Il Metodo Statistico, Teoria e Applicazioni alle Scienze naturali, alle Scienze sociali, e all' Arte.by Alfredo NiceforoReview by: M. G.Journal of the Royal Statistical Society, Vol. 87, No. 2 (Mar., 1924), pp. 294-296Published by: Wiley for the Royal Statistical SocietyStable URL: http://www.jstor.org/stable/2341231 .

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294 Reviews of Statistical and Economic Books. [Mar.

treated, however, are confined to Professor Pearson's types of distributions, and the author only refers to the names of those statisticians who have developed other systems. He concludes this chapter with some remarks on unstable distributions defined as those in which the moments higher than the fourth may be infinite. The argument in this place is based on the fact that the distribution of prices follow a type IV carve of this nature. This instability he justifies by stating that some articles may be abundant during one year but may not be procurable the next. This seems to me to take too anthropometric a view of a mathematical graduation. No graduation formurla can be expected to be true beyond limits set sufficiently evidently by the nature of the data.

There are well-written chapters on the different methods of correlation. In one of these chapters (p. 193) a slip may be noticed. In the formula used for changing Professor Spearman's p

to Professor Pearson's r, the brackets are onmitted around 7 P)

which might give some difficulty to anyone studying the subject for the first time from this book. The book ends with some discussion of index-numbers. J. Br.

3.-Il Metodo Statistico, Teoria e Applicazioni alle Scienze naturali, alle Scienze sociali, e all'Arte. By Alfredo Niceforo. 590 pp. iM1essina: Casa Ed. Giuseppe Principato, 1923. Price 30 lire.

In this book Professor Niceforo has attempted to perform two tasks: to give the educated reader without special knowledge of statistics a notion of what may be called the philosophy of the statistical method, and also to equip him with the elements of statistical technique. In the first three chapters the general notion of a statistical series and the simplest characteristics of such series are explained and illustrated upon a very wide range of examples, including such disparate instances as the heights of Graeco-Roman statues in the Louvre, the ages at death of famous men, the dis- tribution with respect to amount of tax paid by Lombards in the Quartier St. Germain in the year 1292. The author then passes to somewhat more technical questions, such as percentiles and measures of variability; he next briefly considers the characterization of asymmetry, always illustrating the discussion on a wide range of examples. The three following chapters are devoted to the descrip- tion of secular change; the simpler cases of smoothing of non-periodic series and the simplest instance of a periodic curve are here illustrated. In the next chapter examples of statistics capable of representation by a logarithmic method are examined. In the following chapter, some vital statistical indices are explained. Chapter 12 introduces the reader to the elements of mathematical probability and the con- cept of " probable error." In Chapter 13, the practical importance of " probable errors " in the confrontation of statistical constants is illustrated. In the next two chapters the concept of association or co-variation is introduced, and all the widely used indices, correlation

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1924.] Reviews of Statistical and Economic Books. 295

ratio, coefficients of contingency and correlation, coefficients of regression and of partial correlation, are described. The last three chapters of the work discuss the manner in which one may pass dalla qualita alla qr.antita, from a merely qualitative appreciation of phenomena to their numerical appraisement.

It will be seen that Professor Niceforo has covered an enormous range. The demands he makes upon the reader's technical knowledge of mathematics are very small, but the strain upon the reader's mental versatility is not small. If we may be permitted to use the, no doubt, obsolete antithesis between the Teutonic and the Latin mind, we should say that this book is more suitable for the Latin than for the Teutonic student; for the latter a rather duller book would be more satisfying. Thus, a quick-minded person may appreciate without specific warninig that the indices of concordance dealt with on pp. 465, etc., have'little in common with the coefficients of corre- lation and regression discussed immediately before, but the slow- witted reader may fail to mark this.

For anyone who wishes to take a general survey of the statistical field and does not seek a text-book, this volume is eminently suitable, and, when it appears in French or English translation, it should secure wide publicity in this country.

It is implicit in what we have already said that the criticism an English reader is likely to pass is that the range covered is somewhat too wide. We think that a curtailment of the last four chapters, which contain a good deal of matter rather remotelv related to statistics as generally understood, would have improved the book and enabled Professor Niceforo to discuss in more detail some questioins of greater scientific importance. For instance, on p. 464, he quite correctly warns the reader of the risks run in applying the arithmetically simple method of partial correlation to non-linear systenms. The researches, particularly of Dr. Isserlis, have shown that in simple cases the skew analogue of multiple regression coeffi- cients can be brought within the domain of practicable arithmetic. But it remains true that no treatment of non-linear systems, both arithmetically practicable and yielding a constant possessing the simple interpretation of a coefficient of partial correlation, has yet been devised. Suppose, then, that we are confronted with a system of n(n - 1)/2 coefficients of correlation between n variables, the n(n - 1)/2 coefficients perhaps computed by different methods (some of the variables perhaps being non-quantitative) and some of the regressions demonstrably non-linear. Are we entitled to say that the coefficients of partial correlation of various orders deduced from this system are (a) altogether valueless, or (b) that they do throw some light upon the degree of isolated co-variation of the members of the system ? This is a problem which the statistician usually leaves with a few vague words of caution-as, indeed, Professor Niceforo leaves it. Hardly anybody-perhaps nobody-is brave enough to confess that he attaches no meaning at all to, say, the coefficient of partial correlation between hair colour and the teacher's estimate of a child's

VOL. LXXXVII. PART IT. X

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296 Reviews of Stattistixal and Economic Books. [Mar.

intelligence for age, weight, and examination marks constant. Most of us hold that it does measure 8omething, but few of us would sav whether such a coefficient, if found numerically equal to a partial coefficient of the same order deduced from a strictly planar system, implies a higher, lower or equal stringency of association. That is the sort of problem which needs discussion, because some of the prestige of the statistical method depends upon the assumption that we can by a calculus reach without the experimental method, in instances where the experiinental method is inapplicable, what that method strives to obtain. M. G.

4.-International Year-book of Agricultural Statistics, 1922. xl + vii + 364 pp. Rome: International Statistical Institute, 1923. Price 8s.

The General Assembly of the International Agricultural Institute has decided that the Year-book which has hitherto appeared at longer intervals, shall, in future, be published annually. The wisdom of this decision may be questioned. The primary function of the Institute, as originally conceived, was not to compile historical records, convenient as these are for the use of students of, and writers about, statistics. For practical purposes-i.e. for the help of agriculturists and of persons commercially interested in agri- cultural products-the prompt circulatlon of trustworthy statistical information about crops and crop prospects far transcends in value any other service that the Institute can render. It is true that it attempts to do this at present, but ineffectively. The service is ineffective because the information, valuable as it may be, does nlot reach one in a thousand of those to whom it might be of service or interest, and, as a rule, reaches even them so tardily as to have lost its value. If the General Assembly, instead of publishing an annual Year-book which, in the nature of the case, can include statistics having historical interest only, were to publish such a volume quin- quennially, and devote the money thus saved to the better and wider distribution of prompt information, it would render greater service to the world at large.

But, the Year-book being ordered, nothing but praise can be given to Dr. Dore, Chief of the Statistical Bureau of the Institute, and his assistants, for the manner in which they have performed the task entrusted to them. The tables are clearly arranged, the ex- planatory notes are terse and adequate, and the general scheme of the volume is admirable. It is tempting to dip into the pages and to quote many of the interesting facts which the figures reveal. Gener- ally the statistics given relate to the year 1922, or in some cases 1921, as the latest year, with comparative figures for 1919 and 1920 and for the pre-war period 1909-13. It has to be admitted that in the absence of any statistics of agricultural production for Russia or China, calculations of world supplies must be defective. China is probably the most important producer of two products-tea and silk. As regards Russia, certain returns of flax production have

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