Divination by Statistics

IT is fairly obvious that the study of statistics is not exactly what would be termed a popular pastime. Mr. Eugene Richard White, in his telling article in the December Atlantic, protests that they stand foremost among our modern plagues. Librarians do not discover any extensive demand for statistical literature. Sir John Lubbock, if I remember rightly, found no place for a single volume of figures in his hundred best books; and in that flood of articles on Books That Have Helped Me, by authors great and authors small, the same significant silence seemed to be maintained. There were some very curious books that had apparently proved helpful to certain persons, but there was unbroken testimony of a negative kind that nobody had ever been helped by a blue book. To say of anything, “ As dry as statistics,” is at once to consign it to the nethermost Limbo of Aridity. Such is the verdict upon the finished statistical product. As for the methods employed in constructing such tables, — weighted averages, index numbers, or curves of error, — these, to the wayfaring man, are hidden and ingenious refinements of cruelty, to be avoided at all hazards, or at least forgotten with a shudder and a prayer.

This aversion to statistics is doubtless founded in part in sheer mental laziness, or what is more decorously termed the economy of mental effort. The comprehension of statistics puts a heavier strain than common on our attention, and from our earliest experience with the multiplication table we are predisposed, like high Heaven, to reject

Were this, however, the only grievance cherished against statistics, the case would be bad enough in all conscience ; but there is a graver one in reserve. They have the reputation not only of palling on the spirit, but of commonly misleading the judgment. The former could issue in nothing worse than neglect, but doubt as to their veracity results in downright skepticism regarding them. One might reasonably toil after an exacting guide, if only the promised mountain prospect were assured ; but who is going to climb when the reward is a crevasse, or at best a mirage ? So it comes about that the statistical argument is frequently powerless against the popular adage that “ anything can be proved by statistics.”

If this extreme view of the matter seem to be unduly disparaging to a scientific method of inquiry, and to argue small discrimination on the part of its critics, it is encouraging to remember that the ordinary run of men, by their actions, give the lie to their avowed distrust of all statistical induction. The veriest skeptic in this domain loses little sleep over his insurance policy, I suppose, provided only he has met his premium payments ; and insurance of all kinds rests obviously, in the last resort, on the reliability of statistics. Blind unbelief in their trustworthiness is “ sure to err,” and the sweeping condemnation we sometimes hear visited upon them, like the Psalmist’s unsparing impeachment of human veracity, is likely to be the result of haste.

This is very far from denying that much of the skepticism felt toward statistical conclusions has been amply justified. Indeed, it is just this perversion of statistics that I desire to trace. But it is only fair to set in the forefront a grateful recognition of their exceeding great services in a hundred fields of scientific endeavor. Apart from all particular uses they subserve, they have contributed to the mental furniture of this generation a certain definiteness of apprehension of which, very likely, we are for the most part unconscious. It becomes apparent, however, when we reflect that two hundred years ago, for example, it was not only impossible to say numerically what the population of England was, but even to know whether it was growing or falling off. The high mortality in years of epidemic had given color to the notion that the population was diminishing, and there were not wanting alarmists who seriously proposed polygamy as a temporary expedient to remedy the imagined danger. The absence of statistical data explains the appearance of such tracts as Britannia Languens (1680), all voicing the complaint of England’s industrial decay. Nor were the mouths of these prophets of evil effectually stopped until Sir William Petty put forth his Political Arithmetic, grounded largely on statistical calculations. But even then the closest approximation to exact knowledge of these matters was the estimate of the expert, based on chance scraps of fact such as the records of baptisms or burials. Even so recently as a century ago the population of every state in Europe was mainly a matter of conjecture. As for any accurate knowledge of the distribution of population according to age, sex, race, occupation, or of such matters as the growth of population, the movement of prices, of trade, of wages, — this was simply terra incognita.

It goes without saying that to-day the man of average intelligence, while he may not be versed in the figures or averages of the last census, has in his mental make-up a numerical framework, more or less exact, in which, unconsciously, the main facts of political and economic geography comfortably pigeonhole themselves. The pedant and the precocious schoolboy often rudely flutter these statistical dovecots; but while we may find difficulty in keeping them in repair, we are most of us agreed that it is impossible to dispense with them altogether. If at times we are tempted to complain of the mutability and uncertainty of our statistical knowledge, we must needs cease complaining when we survey the unirradiated mist of ignorance which cloaked our great - grandfathers’ vision of things statistical.

The odium anti-statisticum of which mention has already been made is generally explained by statisticians upon grounds much too narrow. Sometimes, it is true, erroneous deductions have been made, upon the basis of inexact or fragmentary data. Sometimes, from reliable data erroneous conclusions have been drawn. Both errors account for some part of the widespread distrust of statistics. But this distrust must in part be traced to two other sources : first, to the towering interpretations which have been foisted upon statistics : and second, to the persistent and commonly unfruitful use of statistics in approaching questions not to be solved with their aid. It is these last two sources of unbelief with which, in this paper, we shall be concerned.

Gottfried Achenwall (1719-72), the so-called father of statistics, although his title rests largely upon his invention, or rather his domestication, of the word Statistik, is, fortunately, not chargeable with either of these errors. He was satisfied with a comparatively modest view of the function of statistics. In his lectures at Marburg and Göttingen he employed statistics simply to define more sharply the outline sketches he gave of the political and industrial geography of Europe. He was a sort of political Baedeker, not content with a mere qualitative description of realms and peoples, but conscientiously bent upon recounting their exact numbers, their military strength, and their precise industrial vocations. In his simple conception of the matter there appears that amusing, halfpedantic German Gründlichkeit which is still so strong among their university traditions. I remember an American student who lately took his degree in a German university, and who grumbled over the way in which the acceptance of his really able thesis was postponed time and again until it was supplemented with the most recent census figures. Said be to me in some indignation, “ Why, old Teufelsdröckh wouldn’t accept a copy of the New Testament itself unless it was evgänzt with the latest statistics.”

But while Achenwall’s narrow conception of statistics was a perfectly safe one, it would never have proved very fertile. It is owing to a contemporary of his, a Prussian military chaplain named Süssmilch (1707—67), that statistics became the exponent of the numerical laws of population. But this result of his studies, though of cardinal importance for statistics itself, was by no means the immediate object of his quest. In 1743 he published a book entitled Reflections upon the providential Ordering of the numerical Variations of the human Species, proved by its birth, death and marriage Rate. This work is said to have been used as a required textbook in Austrian universities until 1846. As the title would suggest, it is as though Butler had written an arithmetical Analogy, or Paley a volume of mathematical Evidences of Christianity. It is withal uncommonly ingenious in places. Thus, that to every twenty-one sons born there are born on the average twenty daughters, whereas at the marriageable age the two sexes, owing to the greater mortality among males, are numerically equal, is for Süssmilch a corroboration of the divine origin of monogamy. The exceedingly small excess of men over women had been cited long before in England by Captain John Graunt, in his Observations upon Bills of Mortality, as a certain indication of the divine disapproval of current " irreligious Proposals of some, to multiply people, by Polygamy,” though the worthy captain is rather graveled to explain why the same numerical equality of male and female does not bespeak the divine disapproval of polygamy among “ Foxes. Wolves and other Vermin Animals.” The outcome of Süssmilch’s work, however, was to cast into the public mind the idea that movements of population are subject to law, and predictable with great exactitude. From this fountain there issued forth water both sweet and bitter. There was given a great impetus to the study of social aggregates, but the attempt to “ justify the ways of God to men ” statistically was gradually discarded. Like other specific arguments from design, it withered under the breath of the Zeitgeist ; and though for a time tolerated as a pious fraud, it was finally repudiated as a pompous failure. In less than a century thereafter the pendulum had taken a long swing to the farthermost point in the opposite direction, and statistics had been made to yield a seeming support to a materialistic as well as fatalistic interpretation of history and society. The scent of this paradox hangs around statistics to this day, and accounts for much of the distrust which many people entertain for statistics generally. Its rise and progress, therefore, are matters of some moment.

The ferment of the French Revolution was congenial to a materialistic conception of history. Condorcet, in his Esquisse d’un Tableau Historique des Progrès de l’Esprit Humain (1794), had declared that general laws, regular and constant, govern the development of the intellectual and moral faculties no less than the phenomena of the physical universe. Even Kant, some ten years earlier, in his proposal for a cosmo-political history, had declared, notwithstanding his metaphysical reservations in favor of volitional freedom, that human actions are as completely under the control of universal laws of nature as any physical or chemical occurrence. It remained for Quetelet (1796-1874), the versatile Belgian statistician, to deck out these abstract doctrines in an attractive literary garb, and lend them the seeming sanction of statistical evidence to make the new conception common property. In 1836 Quetelet published his treatise Sur l’Homme et le Développement de ses Facultés. It consisted of two distinct parts. The first contained tabulated and averaged statements of the growth of the physical and moral qualities of the average man, while part second gave Quetelet’s version of the nature of society itself. It is only fair to say that Quetelet believed in the possibility of social betterment, and was far from looking on society as a wooden automaton that may be studied, but not altered or stopped. But in his anxiety to make out a strong case for the regular recurrence of social phenomena, he uses expressions which suggest the fatalistic view of society; and, unfortunately, these expressions are charged with a tenacious vitality, — hard to forget, easy to misread, and, if we may judge by the example of two eminent English historians, worthy of all adaptation. In speaking of the almost unchanging number of criminal offenses committed yearly, Quetelet remarks : “ A tribute which man pays with more regularity than that which he owes to nature or to the public treasury is that which he pays to crime. Triste condition de l’espèce humaine ! ” And again : “ Experience demonstrates that it is society which prepares the crime, and that the offender is only the instrument which executes it. It follows that the unfortunate wretch who mounts the scaffold or who dies in prison is, in a certain measure, a propitiatory victim of society. His crime is the fruit of the circumstances in which he is placed.”

This view of human society as the matrix of the criminal and the genius has had an overpowering attraction for some thinkers, from Buckle to Lombroso. The former, it will be remembered, made it the foundation of his exact science of history, and avowed that statistics, “ though still in its infancy, has already thrown more light on the study of human nature than all the sciences put together.” And Mr. Lecky, an historian of vastly more penetration than Buckle, and who would dissent most radically from a fatalistic philosophy of life, has also scorched his wings at Quetelet’s candle. Referring to the necessity as well as the extreme difficulty of maintaining the domestic hearth inviolate, he tells us, in perhaps the most eloquent passage he ever penned, that " under these circumstances there has arisen in society a figure which is certainly the most mournful, and in some respects the most awful, upon which the eye of the moralist can dwell. . . . Herself the supreme type of vice, she is ultimately the most efficient guardian of virtue. . . . On that one degraded and ignoble form are concentrated the passions that might have filled the world with shame. She remains, while creeds and civilizations rise and fall, the eternal priestess of humanity, blasted for the sins of the people.”

One would expect this doctrine of the “ not ourselves which makes for iniquity ” to be a very popular philosophy of life in Rogues’ Alley, but, singularly enough, the lowly beneficiaries of the system, to do them justice, have seldom manifested any interest or belief in it. Only the more accomplished of their order, like Becky Sharp, have given it their unqualified adhesion. Unfortunately, too, for Buckle and the fatalists, the logicians and the statisticians of today repudiate totally the idea that the numerical uniformity of man’s actions in the mass makes it even remotely probable that natural law exerts any compulsion or any limitation on the free decision of the will. Constant ratios in social aggregates are statistically established, it is true; but it is just as legitimate to argue that the constant antecedents are free wills — some acting constantly in one way, some in another — as to assume that natural law, with her scorpion whip, coerces a fixed number in one direction, and the remainder in another. The freedom of the will will probably puzzle philosophers in the future as in the past, but many persons will continue to indulge in this delightful illusion until some better argument can be adduced against it than the constant ratios of unaddressed letters or forgotten umbrellas.

It might be supposed that the failure of these two ambitious attempts to found far-reaching speculative systems upon statistical grounds would have impressed upon later adventurers in the field a spirit of caution. Süssmilch’s apologetics had long ago been rejected, and Buckle’s fatalism, much more recently, but with equal certainty, had been discarded. But while scientific statisticians long ago realized the limitations of their instrument of inquiry, there have never been lacking sanguine empirics who have thought to distill from their statistical alembics a charm which has eluded all other kinds of scientific alchemy. It is, of course, impossible to lay down in advance the precise limits within which statistics may yield valuable results. Their employment in insurance of all kinds, in financial and administrative problems, in astronomy, meteorology, medicine, and even in the more recent investigation of problems of biological evolution precludes us from rashly delimiting a priori the bounds of their fruitful application. But there is practical unanimity as to the kind of problem which invites this method of approach.

Where the object studied is absolutely unique, there is no play for statistics. One must certainly be mad who would seek to formulate an æsthetic appreciation of the Venus of Milo by applying to the marble the Bertillon system of measurements. So, too, when the object investigated is known to be a virtual replica of thousands of others in the same class, there is no room for statistics. The number and quality of the nerves or muscles in the human anatomy, for example, may be discovered by the dissection of a single normal subject. Again, where the artificial manipulation of conditions is possible, there is no call for the statistician. Thus, in physics, where the introduction of a single new condition, such as raising the temperature, is possible, the effect of this single change can be gauged by one experiment as certainly as by a thousand. To use statistics in any of these inquiries is simply to make the quest for knowledge harder than it was ever intended to be. It is only where the object studied is not sui generis, where experiment is impossible, and where the thing sought is inextricably bundled up with a thousand diverse and changing elements not to be separately measured or eliminated, that recourse must be had to the statistical method. If, for example, in any large population, we desire to know the average age of marriage, or the tendency to migrate, or the extent of illiteracy, it is hopeless’to go about, with or without a lantern, seeking for the abstraction known as the average man. Buttonhole the first maxi you meet, and you may get a confirmed bachelor, one who has never wandered beyond the limits of his own parish, and who, for aught you can tell beforehand, may be either an illiterate or an adept in Sanskrit. There would evidently be little use in questioning such a one. But ply a large number of persons with questions, and certain approximate answers to your inquiries emerge, — true, perhaps, of no single individual in the population, and yet sufficient to indicate with precision the tendencies operative in the aggregate. Now, while the statistical method, faute de miezix, must be applied to problems of this kind, we have no certainty or guarantee beforehand that it will yield us in any given case even an adumbi’ation of the truth : and this is especially marked in cases where the elements are very complex and very unstable. It is to the neglect of these truths that we must trace many of the foolish attempts of investigators to utilize statistics. To the same source we must trace much of the common-sense contempt for statistics generally.

There is a certain class of problems whose external aspects may possibly yield to statistical tabulation, but which in the last resort must be “spiritually discerned,” and which cannot, like Diana, be surprised in naked essence by the statistical Actæon. To this class of problems belong particularly certain questions in literary analysis, psychology, and pedagogy. Unfortunately, this very tract seems to be the chosen thoroughfare in which the statistical fakir loves to hawk his wares.

Take, for instance, the application of statistical methods to problems of a literary character. Quetelet himself affords one of the earliest examples. In order to illustrate what he terms “ the growth of intelligence ” in one of its phases, he makes an international study of the evolution of the drama. He confines his selection of plays to the French dramas given in Picard, and the English dramas contained in Bell’s British Theatre. The latter, it is interesting to observe parenthetically, contains none of Shakespeare’s works. In parallel columns, he draws up the number of dramas and the corresponding ages of the playwrights at the time their products were first staged. No qualitative distinction is made in regard to the English dramas, — Comus and The Orphan of China, by one Murphy, counting alike in the comparison. The reflective analysis of the figures reveals arcana which had been kept secret from the foundation of the world. First, neither in the English nor in the French dramatist does dramatic talent begin to develop until after twenty-five years of age ! Second, between thirty and thirty-five it manifests itself energetically! Third, it continues to flourish until toward fifty-five ! We also discover that the talent for writing comedy develops later than that for writing tragedy ! One naturally feels, after reading such trivialities, like the old gentleman in Pickwick, who learned the alphabet when eighty years of age, and went no further, doubting “ vether it vas vorth so much to get so little.”

One would suppose that this fatuous attempt would have been sufficient to deter other serious students of literature from using the same method. The fact is far otherwise. A text in English literature which appeared in 1892 states in the preface that the “ work is based throughout upon abundant statistics and other data, soon to be published, concerning the development of form in prose and poetry, both in English and out of it.” Among its contents are to be found the variations in the length of Macaulay’s sentences plotted graphically. Here too a statistical study of various authors demonstrates that in 500 periods of Sordello the percentage of simple sentences is 25, and the average number of “ predications ” and “ clauses saved ” is 3.62 and 11.54 respectively.

Another recent instance of this mechanical application of statistical measurements to literary products appears in the American Journal of Psychology for April, 1901. Two ingenious gentlemen publish therein their Studies of Rhythm and Meter. Their avowed purpose in undertaking this experimental study of certain selected rhymes was “to secure some objective record of rhythms as they actually occur in spoken verse.” In order to secure absolute objectivity, one of them first made a “ census of nursery rhymes.” A large number of presumably complaisant people were requested to set down at random the first ten nursery rhymes that happened to come to mind. Those returned most frequently on the lists, such as Old King Cole and Diddle, Diddle, Dumpling, were selected for rhythmical investigation. Inspection disclosed the fact that four fifths of the rhymes could be grouped under three distinct “ patterns.” The typical character of these metrical “ patterns ” was confirmed by the investigation of a church hymnal. Fully half of the contents of the hymnal, it was found, could be grouped under the same rhythmical rubrics. Each investigator then proceeded to repeat aloud these typical rhymes, and to mark the rhythm both by the tap of his finger and the stress of his voice. The time intervals between finger taps and between vocal stresses were recorded upon an instrument measuring to the hundredths of a second. These intervals were then averaged, and tabulated statistically. The following conclusions were then reached : (1) there was found “ a general uniformity in the intervals between stresses,” with " a tendency to a quickening in the rate from first to last; ” (2) there were found characteristic movements, depending “ partly on the distribution of pauses, and partly, perhaps, on this tendency to increase of rate.” — " O trumpery ! O morris ! ”

Another field in which, so far as I can determine, the results of statistical investigation have been extremely desultory and of very questionable utility is the sociological or psychophysical study of criminals and children. A pamphlet published last year has an appendix containing a Plan for the Study of Man. The proposal is there made that the federal government shall establish a psychophysical laboratory, “ to compute, tabulate, and publish the results ” of such investigations. To clinch the necessity for such investigations a summary is given, at the close of the pamphlet, of the most “ recent results from the study of man.” We are indeed warned that most of the thirty-nine conclusions cited, “ although based upon a considerable number of cases, can be held only as tentative. They are also true only in a general sense, which might mean true in three fourths of the cases and false in one fourth.” I trust the following selections, taken at random, are fair samples of the results attained: —

“ Truant boys are inferior in weight, height, and chest girth to boys in general.”

“ Among U. S. Naval Cadets there is a great preponderance of blonds.”

“ Visual perceptions are not copies of a physical world, but mainly the result of experience and utility.”

“ In boys, fear increases from ages 7 to 15, and then declines ; in girls from 4 to 18. Girls fear more than boys.”

“ Great men, though often absentminded, have strong memories in the lines of their interests.”

I submit that the first two theorems, though curious, are apparently of no earthly use; that the third has been known since Bishop Berkeley’s time; and that, barring the affectation of mathematical nicety in the fourth, both it and the last have always been apparent to all persons of ordinary powers of observation, A recent report of the Commissioner of Education of the United States contains a somewhat extensive account of Child Study in this country. As humorous literature it is unsurpassed. The compiler of the article, in reply to the criticism Cui bono ? replies that “ the primary object of science has always been truth for its own sake.” Unfortunately, it is one thing to unearth the true, and another and a very different thing to vociferate the obvious.

The new psychology is another field in which the statistical humbug delights to dig pitfalls. It may seem ungracious to animadvert upon the pseudo-scientific performances of the most injudicious exponents of an embryonic science, but the really solid achievements of the new psychology, such as the localization of mental functions, or the scientific study of mental processes, both normal and pathological, must profit by being severed from the rabble of statistical conjecture which parades under the psychological banner.

To illustrate a common misuse of statistical processes in this field, I shall first cite an article which appeared about a year ago in a popular magazine, and which purported to explain the results obtainable by the use of the kymograph. This instrument, it should be said in passing, is an apparatus which records, by a wavelike line upon a plate, the variations in the contraction and expansion of the chest. It is employed upon various persons, and the tests are “ repeated and verified for accurate statistical work.” Auto-suggestion is generally employed to affect the emotions of the subject, and the different wave lines produced by the altered breathing under such conditions are held to be tests for surprise, pain, anger, love, vanity, and the like. The variation in the wave forms are pronounced “ graphic pictures of laughter, of crying, of sighs, coughing, and of thought processes.” Indeed, with the resources of the psychological laboratory, the writer affirms that “ the physical senses, mental faculties, and emotions can now be measured. Sight, hearing, touch, smell, taste, imagination, reason, association, fatigue, can now be tested.”

The article in question consists of pictures of the various waves obtained by the kymograph, and an accompanying explanation of what the waves, wild or otherwise, are saying. These photographs are labeled, Surprise, Pain, Vanity, and so forth. Sometimes, it appears, the unfortunate individuals subjected to these tests undergo very drastic stimulation, in order that the desired emotion may be induced. Pain, for example, is occasioned " by pricking the subject’s neck with a sharp needle.” “ The subject’s thought, when this stimulus, used in the illustration, was given, was, ' Oh, Lord! ’ showing,” as the investigator naively remarks, “ a genuine reaction in feeling and thought.” The wave supposed to be representative of the emotion of modesty is induced by telling the subject to imagine that she is repeating the experiment of Godiva, — though this, the learned writer observes, is “ a narrow test for modesty, inasmuch as it relates to clothes alone.” “ Fear is secured by pressing a cold steel tube against the temple, and assuring them it is an electric battery, which will hurt them but little if they do not move.” To induce the emotion of vanity, the subject needs only to be given a mirror and requested to look at herself ! What is sought in this process of psychic photography is to “ obtain definite facts regarding the emotional life of students and criminals.” I have quoted the paper at this length simply because of its typical quality. The hopeless pathos of the quest pursued on such lines should protect the investigator from aught but pity.

I shall refer to but one additional illustration of what I conceive to be a singularly futile and a singularly pretentious application of the statistical method in this province. There appeared in 1900, from the pen of Professor Starbuck, of Stanford University, a book entitled The Psychology of Religion. The work is well accredited, for Professor William James contributes a preface, in which he pronounces the treatise to be " a weighty addition to the current process of taking account of psychological and sociological stock,” and declares that in the book " the statistical method has held its own.” Professor James says of the educational inferences deducible from the author’s researches that " Christians and Scientists alike must find in them matter for edification and improvement.” Perhaps this latter statement is to be taken partitively, the Christians finding therein matter for edification, and the Scientists for improvement; but let us not prejudge the case.

The author of the work in question does not underestimate the importance of his investigation, as may be judged from his opening sentences : " Science . has conquered one field after another, until now it is entering the most complex, the most inaccessible, and, of all, the most sacred domain, — that of religion. The Psychology of Religion has for its work to carry the well-established methods of science into the analysis and organization of the facts of the religious consciousness, and to ascertain the laws which determine its growth and character.” “ It is an equally important step with that which marked the beginning of experimental psychology that now the whole range of human experience, including its most sacred realm, is thrown open to scientific investigation.”

Professor Starbuck secured his data from religious “ autobiographies ; ” that is, from replies to a circular list of questions drawn up by himself. Thus in the first problem attacked — that of religious conversion — the data (apart from the Drew Alumni Records of “ 776 Male Methodists”) consisted of replies from several hundred persons, most of whom were found at two conventions of the W. C. T. U. in California, or among two regiments, one from Iowa and one from Tennessee, temporarily stationed at San Francisco.

By means of statistical tables whose figures are afterward plotted into curves, he ascertains that this religious experience occurs with boys most commonly at the age of seventeen or thereabouts, and with girls most frequently at thirteen, sixteen, or eighteen years of age. The inference is plain even without Professor Starbuck’s italics, — “ conversion is a distinctly adolescent phenomenon.” So, be it observed in passing, is taking one’s first interest in politics, or reading one’s first novel, or getting one’s second teeth, or learning to swim. But our investigator apparently thinks an " adolescent phenomenon ” a rara avis, and divines a hidden significance in the figures which his tables have disclosed. He remarks that, “ since nearly all the respondents were above twenty years of age at the time of making the record, the probability is the same that a given conversion would fall in any year up to twenty. . . . But the dice seem to be loaded,” etc. Now I confess it is hard to work myself up to this dogmatic level. I should have imagined that the chances that conversion would be experienced, say, at five years of age decidedly less than at some subsequent period. I remember to have read of a young lady of five, in Jonathan Edwards’s congregation at Northampton, who experienced a change of heart at that early age, and who insisted daily upon several long, uninterrupted periods for her private devotions, but I had always thought of her as a precocious prig. It is pleasant to think that this was a misapprehension. Having determined the age of conversion, Professor Starbuck next demonstrates that it is also the age when the most rapid bodily growth in length and weight takes place. This unsuspected coincidence is established, however, only by neglecting the rate of growth up to two years of age, — the period at which it is most rapid, and in which not even Professor Starbuck has unearthed any evidences of conversion. The statistics of the age at which physical maturity is commonly attained are next in order overhauled. The age at which this is most frequent does not prove to coincide with the age of most frequent conversions. But this makes no difference, for the law of their relation is worded thus (in italics) : “ The spiritual and physical aspect of development in individual cases tend to supplement each other.”

Thus Professor Starbuck proceeds most industriously from topic to topic ; tabulating the Motives and Forces leading to Conversion, Experiences preceding Conversion, The Beliefs of Adult Life; probing with his figures to the heart of Sanctification, and concluding with Some Educational Inferences. At times one’s risibles are provoked by the phraseology, as when an individual case is quoted as “ Non-revival female 16,” or when the author nudges our elbow to observe “ how readily Sanctification passesover into a pathological condition.” Indeed, the only glimpses of religious psychology which the book affords are the fragmentary bits occasionally contained in the replies of his respondents. These disclosures of the vie intime often glow with feeling or shine with tears, but to the author they are merely straw for his statistical bricks.

The statistical empiric to-day is abroad, and his marks are these: he employs statistical tables to prove facts that have been commonplaces of ordinary observation years out of mind. He batters himself and his hearers into an attempt to extort an occult meaning from facts which, upon a little careful analysis, are recognized as practically self-explanatory. He parades pedagogical principles avowedly based upon a scientific psychology which, in so far as they are either true or important, have been the common possession of intelligent and sympathetic teachers for generations. And worse than all else, because at the source of all his errors, he neglects any adequate preliminary inquiry into the probability of employing statistics in a given field with success. The statistical implement is a crude one at the best. Its readings are necessarily very rough in many a province where its use is unquestionably necessary. But it is hardly probable that for centuries to come it will be happily employed in deciphering the life of the spirit whose fabric is “ as fragile as a dream,” and whose endurance “ as transient as the dew.”

Winthrop More Daniels.