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mate employment in aid of legislative or administrative purposes. On each of these heads M. Quetelet gives us a letter - short, indeed, and somewhat desultory; but abounding in useful and sensible remarks. Each of them would, in fact, require a treatise for its complete illustration.
A fool can ask questions, but only a wise man pertinent ones; and it often takes a wiser man to ask than to answer. After recommending to the statist a due and ample course of preparatory study of the subject in hand, our author goes on to observe, on the collection of statistical information:
• The principal considerations which should guide an administration as to the questions to be asked are the following:
. 1. Only ask such information as is absolutely necessary, and as you are sure to obtain.
62. Avoid demands which may excite distrust, and wound local interests or personal susceptibility, as well as those whose utility will not be sufficiently appreciated.
63. Be precise and clear, in order that the inquiries may be every where understood in the same manner, and that the answers may be comparable. Adopt for this uniform schedules, which may be filled up uniformly.
14. Collect the documents in such a way that verification may be possible.
Simplicity and clearness of demand, together with uniformity in the forms to be filled up, are essential conditions to obtain comparable results. Without them, no statistics are possible. When the question relates to ages, professions, or diseases, it is of the greatest importance to employ classifications perfectly identical, in order that the general information may be compared even to the slightest detail. The most perfect unity should reign throughout the whole. It is to establish a unity like this that in certain States, such as Belgium and Piedmont, central commissions have been formed to collect and arrange the different elements which should be included in the national statistics. The necessity of such institutions is particularly shown when we see in very enlightened countries the principal departments sometimes publish very different numbers to express the same things, or make classifications which render comparison impossible.. (Transl. pp. 196, 197.)
Not to secure facility for the verification of the documents we collect, is to miss one of the principal aims of the science. Statistics are only of value according to their exactness, without which they can serve but to establish error. Every statistical document requires a twofold examination — a moral and a material one; the former being, in all cases, by far the most important, as it involves the inquiry into the influence under which it has
been collected — a point on which the whole colouring of the docuinent essentially depends: —
During the war of independence, the United States carefully misrepresented the true number of their population : they exaggerated considerably the numbers of inhabitants in maritime cities, in order to put the enemy on the wrong scent. Assuredly no good appreciation of the American population could be founded on the documents of this period.' (Transl. p. 202.)
Every statistical document ought to carry on the face of it the exceptions, exemptions, and limitations, under which its entries are made. In respect of the use which may be made of it, negligence in this respect may amount in effect, if not in culpability, to a falsification.
• Thus, by means of official numbers, M. Sarauw pretended to prove that in the island of St. Croix, in the Danish Antilles, the mortality of the black slaves was less than that of white men even in Europe; and this assertion might appear so much the more im- . posing, as M. Sarauw resided in the island in question.'
This result (which was arrived at in good faith) rested solely on the omission of negro children dying before attaining their first year from the register of births, such children being exempt from poll-tax, and therefore their omission being deemed of no importance.
The material examination of statistical documents rests chiefly on the internal evidence they may offer of self-consistency. It is singularly aided by diagrams. A simple line, properly laid down from a consecutive series of numbers, by what is called graphical projection, enables us to appreciate at a glance the continuity and regular progression of their succession; and, what is of still more importance, to apprehend correspondencies between two series so projected, which often afford immediate conviction of a relation between them, such as the most subtle mind would find it difficult to perceive without such aid. They give to the study of phenomena the same advantage which algebra has introduced into calculation — they generalise and allow of abstraction; and they enable us at once to detect and often to rectify errors which, if undetected, would effect mean results, and throw every thing into confusion. We are glad to find M. Quetelet strong in his advocacy of this mode of dealing with a series of observations; though the generality of French savans affect, very unwisely, to despise it as inconsistent with their notions of mathematical rigour.
There is nothing more indicative of a man's fitness or unfitness for the duties of a legislator and a statesman than his manner of
VOL. XCII. NO. CLXXXV.
dealing with statistical documents. When appealed to, as they too commonly are, for the purpose of establishing extreme positions, or of lending support to party views, or to particular interests, we are continually reminded of the doctrine of one long accustomed to listen to such arguments. Nothing can be more
fallacious than theories — except facts!' Those who use them in this manner will be found invariably to sin against truth and common sense in one or other of the following ways, viz:
1. By “ having preconceived ideas of the final result.”
2. By “neglecting the numbers which contradict the result they “wish to obtain."
. 3. By “incompletely enumerating causes, and only attributing to “one cause what belongs to a concourse of many."
• 4. By “comparing elements which are not comparable.” To which we may add a 5th, the most common of all and the most inexcusable, viz. : singling out the extreme partial results . which tell on the side to be defended, and ignoring all the rest.
With such eclecticism we may find in statistics the means of defending almost every position. In politics, especially, they
• Become a formidable arsenal, from which the belligerent parties may alike take their arms. ... Some figures, thrown with assurance into an argument, have sometimes served as a rampart against the most solid reasoning; but when closely examined, their weakness and nullity have been discovered. Those who allow themselves to be frightened by such phantoms, instead of looking to them themselves, prefer rather to accuse the science than to confess their blind credulity, or their inability to combat the perfidious arms opposed to them.
* We see persons profoundly convinced of a truth, seek to establish it directly by the authority of figures, and give, as they think, a mathematical demonstration. However, by means of the statistical documents which they unskilfully employ, they most frequently produce an opposite effect to that which they desired. Thus we cannot reasonably doubt that enlightenment contributes to man's happiness, by illuminating his intellect and fortifying his morals. In the attempt to demonstrate this, what has been done? It has been thought necessary to establish that the number of crimes is inversely as the number of children sent to school - as if the number of crimes, even were it known, had as its only cause the greater or less developement of the intellect; and as if the developement of intellect were measured by the number of children sent to school. What has been the result of this? It has been found, after well examining statistical documents, that the number of crimes is more generally in a direct proportion to the number of children sent to school, than in the inverse proportion. The conclusion is exactly the opposite of what was at first desired a new error, which some have, with the same levity, admitted.' (Transl. p. 214.)!
The necessary incompleteness of all statistical documents is
s differ from the enumerates are
sometimes urged as a general argument against trusting implicitly to conclusions drawn from them. The argument is valid, in so far as we have reason to believe that the unenumerated cases differ systematically, i. e., in some essential point of classification, from the enumerated ; so as to render the proportions in which the several classes are represented in the returns different from what they would be were the enumeration complete. But granting their incompleteness — and granting even that the incompleteness is such as to affect injuriously the proportionate numbers in classified results—this does not preclude the drawing of many sound and valuable conclusions from such documents, if only we are assured that in comparing similar ones for several successive years, or under circumstances otherwise different, the same causes of incompleteness prevailed and continued to affect the several classes in an invariable ratio.
This position M. Quetelet illustrates by a reference to the Criminal Statistics of Belgium. - Prior to 1830 the official returns gave only the number of crimes known and prosecuted, but for the seven years from 1833 to 1839 they included also the number of crimes known, but which were not prosecuted because the authors were unknown. Now it was found that this latter number proceeded from year to year with even more regularity than that of crimes prosecuted. No doubt, therefore, the number of crimes altogether unknown to justice, could it have been made a matter of registry, would have presented a similar constancy. Of known crimes against person, two-thirds were regularly prosecuted, and one-third escaped, the authors being undiscovered. In the case of crimes against property the proportions were reversed, and were nearly those of one-fourth and thfee-fourths ; the graver crimes being those most sure of detection. On the whole it would appear from these records that out of 1154 crimes annually known to justice in Belgium, only 416, or little more than one-third, formed subjects of prosecution. Assuming, then, that the number of unknown crimes is equal to that of known (this would hardly be admissible for crimes against person), the amount of prosecuted crimes in Belgium would not exceed one-sixth of those actually committed.
I am absolutely ignorant and shall never know whether the crimes on which the tribunals have to pass judgment form the sixth or seventh or any other part you will of the total number of crimes. What is important for me to know is that this ratio does not vary from year to year. On this hypothesis I can judge relatively whether one year has produced more or less crimes than another.'
Admitting that this ratio remains invariable from year to year, and that justice pursues criminals with the same activity, two countries or two provinces of the same country might be compared in respect of morality. But as the latter condition almost certainly does not hold good under different administrations, it becomes impossible, from the official returns of prosecutions, fairly to institute such a comparison between nations, even should the same legislation, the same repression, and the same activity to bring criminals to justice, subsist. If the result be made to depend on a comparison of the number of condemnations, instead of those of prosecutions, a difference in the mode of trial would alone suffice to destroy the comparability of the cases.
We know, in fact, that the establishment of the jury in Belgium has doubled the number of acquittals.' (Transl. p. 227.)
On the subject of Medical Statistics, M. Quetelet has a brief, digressive, and somewhat pungent letter, and presents what must be confessed to be rather a deplorable picture of the actual state of this branch of the general subject.
• All reasonable men,' he says, ' will, I think, agree on this point, that we must inform ourselves by observation, collect well recorded facts, render them rigorously comparable before seeking to discuss them with a view of declaring their relations, and methodically proceeding to the appreciation of causes. Instead of this what do we see? Observations incomplete, incomparable, suspected, heaped up pell-mell, presented without discernment, or arranged so as to lead to the belief of the fact which it is wished to establish ; and nearly always it is neglected to inquire whether the number of observations is sufficient to inspire confidence.'
This is, no doubt, the impression which the perusal of the generality of medical books and dissertations leaves on the mind. The fact is, that in a science like medicine the statistical method of inquiry is not the most natural and obvious. Under circumstances of excessive complication in any line of research, and more especially in one in which success leads so directly to celebrity and fortune, men usually look for what Bacon terms • instantiæ luciferæ,' those luminous instances where the result of a single experiment, the striking issue of a novel process, makes its way at once to the inductive instinct without being subjected to the scrutiny of reason. The comparison of multitude with multitude, the destruction of errors by mutual collision, and the slow emergence of truth from the conflict by its outstanding vitality, belong to a maturer age of science than that in which medicine had its origin or attained its present importance. Yet there have not been wanting in its walks men