M. G. Kendall

The Distribution of Spearman's Coefficient of Rank Correlation in a Universe in which all Rankings Occur an Equal Number of Times:

3. Certain simple properties of this distribution are obtainable immediately. (a) Any value of S(d2) must be even. For S(d) = 0, being the difference of the sums of the first n natural numbers; hence the number of odd values of d is even, and so is the number of odd values of d2. (b) The possible values of S(d2) range from 0 to 4(n3 -n) and hence there are 1 (n3-n) + I of them. (c) The distribution is symmetrical, about a central value if i,(n3-n) is even, or about two adjacent central values if J(n3 n) is odd. This follows from the fact that to any given value ofp corresponding to a permutation P there will correspond a negative value of p of the same absolute value arising from P inverted. For, if the permutation P is X1, X2, ..., Xn the inverted permutation is Xn) Xn) ...,) X,1. S(d2) calculated from P is then S(Xi-i)2 and that from P inverted is S(X, n + 1 + i)2. The sum of these two is S(X2) + S(i2) 2S(Xi i) + S(X;) + S(n + i)2 -2S{Xi(n + 1i)}.

Time Series (2nd Edition)

Time Series (2nd edition). By Sir Maurice Kendall. London, Griffin, 1976. ix, 197 p. 24 cm. £6·20. Multivariate Analysis. By Sir Maurice Kendall. London, Griffin, 1975. 210 p. 24 cm. £6·80.

Hiawatha Designs an Experiment

Hiawatha, who at college, Majored in applied statistics Consequently felt entitled To instruct his fellow men on Any subject whatsoever, Waxed exceedingly indignant Talked about the law of error, Talked about truncated normals Talked of loss of information, Talked about his lack of bias Pointed out that in the long run Independent observations Even though they missed the target Had an average point of impact Very near the spot he aimed at (With the possible exception Of a set of measure zero.)

Statisticians—Production and Consumption

There are more than 10,000 members of the American Statistical Association. There are more than 4,000 Fellows of the Royal Statistical Society and about 3,000 of the Sociedad Mexicana de Geografia y Estadistica and sizeable groups in most other countries of the world. Not all these people are working statisticians and there is some overlap in membership. But without carrying out a study in depth, I should guess that there are somewhere between twenty and thirty thousand of us at large. Indeed, if we add peripherally related societies such as Econometrics with about 3,000 members and the American Society for Quality Control, with 20,000; and if we further adjoin people working on statistics in the whole range of social sciences, geographers, regional planners, anthropologists for example, the number who may fairly claim to be statisticians is very much higher. This seems a good occasion to take a look at ourselves, not only in our relations among different groups of statisticians but in our relations to the external world of government, business and all the other disciplines in which the statistical techniques are used. We are bound together by common interest in a natural philosophy and an armoury of techniques which range over practically every field of human endeavour. Our science, that of numerical measurement and uncertainty of inference is, in a broad sense, the matrix of the sciences, both physical and behavioural. With this degree of importance and spread of interest it is not surprising that some of us become intolerably self-opinionated and are puzzled by the fact that the world of practical men does not always seem to appreciate us at our true worth. Instead of lamenting the fact, perhaps we should consider why this is so. But before considering relations with foreign powers let us look at some of our internal prolems. First of all, the way in which we swamp ourselves with our own literature. Papers on statistics are published in several hundred journals and probably amount to well over a thousand titles a year. Those of us for whom English is a native language are lucky that so much of the published work is in English of a kind, but even we cannot cope with the flood. It is as much as most of us have time for to look at the titles. The International Statistical Institute has succeeded, in the admirable periodical called Statistical Abstracts, in providing at least a part cover of the field. But I doubt whether anyone has time even to read through Statistical Abstracts; and in any case it sells less than a thousand copies. I contend that this is important, because the adepts of our subject ought to know what is going on, even in broad outline, and not get themselves identified with a particular subset of available knowledge. Unfortunately, circumstances are against us in attempting to stem the flood or even to control it. In the academic world a man is judged by the volume of his publications, without very profound regard to their quality. Many people cannot obtain the financial support necessary to attend conferences unless they submit a paper. It is not necessarily an ignoble ambition, to obtain respect and recognition among ones fellows by the publication of papers or booksI should be the last to deny it, having inflicted more on the statistical world than most. I see little that can be done or that should be done in limiting this volume of publication. The mounting economic cost may do something in the desired direction but more, perhaps, in restricting the size of articles than in restricting their number. Nor is the mass of literature limited to publication in the ordinary sense. The fatal facility with which documents can be reproduced nowadays leads to a large volume of circulated typescript of highly variable quality and even abstracts promulgated on the principle that what cannot be accepted for publication can always be presented at a conference. In contrast statisticians working in business or government publish too little. There are several reasons for this-the reluctance to publish information which may be useful to competitors, the general pressure of day-to-day work, various restrictions on confidentially obtained information. The general upshot is that our volume of publications is unbalanced-it usually stems from theoreticians who look for data to illustrate their work rather than from practicing statisticians who look for theory to solve their problems. Humanity in the past has dealt with surfeits and surpluses in various ways: by a period of abstinence like Lent or Ramadan; by the controlled release of commodities like diamonds on to the market at rates which it can absorb; even, in times of economic crisis, by paying people to refrain from producing. I cannot see that any of these methods are likely to help us much. I suppose that we shall have to do the best we can be abstracting services, by the construction of computer files of titles and by the organization of review papers. I would have made some similar comments about the terrible plethora of organized meetings with which the statistical world is faced, were it not for the fact that the usefulness of most of them arises from the * Project Director, World Fertility Survey, 35-37 Grosvenor Gardens, London SWIW OBS, England. Presented at the 135th Annual Meeting of the American Statistical Association, Atlanta, Georgia, August 26, 1975, as the Special Address Invited by the President.

Symmetric Function and Allied Tables.

In undergoing this life, many people always try to do and get the best. New knowledge, experience, lesson, and everything that can improve the life will be done. However, many people sometimes feel confused to get those things. Feeling the limited of experience and sources to be better is one of the lacks to own. However, there is a very simple thing that can be done. This is what your teacher always manoeuvres you to do this one. Yeah, reading is the answer. Reading a book as this symmetric function and allied tables and other references can enrich your life quality. How can it be?

The Advanced Theory of Statistics. Volume 1, Distribution Theory.

A method for continuously effecting reactions in a liquid phase in the presence of a gas and of a finely divided solid catalyst in a bubble column-cascade reactor with little or no liquid back-mixing, dwell time in the reactor being dependent on the liquid and gas throughputs, said reactor comprising a vertical column and a plurality of equidistantly-spaced, horizontally mounted, uniformly-perforated plates therein, the aperture area of each plate being dependent on the cross-sectional area of the column and the plate spacing within the column being such that adjacent plates are separated vertically by a distance at least three times the diameter of said columnar reaction zone.

Probability and Statistical Inference

The Foundations of StatisticsBy Prof. Leonard J. Savage. (Wiley Publications in Statistics.) Pp. xv + 294. (New York; John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1954.) 48s. net.

Statistical Quality Control

BEFORE the War, quality control methods of the statistical type were to be found in comparatively few industries. The War itself saw them introduced, frequently under Government auspices, into a wide range of industries which had previously never used them ; and in consequence there was a sudden load on the available training centres, particularly in the United States, which had any acquaintance with this kind of work. Stanford University bore a full share in the training schemes which were drawn up, and Prof. Grant, who had been lecturing there on the applications of statistical methods to engineering for some seventeen years, found his field of engagements greatly enlarged. His experience as a teacher has now assumed concrete form in this book, which exhibits throughout a most admirable appreciation of the practical aspects of the subject.Statistical Quality ControlBy Prof. Eugene L. Grant. (McGraw-Hill Industrial Organisation and Management Series.) Pp. xii + 563. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 25s.

Science and Reconstruction

SIR JOHN ANDERSON states in Nature of December 22, p. 733, that “a good grounding in natural science can be a passport to the higher Civil Service, equally with the more usual training in the humanities, or in the history schools”, and that “public administration does provide scope, apart from the professional or specialist grades, for men with a scientific training”. Sir John is, of course, quite correct in the sense that the entrance examination for the Administrative Class of Civil Servants can be taken in almost any subject. But in spite of the theoretical possibility, there are very few successful entrants to the Administrative Class with a grounding in natural science. Some figures on this point may be of interest.