great deal of information is obtained in this manner for the wants of public administration. Thus the amount of the finances rests upon mathematical elements, and error is impossible. The case is about the same with the statistics of hospitals, prisons, births, marriages and deaths, justice, means of communication, the post-office and other similar things. But there are statistics, like those of agriculture, industry, consumption, the revenue, and, in general, of all facts which can not be determined by exterior, palpable signs, which often leave something to be desired on the score of exactness, and give occasion for serious criticism. However, there are two kinds of exactness; one is absolute, the other approximative. The approximation is a makeshift; but at bottom it is makeshifts which rule in life; the absolute contrary of the makeshift would be the ideal. But we do not insist upon this. Every one understands that approximation is sufficient for almost every use, even when there is question of information which can be obtained with great exactness. For example, if we should say: The budget of receipts is 2,450,000,000, would it not be generally satisfactory? and would it be necessary to give it to a cent? We said, for almost every use, and notably for the descriptive part of statistics; mathematical exactness is indispensable only when it is intended to state laws. For the rest, it is necessary to beware of the evil tendency of certain authors to set up statistical laws, and to have ever present to the mind that an average is not a law. Averages only show that there are constant relations between such a fact and such another; this constancy permits us to think that these relations are necessary, and often this conjecture will be seen to be well, founded, but the indication of figures has need of confirmation. Therefore, leaving out of the question all bad faith, there are statistics naturally exact, and others more or less so, according, 1, as the external signs of the facts to be collected are more or less evident; 2, as individuals are less interested to dissimulate; and 3, as agents bring more skill, knowledge or conscience to bear upon their statements. But there is also a secondary cause of inaccuracy, or rather of apparent contradiction, in the statement of statistical facts, namely, that different figures often bear the same title. It often happens that one lays stress, without knowing it, or saying so, upon the net product, another upon a gross product, a third upon a product still more gross. Again, one will understand by the word England only the country which bears that name, a second will add to it the principally of Wales, a third the islands, a fourth may go so far as to confound England with Great Britain or even with the United Kingdom: this confusion often occurs in ordinary conversation. We could cite examples by the hundred in which there was no question of ignorance, or of bad faith, or of negligence, but of too great conciseness or a lack of precision.
—These examples explain, in some measure , the reproach so often brought against statistics, of furnishing arms at once both for and against the same proposition. To the extent that this reproach is founded—and this extent is not large—it is deserved by the statistician, and not by statistics. Thus, the art of grouping figures is only a branch of the art of maintaining all theses, of having arguments for all paradoxes and all sophism. When one wishes to defend his point of view at any cost, he chooses figures, or makes some prominent, and leaves others in the shade. The enthusiastic man may sometimes proceed thus with the best faith in the world: passion blinds. Still, beyond the art of grouping figures, there remains also, to justify the difference of conclusions, the possibility and even a certain facility of interpreting the same fact in different ways. It is wrong to say of a fact or of a set of figures that it is brutal. A man stretches out his hand to another: is it to give him an alms or a thrust with a dagger? A man places a sum of money in the hand of his companion: how will you interpret the act? Is he giving aid, or the price of a crime? In such a year 100,000,000 kilogrammes of meat were consumed in Paris: was it evidence of plenty or of dearth? The fact or the figures alone mean nothing; it is the interpretation which renders them eloquent. Now, the field of interpretation is vast, and commentators can often launch out in opposite directions; so much the worse for the one who is deceived and for those he deceives. To sum up: if statistics gives arms for and against, it is not because of the nature of statistics, but because of the nature of our mind, for the same reproach is applied to religion, philosophy, the law, and to all moral and political sciences, and, in a less degree but still in a degree great enough, even to the sciences called exact.
—Statistics must have a very certain utility, if it has been able to withstand all the attacks of which it has been the object, attacks which embrace in their generality at once the accurate part and the inaccurate part of the science of "numerical terms". In fact, it remains always true that statistics is the budget of things, that inventory which no government can dispense with. It is no less true that the comparison of many well-proven facts makes us find, or at least catch a glimpse of, truths which might have escaped us. The faults of the instrument impose upon us a prudence which is nowhere out of place, but do not oblige us to renounce its employment. Fortunately, it is not with this instrument, as with many others, whose use is prohibited for fear of abuse. The person who does not know how to manage it, does not touch it, therefore no one will be wounded through his awkwardness; the only inconvenience which it can have is to remain inert in hands which have not learned the use of it. In other words, figures are a language which everybody does not know how to read, and from which few know how to draw all the information contained in it..