# Reviews of William Gemmell Cochran's books

We present below a list of the books authored, or co-authored, by William Cochran. We list these in chronological order of the first edition, but we place second editions below the first, and third editions below the second. The fact that Cochran wrote books for application of statistical methods to a wide variety of areas mean that his books have been reviewed in specialist journals in different areas, so we have found more reviews of his texts than anyone else in our archive. We make no attempt to quote from all reviews, only a selection. We present short extracts from some reviews but a longer extracts from others.

Click on a link below to go to the reviews of that book

Fifty Years of Field Experiments at the Woburn Experimental Station

Experimental Designs

Experimental Designs (Second Edition)

Sampling Techniques

Sampling Techniques (Second Edition)

Sampling Techniques (Third Edition)

Statistical Problems of the Kinsey Report

Statistical Methods (6th Edition)

Statistical Methods (7th Edition)

Statistical Methods (8th Edition)

Contributions to Statistics

Planning and Analysis of Observational Studies

Click on a link below to go to the reviews of that book

Fifty Years of Field Experiments at the Woburn Experimental Station

Experimental Designs

Experimental Designs (Second Edition)

Sampling Techniques

Sampling Techniques (Second Edition)

Sampling Techniques (Third Edition)

Statistical Problems of the Kinsey Report

Statistical Methods (6th Edition)

Statistical Methods (7th Edition)

Statistical Methods (8th Edition)

Contributions to Statistics

Planning and Analysis of Observational Studies

**1. Fifty Years of Field Experiments at the Woburn Experimental Station (1936), by William G Cochran, Edward J Russell and John A Voelcker.**

**1.1. Review by: P H.**

*Science Progress (1933-)*

**32**(125) (1937), 181-182.

The Woburn Experimental Station was founded jointly by the Duke of Bedford and the Royal Agricultural Society in 1876 as the direct outcome of the passing of the Agricultural Holdings Act in 1875 whereby the giving of compensation to an outgoing tenant for the unexhausted value of purchased food was made a subject for arbitration. One of the chief problems for investigation was, therefore, to ascertain to what extent the productiveness of the soil was influenced by the feeding of concentrated foods, such as cake or corn, to the livestock on the farm. This problem proved to be more difficult than had been anticipated and after sixty years of experiment it remains uncertain whether any rigid basis of compensation can be drawn up. Notwithstanding this, valuable information has been obtained about the effects of soil and climatic conditions on the effects of fertilisers and manures on plant growth. ... The book ... is divided into 4 parts of which ... the second part by Mr Cochran deals with Statistical examination of the results ...

**2. Experimental Designs (1950), by William G Cochran and Gertrude M Cox.**

**2.1. Review by: Frank Sandon.**

*The Mathematical Gazette*

**36**(315) (1952), 78-79.

The two writers of this book have worked together at Iowa State College. Cochran was one of the statisticians at Rothamsted until he left there in 1939 for a Chair at Iowa; Cox is an American, who has been trained entirely at Iowa: she recently gave to the Royal Statistical Society a picture of the work of the large Institute of Statistics of the University of North Carolina (there is a staff of 67), of which she is Director. The volume, one of the Wiley Mathematical Statistics Series (Wald's Sequential Analysis, reviewed in the Gazette in February, 1949, is another), is intended as a source of reference to the numerous procedures that have been developed in the design of experiments since Fisher and Yates opened up the modern-day treatment of this matter. The book is primarily a handbook: it is for reference and does not itself present much original work, though, of course, it quotes from research of each of the authors. It is gleaned from many different sources, both for its designs - the publisher claims that 150 of the most useful experimental designs are given - and for its worked examples. Most of these are based on agricultural experiments, different aspects of some of these being dealt with in different chapters. But there are some on nutrition and on toxicology, and two, as a result of what the authors call their strenuous efforts to get examples from diverse fields, on the preparation of chocolate cakes and on roast beef: these are from students' theses: in the former a breaking angle test is employed. It is essentially a practical book (see, for example, the notes on randomisation, checks on computation, number of figures to be retained, identification of data, the use of confounding, missing data).

**2.2. Review by: Asa O Weese**.

*Bios*

**21**(3) (1950), 207.

Biological investigators who have some knowledge of the principles of statistics will find in this work detailed descriptions of the most useful experimental designs which have been developed. Each type of design is illustrated by concrete examples to which the appropriate techniques for the analysis of variance are applied. Emphasis is directed toward the importance of proper planning of experiments to yield information of the greatest reliability. The bibliography accompanying each chapter is useful in directing the investigator to further information as to the development and use of the methods illustrated.

**2.3. Review by: Francis M Wadley.**

*Science, New Series*

**111**(2893) (1950), 637.

Application of biometric analysis to research problems has made much progress in the past generation. Experimental design is the culmination of such statistical work; after a little experience in analysis of results, the need for better planning becomes very evident. Plans to insure validity and increase efficiency of experimental work have received increasing attention. The present textbook has been eagerly awaited for several years, and a preliminary mimeographed version has already proved useful. The book follows the path of useful and usable application of techniques, opened up by Fisher, Yates, Snedecor, the authors, and others. The book is put together substantially and printed clearly. Material heretofore widely scattered, if available at all, is here given organised treatment. ... On the whole this volume will be indispensable to forward-looking experimenters and biometricians.

**2.4. Review by: David W Calhoun.**

*Ecology*

**32**(2) (1951), 355-357.

The authors have guided themselves first by the needs of an investigator preparing a new experiment. The designs are selected for their usefulness, and their relative advantages are expertly discussed. Directions for the experimental plans and the entailed arithmetic are verbally at a minimum, but logically complete. this should be a very good handbook for executing the designs it describes.

**2.5. Review by: M G K.**

*Journal of the Royal Statistical Society. Series A (General)*

**113**(4) (1950), 577-578.

It was once said of Fisher's

*Design of Experiments*that it was not a book which a beginner ought to read unless he had read it before. This was a tribute to the originality of the work, a comment on Fisher's condensed way of stating his results and a plea for a more extensive account of the subject. In view of the interest in experimental design throughout the scientific world, there has been a striking lack of textbooks about it. There are chapters in general textbooks, some rather specialized bulletins, and a scattered literature in scientific journals; but no comprehensive development within the covers of a single book.

Fortunately, it is one of the features of the Rothamsted strain of statistician that it flourishes on a variety of soils. Professor Fisher himself has been transplanted twice with no diminution of vigour or fertility. Professor Cochran, a member of what may perhaps be called the $F_1$ generation, and Miss Cox, who, I suppose, belongs to $F_2$ (Professor Snedecor being the intermediate $F_1$), are in the direct line of descent. Their work at Iowa, and later in North Carolina, in carrying out experimental designs, in advising their colleagues and in teaching the subject to students has given them exemplary qualifications for writing a book on experimental design. Those of us who knew that the work was in contemplation have been looking forward to its appearance with keen interest, and an anxious hope that their preoccupations in other fields would not prevent them from finishing it.

One opens this book, therefore, with high expectations; and let me say at once that they are not disappointed. By way of overture there are two lively introductory chapters on fundamentals with some admirable practical illustrations, and a chapter on the statistical analysis of experimental results. The remainder of the book, twelve chapters in all, deals in detail with the principles of randomisation, factorial designs, balanced and partially balanced blocks, confounding and the various kinds of layout to which they lead. Altogether about 150 designs are described, analysed and discussed. Great pains have been taken in the exemplification.

...

There has been a growing need for such a book, and it is a most welcome addition to statistical literature.

**2.6. Review by: Norman L Johnson.**

*Biometrika*

**38**(1/2) (1951), 260-261.

*Experimental Designs*should prove especially valuable to statisticians requiring a compendium of all the more useful designs accompanied by an outline of the relevant theory, and also to experimenters with sufficient time, inclination and ability to apply modern statistical methods in a serious manner to the design, analysis and interpretation of their work. The first three chapters contain a brief introduction to tests of significance, estimation, and related concepts, followed by an account of the type of procedure employed in the analysis of variance. A warning must be given that the reader cannot expect to appreciate this part of the book without previous study of general statistical theory and some experience in the application of at any rate the simpler forms of analysis of variance. The third chapter, in particular, while an excellent summary of the principles underlying the analysis of variance, will not be fully understood at a first reading, without a background built from experience of the problems arising in a variety of experimental situations.

The next twelve chapters deal with different forms of experimental design. Each chapter contains a description of the conditions under which the particular design is likely to be useful, and the appropriate analysis, with a simple account of its theoretical basis. In the more complicated cases a selection of suitable designs ('Plans') is given at the end of the chapter. This feature greatly increases the value of the work as a reference book. The sixteenth chapter ('Random permutations of 9 and 16 Numbers') constitutes a rather odd, though useful, tailpiece.

**2.7. Review by: Albert H Bowker.**

*The American Journal of Psychology*

**64**(2) (1951), 308-309.

The increasing utilisation in research of methods of experimental arrangement and statistical analysis originally elucidated by R A Fisher has created a need for a systematic account of the subject, which the present book satisfies. A major contribution of the book is a relatively complete compilation of the designs which have proved useful in research. For each design, the book contains comments on the appropriate experimental situations, directions for the selection of a particular arrangement, discussions of the relevant statistical analysis, worked examples, and references to mathematical derivations and practical examples. In addition to a discussion of completely randomised, randomised block, latin square, factorial founded factorial experiments, which are treated in Fisher's

*Design of Experiments*and some other books on statistics, the book includes chapters on split-plot designs, factorial experiments confounded in quasi-latin squares, balanced and partially balanced incomplete block designs, lattice and cubic lattice designs, balanced incomplete blocks, lattice squares, and Youden squares, for which complete treatment has been available scattered literature.

...

Though most of the examples are drawn from biology, the book should be very useful to psychologists with a serious interest in experimental work. The excellent treatment of the principles of experimental design and the discussion of the simple experiments will probably prove more useful to them than the details of the more complex experimental arrangements.

**2.8. Review by: Palmer O Johnson.**

*Journal of the American Statistical Association*

**45**(251) (1950), 454-455.

The authors have written this book primarily for the experimenter, who will find here the description of the most useful designs that have been developed up to this time. It is a handbook to which he may refer for intelligent guidance when he contemplates an experiment. The experimenter should possess, besides first-hand knowledge of the problems in his field, a working knowledge of the analysis of variance. With this background he opens a book unexcelled in its exposition of the scientific and statistical basis of the principles of experimentation and their transition into designs. On the maxim that example is better than precept, an unusually successful attempt has been made to exemplify the processes by a comprehensive selection of examples. These are for the most part drawn from biology, particularly agriculture, in which field the greatest part of the experience of the authors has been gained.

...

This book will set the standard for a long time to come. Mathematicians have, at least since the time of Euler, found much interest in combinatorial problems dealing with the arrangement of things in configurations of various kinds. It remained for R A Fisher to show how to put these combinatorial principles to work. The principles of experimentation have stood the test of time and are finding increasing application in many fields of science. This book will undoubtedly serve to increase and elevate the standards of their use and in doing so demonstrate the most important practical application so far made of statistics.

**2.9. Review by: William E Felling.**

*The Mathematics Teacher*

**45**(7) (1952), 551.

This book is very well organised and written in a clear, concise manner to make it appealing to anyone interested in the field of statistics or experimental design. The first three chapters present a classic discussion of the objects, construction, and conclusions to be drawn from experimental design. The initial stages of the problem; what data to use, what techniques, and in particular certain pitfalls to be avoided, all are thoroughly discussed. The remaining twelve chapters are concerned with a detailed study of the first three chapters as applied to over 150 experimental designs. This book should certainly be in the library of every statistician.

**2.10. Review by: Henry B Mann.**

*Quarterly of Applied Mathematics*

**8**(3) (1950), 320.

In this book the authors present a large number of different designs covering a great variety of experimental situations. The application of these designs and their analysis is illustrated by well chosen examples. The book being intended as an elementary text and as a guide for research workers with little or no mathematical training, the authors do not fully discuss the basic assumptions underlying the analysis and the principles of statistical inference that lead from the assumptions to the analysis. However, the book distinguishes itself from many other elementary books in Statistics by giving a correct, although incomplete discussion of the necessary fundamental statistical principles. The greatest value of the book in the reviewer's opinion is the extensive collection of experimental designs presented. A disadvantage for the reader with more mathematical background is the absence of closed expressions for the computation of test functions. Such closed expressions, which would inform the mathematically trained reader at a glance, are replaced by numerical examples, probably because formulae involving multiple summation signs and other formidable mathematical symbols would deter the average reader. The reviewer believes, however, that the book will be very profitable reading also for the student of Mathematical Statistics, particularly when used as complementary reading to a treatise presenting the mathematical theory of the design of experiments and the analysis of variance.

**2.11. Review by: Charles W Eriksen.**

*The Quarterly Review of Biology*

**26**(2) (1951), 242-243.

This book is designed as a handbook for experimental workers in the fields of biology, psychology, and agriculture. As such, it should prove of considerable value. Detailed consideration is given to 150 different experimental plans based on the analysis of variance, covariance, and latin square techniques. Each design is considered in detail, not only with respect to the plan of the experiment and the computational steps, but also in terms of the advantages and disadvantages of the particular design. ... The authors have assumed that the reader will have a basic understanding of the analysis of variance, and granting this, their presentation is clear and concise. Experimental workers in the biological sciences have been in need of an authoritative and handy source to assist them in selecting the more efficient plans for their experiments. This need has been admirably met by

*Experimental Designs*.

**2.12. Review by: Frank Yates.**

*Science Progress (1933-)*

**39**(154) (1951), 352-353.

Within the limits set by the authors this is an excellent book. It is primarily intended to provide an account of the more useful types of experimental design that are in current use, set out in such a manner that the practical experimenter can use them correctly and with confidence. In this task it succeeds admirably. The various practical problems which arise in the design and in the analysis of the results axe comprehensively dealt with. Detailed plans are given, together with instructions as to the randomisation necessary in the assignment of the treatments to the experimental units; the necessary formulae for the statistical analysis are presented and frequently illustrated by numerical examples. The formulae for dealing with missing data are given and also methods for calculating from the experimental results the efficiency of the chosen design relative to alternative simpler designs. The designs covered in this manner range from simple randomised blocks and lattice squares to the more elaborate incomplete block and lattice designs.

...

This is undoubtedly a book that will be invaluable to all who are actively engaged on experimental work on variable material. It assembles in convenient form a mass of detailed information on particular designs which was previously only available in scattered scientific papers, bulletins and monographs. It has those three essential characteristics of a reference manual, soundness, comprehensiveness and accuracy. Every serious student of experimental design should also study it thoroughly. There is a wealth of wisdom contained in its pages, not only on the more routine matters, but also on those exceptional points that frequently arise in the interpretation of experimental results.

**2.13. Review by: David J Finney.**

*Nature*

**167**(4247) (1951), 455.

This book is essential to every statistician concerned with experimentation. When the discipline of experimental design was first introduced into quantitative biological research, materials and treatments were made to conform to one or two simple patterns, notably the randomised block, Latin square, and simpler factorial types ; more recently, the trend has been reversed, with the better purpose of constructing designs that will compare the treatments most precisely within the limitations imposed by the materials. The consequent proliferation of designs has made difficult even the remembering of where papers describing their construction and analysis may be found. Here, for the first time, is a codification of most of the simpler and more useful types.

...

Had the authors done no more than list designs and methods of analysis they would have performed a valuable service. In addition, their extensive experience of statistical science has enriched their catalogue with an immense amount of information and advice about the interpretation of experiments. The importance of assumptions used in the analysis of variance, the analysis of experiments when some observations are missing, and the interpretation of series of experiments are among the topics so considered.

**3. Experimental Designs (Second Edition) (1957), by William G Cochran and Gertrude M Cox.**

**3.1. Review by: Alva E Brandt.**

*Science, New Series*

**126**(3279) (1957), 930.

The second edition of

*Experimental Designs*, by William G Cochran and Gertrude M Cox, consists of 611 numbered pages and five unnumbered pages of tables, compared with 454 pages in the first edition. This increase of approximately 36 percent has not allowed the authors enough space to list all designs that are now known and commonly used but has enabled them to present, in part at least, the important developments in experimental design that have appeared since the first edition was published (1950). Since the first edition was so well received, the general framework has been retained.

...

One does not have to be a seer to predict that the second edition of

*Experimental Designs*will be well received.

**3.2. Review by: Boyd Harshbarger.**

*AIBS Bulletin*

**7**(5) (1957), 55.

The text, Experimental Designs, by William G Cochran and Gertrude M Cox is a revision of the earlier book by the same authors. The text consists of a logical exposition of the practical aspects of experimental designs and a detailed presentation of most of the modern statistical designs. The mathematical models and assumptions are listed for each design and they are illustrated, in most cases, by practical examples. The book is an excellent reference work, both for the mathematical statistician as well as the non-mathematical statistician. Besides a reference text the book serves equally well for a classroom text, both for the mathematically inclined student as well as the non-mathematically inclined group providing the lecturer provides his own exercises and supplements the text with his own discussions.

The revision treats a number of new topics not mentioned in the first edition; namely, fractional replications of factorial experiments, response surfaces, generalised chain-block designs, and a number of other topics such as sequential experimentation, method of preference testing, and effect of errors in the weights on recovery of intra-block informations.

**3.3. Review by: Corrado Gini.**

*Genus*

**13**(1/4) (1957), 192.

In this work the authors set out to describe in detail the most useful of the experimental designs that have been formulated, accompanying them with their respective plans and with the experimental problems for which each of them is particularly suitable. It is therefore a reference manual for the investigator. This second edition follows 7 years after the first one: in it two chapters have been added and new material has been included without changing the general lines of the work.

**3.4. Review by: Frank Sandon.**

*The Mathematical Gazette*

**42**(342) (1958), 334.

The first edition of this book was reviewed in the Feb., 1952, issue of the Mathematical Gazette. In it we noted that the book was "intended as a source of reference ..., primarily a handbook" and that the "real value of such a handbook can ... only properly be assessed by the worker who has occasion constantly to refer to it ..."

The book, with, in particular, the sets of plans of experimental designs, has been much used by such workers, and the new selection should be even more valuable, for it adds, to all those designs originally given, many of the newer types, with indices of other designs now available, from any of which the worker can make his choice. There are, of course, many difficulties that may arise if "home made" designs are used, and it is of great value to have to hand in one volume details of such a variety of approved designs, with notes on their use. The framework of the book is unchanged, and the chapter and section number references are unaltered. To each chapter are now added further references to the literature, and a list called "Additional Reading", though the "Selected Bibliography" at the end of the book is now much reduced - to one page of eighteen references, the majority of them new. ... The new book should thus be of much value to all who wish to use modern designs in their experimentations.

**3.5. Review by: D F.**

*The Incorporated Statistician*

**8**(3) (1958), 140-143.

The first edition of Experimental Designs by Cochran and Cox has for some time now been an authoritative, even if not wholly exhaustive, source of information on experimental strategies available to the experimenter. The book had its roots in the frequent questioning of the authors by research workers wanting either guidance on the appropriate statistical technique to be used in a specific experiment, or an experimental plan for carrying out a technique already chosen; the authors felt that the requests indicated a need for a handbook of experimental design setting out, and evaluating, those designs that experience had shown to be most useful. As a handbook of experimental arrangements it does not try to present a unified exposition of the subject, proceeding from the basic principles and assumptions through to a general theory of experimenting and then particularising: throughout, the book assumes a knowledge of the principles of analysis of variance and also of the computational methods to be used in the analysis. The second edition of this book has taken advantage of the lapse of six years to include some more recent work on the exploration of response surfaces, including the work following on the paper by Box and Wilson in 1951. It has also been able to draw on a larger fund of experimental material and this led to a reassessment of the usefulness of fractionally replicated factorial designs and to the inclusion of these designs in a new chapter. The general structure of the book remains as before but additional material has been included on many topics.

...

The great advantage of this book is its extensive use of practical examples to illustrate the working of particular experimental schemes. Theoretical experimental arrangements never carry the conviction of one that has been tried and proved. At the end of each chapter there are useful bibliographies providing both experimental results and experimental designs so that the text can be amplified from the original sources.

**3.6. Review by: Franz E Hohn.**

*Pi Mu Epsilon Journal*

**2**(9) (1958), 431.

The purpose of this second edition of a well-known work is "to present the plans of all the useful types of experimental designs, showing the kind of work for which each design is appropriate, and giving illustrations of its practical use." New sections have been added throughout, and two new chapters have been added in order to make the material complete and up-to-date. The new edition also takes account of the fact that "research workers in the medical and social sciences, in physics and chemistry, and in industrial research have become increasingly attentive to the principles of experimental design." More than ever, this unique volume is an indispensable tool of the practitioner and student alike.

**3.7. Review by: Philip J Clark.**

*Bios*

**28**(4) (1957), 250.

This is the second edition of the most comprehensive book in its field. Written by two of the foremost authorities on its subject it is intended as a guide for the research worker in planning and executing carefully controlled experiments. It discusses the relative merits and methods of analysis of a wide variety of experimental designs and answers such perplexing questions as how many observations are needed and how they can best be allocated to the various factors under investigation. This edition has been considerably expanded. Two new chapters have been added, one on fractional replication of experiments and one on new designs involving continuous quantitative variables. New sections have been added to many of the original chapters, especially those dealing with incomplete block designs. Although the average biologist will certainly not find this book elementary, its study can be recommended to all those who are engaged in experimentation, whether they be ecologists working in the field or physiologists in the laboratory.

**3.8. Review by: Oscar Kempthorne.**

*Quarterly of Applied Mathematics*

**16**(4) (1959), 334.

This book is "intended to serve as a handbook which is consulted when a new experiment is under consideration." The first edition was highly successful in this aim and the second edition is an augmentation of the first edition to take care of advances in the design of comparative experiments in few years. This is the best book in existence on the down-to-earth practice of experimental design. There are aspects of the second edition which are unsatisfactory and these arise because the material of the first edition was transferred to the second edition

*in toto*. Some of the material of the first edition could have been improved and the continuity of old and new material improved. The book will be of very high value to experimenters and experimental statisticians and one can also surmise that workers in mathematical statistics will obtain some benefit in knowledge and outlook by perusing the book, since statistics is a subject which has in the past gained so much from understanding the needs of research workers.

**3.9. Review by: W A W.**

*Journal of the American Statistical Association*

**53**(281) (1958), 214-215.

The first edition of this book was reviewed by Palmer O Johnson in the September 1950 issue of the Journal. The framework of the book is unchanged, but a good deal of new material has been added, and some topics have been treated more briefly. The added material includes two new chapters, one dealing with fractional replication of factorial experiments, the other with factorial experiments in which the factors represent quantitative variables measured on a continuous scale. At the end of Chapter 9 there has been added an index to incomplete block designs now available. A number of sections have been added to various chapters. "Topics that are presented more briefly are sequential experimentation ..., the testing of effects suggested by the data ..., the problem of making several tests of significance in the same experiment ..., Yates' automatic method of computing factorial effect totals ..., additional standard error formulae for split-plot experiments ..., the effects of errors in the weights on the recovery of inter-block information ..., and the use of balanced incomplete block designs in taste and preference testing... ." The numbers of new chapters, sections, and tables carry the letter a to identify clearly the material that is new in this edition.

**3.10. Review by: G Ronald Herd.**

*Operations Research*

**5**(6) (1957), 872.

This is a revised and enlarged second edition of a book which first presented a comprehensive coverage of the types of experimental design most frequently encountered in practice. It deals with a number of real problems in research, points out practical approaches, and identifies the methodology developed for these problems. The industrial experimenter will find areas of particular interest which were not included in the previous edition. In its new form this book includes the use of (1) response-surface explorations, (2) attribute data, and (3) multiple-decision procedures, all of which are extremely valuable in the industrial applications of experimental designs.

**3.11. Review by: David F Votaw Jr.**

*American Scientist*

**46**(1) (1958), 80A.

This book is an outstanding contribution to literature on the design of experiments. Logical principles underlying experimentation are neatly set forth in R A Fisher's book

*The Design of Experiments*(first published in 1935). The authors found, however, that there was a need for a book that would describe "... the most useful of the designs that have been developed, with accompanying plans and an account of the experimental situations for which each design is most suitable." This book aptly fills that need. ... This book should be of interest to research workers in science and engineering - particularly those in the biological and social sciences, physics, chemistry, and industrial research and development. Experimenters can use it as a handbook. Teachers will also find it useful.

**3.12. Review by: J D.**

*OR*

**9**(3) (1958), 260.

By the end of the war the main principles and techniques of the design of experiments in agricultural and biological research had been well established and the resulting body of knowledge was authoritatively set out in 1950 in the first edition of this excellent book. Since then, however, there have been extensive developments in other fields of application such as industrial, social and medical research. The attempt to cover these developments as well as elaborations of previous material has led to a size increase of about a third compared with the first edition. Much of the new material should be of particular interest to those concerned with the technological applications of statistics. For example, of the two new chapters, the first, dealing with fractional replication, has particular value for certain types of exploratory research in which a quick indication is required of which factors are likely to be of greatest importance. The second of the new chapters describes the important recent work of Box and others on the study of response surfaces. A response such as output is regarded as a regression function of input factors. The problem is to allocate the input combinations at which the experiment is to be conducted so as to give economic estimation of the regression function. Designs and analyses are given for linear and quadratic functions. Further developments for locating the input combination yielding maximum response are also described.

**3.13. Review by: Norman L Johnson.**

*Biometrika*

**45**(1/2) (1958), 287.

The first edition of this book was reviewed in Vol. 38 of this journal. In that review it was remarked that the book should prove especially valuable to statisticians requiring a compendium of all the more useful designs. In the intervening period there has been considerable research activity in the field of experimental design. The authors are, in consequence, no longer able to give plans of all the more useful designs. As a compromise they have included an exhaustive index to those designs for which a plan is not provided. Two additional chapters have been inserted. One, on fractional replication, corrects a notable, and surprising, deficiency in the first edition. The other contains material on the study of response surfaces, based for the most part on the work of G E P Box. This chapter is rather out of keeping with the rest of the book, 88 is perhaps to be expected of a late addition. Nevertheless, many statisticians will probably find this chapter. and particularly the attached plans, of considerable usefulness.

It is evidence of the soundness of the first edition that very little of the original text has been altered or removed in the present edition. A number of additional paragraphs have been inserted, usually on points of detail omitted in the first edition. In particular, the inclusion of a section describing Yates' well-known tabular method of analysing a $2^{n}$ table may be mentioned. It is unfortunate that no space has been found for some material on the economic choice of amount of experimentation, a topic which has attracted some attention in recent years.

The overall effect of the changes has been to consolidate the position of an already well-established text-book. The second edition is about one-third larger than the first, but the price has gone up by more than three-quarters. Even so, the book is still excellent value for the practising statistician.

**3.14. Review by: David R Cox.**

*Journal of the Royal Statistical Society. Series A (General)*

**121**(2) (1958), 237-238.

The first edition of this book, reviewed in this Journal, has deservedly established itself as a standard textbook. It is notable especially for the series of detailed plans of the more complex designs and for the clear examples of the corresponding methods of statistical analysis.

For the second edition the authors have added two new chapters and a number of additional sections and plans. Of the relatively minor additions the most important are the account of the use of Latin squares when carry-over treatment effects are expected, and the index to the numerous partially balanced incomplete block designs that have been enumerated in recent years. New topics which get very brief mention include sequential sampling and multiple comparisons. The first of the new chapters deals with fractional replication, a device whose use has increased greatly in recent years. There is a clear account of fractional replication in the $2^{n}$ system with data from such an experiment analysed by Yates's adding and subtracting method. Detailed plans are given for 17 of the simpler designs; it is worth noting that since the book went to press the National Bureau of Standards has published an exhaustive catalogue which should be consulted by anyone wishing to embark on one of the more complicated cases. There is a brief discussion of fractional replication when all factors are at more than two levels.

The second new chapter is concerned with the application of regression methods to the study of those factorial experiments in which the factor levels correspond to values of quantitative variables, such as temperature, amount of fertilizer, etc. ... The new material maintains the high standard of lucidity of the first edition.

**3.15. Review by: Florence N David.**

*Science Progress (1933-)*

**46**(183) (1958), 530-531.

The first edition of this book appeared in 1950 and was among the first - if not

*the*first - of the many books which have been published on experimental design since the end of the war. In the opinion of the reviewer, "Cochran & Cox," as it is familiarly called, is the best book which has been written on the subject of experimental design whether considered from the point of view of those who have to teach or those who read to learn. Because the original volume has become so well known it is enough here to list changes which appear in the second edition. The authors have retained - as far as the reviewer is able to judge - the numbering of paragraphs and chapters and have interpolated material giving anything new a number plus the letter a or A. Thus there are two new chapters, 6A and 8A, in addition to the old Chaps. 6 and 8, a fact which may possibly cause confusion in the years to come. Chap. 6A is on "Factorial Experiments in Fractional Replication," a statistical application originally suggested by Finney. The construction of designs with fractional replication and the properties of these designs are succinctly set out and are followed by a common-sense discussion of the use of fractional factorial designs in practice. A welcome feature from the applied statistician's point of view is the summary of various designs - fourteen of them in the "plans" at the end of the chapter.

Chap. 8A is interesting in that it summarises recent work on the form of design analysis called response surfaces. The authors write "First a word of caution. Polynomial response surfaces have the great advantage that they are easy to fit. ... On the other hand polynomials are notoriously untrustworthy when extrapolated." This seems to the reviewer to sum up the situation admirably and the further discussion in this chapter is both fair and informative.

**3.16. Review by: Eberhard Fels.**

*Jahrbücher für Nationalökonomie und Statistik / Journal of Economics and Statistics*

**171**(1/2) (1959), 141-142.

The fact that the first edition of this guide to the planning of experiments is 7 fewer pages is an outward sign of the progress made in this area of research since 1950. This second edition is more than a corrected reprint and suitable for increasingly competing with the relevant monographs of the last few years ...

**3.17. Review by: W B Michael.**

*Educational and Psychological Measurement*

**19**(2) (1959), 259-260.

The present edition represents an updating and expansion of the 1950 text. As the authors note, the framework of the book is unchanged. The plans of all the useful types of experimental designs are presented, with a statement of the underlying assumptions and practical illustrations.

The first three chapters consider fundamental topics, including statistical inference, the function of randomisation, methods of increasing the accuracy of experiments, the number of replications for tests of significance, the number of replications for prescribed limits of error, and the statistical analysis of the results. The method of least squares is described, and from this the reader is led to the estimation of treatment effects and the elements of the analysis of variance. Various subdivisions of the sum of squares for treatment are considered, including subdivision into single components, and incomplete subdivisions. Among the other topics considered are methods of handling missing data in the analysis, the analysis of covariance, and the effects of errors in the assumptions underlying the analysis of variance.

The main section of the book, Chapters 4 to 13, is devoted to various classes of experimental designs. Some of these will be familiar to psychologists and educators, such as factorial experiments and latin squares. We do use randomised block and cross-over designs, al though we generally do not call them that, and sometimes we use one when we should use the other. Confounding is not new, even if it is not always intentional. Most of us will not be familiar with split-plot designs, lattice designs, lattice squares, and many others.

**4. Sampling Techniques (1953), by William G Cochran.**

**4.1. Review by: S Ferrer.**

*Revista Espanola de Pedagogía*

**12**(48) (1954), 550.

It is a well-planned, easy-to-read book, and one of the most modern on Sampling Techniques, published in March 1953; 50 percent of the books cited as bibliographic references have appeared in the last six years. ... The book is useful for both a textbook and a reference book. It is well presented typographically, and there are hardly any misprints.

**4.2. Review by: Bernard G Mulvaney, C S V.**

*The American Catholic Sociological Review*

**14**(3) (1953), 177-178.

The announcement for this book stated that it "can be used by anyone who is well grounded in basic statistical concepts and familiar with a minimum of mathematics (in particular with elementary algebra and summation notation)." For one wanting to do more than "use" the book, however, it is somewhat dis- concerting to discover that it aims at explaining "the relation between sample theory and the main stream of statistical theory". The sample theory analysed is restricted mainly to predicting the precision (variance of estimates) and cost of sampling finite populations, an area of lively recent developments. The author, currently President of the American Statistical Association, seemed to this unsophisticated ad-reader, to present a classically clear and critical systematisation.

Moreover, the explanation of the formulas is pointed to suggestions for their use; each chapter cites some illustrative surveys, and concludes usually with recommendations ("Summary comments") and problems ("Exercises"). Anyone who has puzzled through the terminology of

*ad hoc*complicated sample designs will find his way surprisingly easy here, and will move toward a meaningful clarification of the feasibility and limitations of sound sampling. As he reaches the final chapter on non-response and errors of measurement, he will find a particularly rewarding statement. Thus the book bridges from theory to application; it may be readily integrated into the readings for courses in social statistics. It certainly deserves more than consignment to the sociologist's crowded reference shelf. It is an apt treatise and a compelling text.

**4.3. Review by: Glenn L Burrows.**

*Social Forces*

**32**(3) (1954), 304-305.

Sampling Techniques is a highly readable book suitable both for classroom and reference purposes. Because its function is to present the existing theory of sampling as an aid to suitable choice among survey techniques, it necessarily contains some fairly routine mathematics. However, the author's informal style keeps the mathematical reader from being bored and the nonmathematical reader from being overwhelmed. His effort to "prevent an epidemic of subscripts" and his conclusion that Tables 13.2 and 13.3 "tell a sad story" are only two bits of evidence revealing the author's experience with the painful road that students and researchers must follow in seeking advice from the sampling expert. The book presupposes some knowledge of elementary mathematics and statistics, but any reader familiar with the use of summation signs will find and be able to understand the answers to most problems of estimating population means (or totals) and variances and of setting sample sizes; results have been stated clearly for those who do not wish to perform the algebra necessary to prove the substantiating theorems. The proofs are generally quite easy to follow, however.

**4.4. Review by: Allyn W Kimball.**

*The Quarterly Review of Biology*

**29**(2) (1954), 203-204.

*Sampling Techniques*is a truly worthwhile and badly needed addition to the statistical literature. Although sample surveys have been conducted for many decades, only in recent years have statisticians developed the theory of sampling into an organised well-founded discipline. Before World War II, very little of modern statistical theory could be found in book form. After the war, due in part to the efforts of a few publishers, there was a rapid rise in the number and quality of statistics textbooks dealing with both theory and applications. Now, with the appearance of Sampling Techniques, almost every major field of statistics is well represented in textbook form.

The author needs no introduction to statisticians and should be familiar to most biologists as co-author with Gertrude M Cox of

*Experimental Designs*, almost a necessity for any conscientious experimenter. In

*Sampling Techniques,*the author's former students will recognise the extremely lucid and logical method of presentation which has always characterised his lectures. Cochran's philosophy with regard to the teaching of statistics is described clearly in this quotation from the preface:

"By the use of powerful operation methods, the bulk of existing theory can now, I believe, be developed in a very compact space as particular cases of a few general results. Such a development would be illuminating in clarifying the interrelationships between the different parts of the subject, and might prove a stimulus to further research and discovery. But my experience in teaching has been that most students who wish to learn something about sampling theory find this kind of presentation heavy going, and prefer a more leisurely progress."

In this matter most readers will agree with the author. For a reasonable understanding of the proofs, familiarity with algebra and with parts of the calculus is necessary, although the author discusses many points which can be understood without a mathematical background.

...

The author hopes "that the book will be useful both as the basis of a course on sample survey techniques in which major emphasis is on theory, and for individual reading by the student who does not have access to formal instruction." Although the emphasis is on theory, the manner in which it is presented would allow the book to be used as a textbook in a course on applications provided that it was supplemented with sufficient illustrative material.

**4.5. Review by: Marvin Zelen.**

*Science, New Series*

**118**(3070) (1953), 523-524.

Sample surveys have played an important part in government operations for the past 20 years. They have served as invaluable research tools whenever accurate information is needed about a population, without entailing the comparatively large expense of a complete enumeration. Even if a complete enumeration were possible, it might not be as accurate as a good sample survey owing to the necessarily longer time for a complete enumeration in which time the population might change. Within recent years sample survey techniques have become increasingly more important in many of the social sciences, business, and technical fields. This book, written by a prominent statistician, gives a comprehensive outline of modem sampling theory as it has been developed for use in sample surveys.

Professor Cochran is to be commended for not only writing an excellent, well-organised exposition of sampling, but also for attempting to impart some of his own experiences to help the reader develop a "feel" for the manner in which sample surveys are used. The author succeeds admirably in this respect. The tempo of the book is one at which the reader is being led through new material, always with Professor Cochran's kind but steady guidance.

Sampling Techniques is written so that the reader possessing knowledge of elementary algebra and the equivalent of a first course in statistics will be able to comprehend most of the material. Among the different techniques discussed are simple random sampling, stratified sampling, systematic sampling, subsampling, and double sampling. The chapters devoted to ratio and regression estimates are particularly well written. Illustrating much of the sampling theory are many carefully explained, well-chosen examples. Many of the exercises completing the chapters consist of real data that enable the reader to get the necessary practice for a fuller understanding of sampling theory. The book is carefully documented with many up-to-date references.

The main emphasis is to help the reader attain a grasp of sampling theory without being bogged down with too many mathematical details. There is much in this well-written book to recommend it to practicing statisticians, students of statistics, and those who wish to learn about sampling through individual study. This volume will long remain a classic in the field of sample surveys.

**4.6. Review by: Florence N David.**

*Science Progress (1933-)*

**42**(166) (1954), 321-322.

The use of statistical methods in sampling surveys may be said to have originated with A L Bowley's book

*Measurement of the Precision Attained in Sampling*of 1925. The sampling survey was used by many organisations between the two wars and at the time of the outbreak of the second World War had become an established branch of statistical methods with the principal techniques well worked out. During the second World War the sampling survey was used to estimate the minimum incidence of various characteristics of the country from sickness to crockery replacements and the end of the war saw it firmly entrenched in the favour of the bureaucrat. Possibly partly because of this and partly because of the general eagerness everywhere since the war to employ statistical methods, there have been several treatises written on sampling survey techniques. Of these the present book under review - which might more correctly be designated Sampling Survey Techniques - is by far the most notable. Prof Cochran has made distinguished contributions to statistics in the fields of research ; he has here shown himself equally distinguished as an expositor. His book is intended for the student, who, possessing elementary training in statistics and probability, is anxious to specialise in sampling survey work. If this hypothetical student does in fact work through and understand Prof Cochran's book he will be admirably fitted to do this.

**4.7. Review by: Florence N David.**

*Biometrika*

**41**(3/4) (1954), 565-566.

Prof Cochran's book deals entirely with that aspect of statistics which concerns itself with what are sometimes called sampling surveys; a somewhat narrower field than the title of the book might suggest. It is clearly written with lucidity and logic in the development of the ideas put forward. and will take its place with the other

*vade-mecum*of the would-be sample surveyor: Deming on

*Some Theory of Sampling*and Yates on

*Sampling Methods for Censuses and Surveys*.

The book begins with a short discourse on the advantages to be gained by using valid sampling techniques. We then start immediately on sampling from a finite population with the standard errors of various estimates worked out. There is some discussion on the validity of the normal approximation for the sample mean even when the sampling fraction is not small. Rarer still in such statistical literature as this, there is also a recognition that non-normality in the population may make a difference to the distribution of the variance, although we are left a little uncertain as to what use we should make of this information except to be cautious.

Chapters follow on sampling for proportions and percentages, the estimation of sample size, stratified random and systematic sampling, ratio and regression estimates, double sampling and sources of error in surveys. The whole field appears to be well covered; authors from whom the various techniques originated are acknowledged in the text and a full reference given at the end of each chapter. This enables the student wishing to find out things for himself to go to the first beginnings. Also at the end of each chapter are exercises with solutions at the end of the book.

The would-be worker in sample surveys will find his subject presented with freshness and imagination in Prof Cochran's book. This is perhaps somewhat surprising in view of the well-trodden track to the well, created by both theoretical and practical workers in the past ten years. However, in this book everything that could and should be said has been written down. The applied statistician will find the discussion and results useful; the theoretical statistician will find out where to go in the literature in order to develop his own problems a stage further. Perhaps the one flaw is in the algebraic formulation of the sampling problem which is not elegant.

**4.8. Review by: Anders Hald.**

*Econometrica*

**23**(3) (1955), 350.

This book will serve as an excellent basis for a course in sampling theory as it has been developed in connection with sample surveys. The student is supposed to have had a first course in statistical methods including the simpler types of analysis of variance and regression. With this background he will find the book relatively easy reading, and it will be extremely helpful for the teacher in organising a course. The exposition of theory is very clear, principles are emphasised rather than details, and references are carefully selected with a view to supplementing the text both with regard to details omitted and to more advanced theory.

Besides the introductory chapters on simple random sampling and the estimation of sample size, the book contains nine chapters treating stratified random sampling, ratio estimates, regression estimates, systematic sampling, choice of type of sampling unit (cluster sampling), subsampling with units of equal size, subsampling with units of unequal size, double sampling, and sources of error in surveys (non-response and errors of measurement). The book does not cover the more practical problems arising in the planning and execution of a survey such as the definition of the population, the construction of a frame suitable for the purpose of the survey, the design of the questionnaire, methods of collecting the information, administration of the survey, and methods of processing and tabulating the data....

The book can be highly recommended as an introductory text giving a review of standard sampling theory for finite populations as applied to the field of sample surveys

**4.9. Review by: Alan Stuart.**

*Economica, New Series*

**21**(82) (1954), 171-172.

Sample survey theory has a purpose which should appeal to the economist: to attain maximum accuracy in estimation for a given total cost or, equivalently, to attain a given standard of accuracy at minimum cost. To achieve this purpose a large number of techniques has been developed, mainly in the past fifteen years, which enable the precision of sampling to be increased by utilising available information about the population to be sampled. If no such supplementary information is available, a simple random sample, with every unit in the population being given an equal chance of selection, is the only respectable technique. Far more commonly, something is known of the population in advance, and this information may be used in one or more of several ways.

...

Professor Cochran's full theoretical account of the subject is complementary to Dr Yates' monograph,

*Sampling Methods for Censuses Surveys*, which is much more of a practitioner's manual. Inevitably, there is lengthy algebra involved in some of Cochran's proofs, but there is no difficult mathematics - even calls on the differential calculus are few. However, a necessary prerequisite for the reader is a knowledge of the principal topics of general statistical theory, particularly a basic course on probability and some knowledge of correlation and regression theory. There is little fault to be found with the exposition, which is smooth and natural. Occasional clumsiness of notation is the fault of the subject rather than of the writer.

**4.10. Review by: Morris H Hansen.**

*Journal of Marketing*

**18**(2) (1953), 202-203.

The purpose of this book, in the words of the author, is "to present a reasonably comprehensive account of sampling theory as it has been developed for use in sample surveys, with sufficient illustrations to show how the theory is applied in practice, and with a supply of exercises to be worked by the student. My hope is that the book will be useful both as the basis for a course on sample survey techniques in which the major emphasis is on theory, and for individual reading by the student who does not have access to formal instruction."

The statistical and mathematical levels assumed for the reader include a familiarity with elementary algebra and some knowledge of calculus, although the calculus is required for only a limited number of proofs. On the statistical side, the book presupposes an introductory course in mathematical statistics. To aid the beginner the earlier proofs are spelled out fully, and these, together with the numerous exercises, will assist the reader in mastering the notation and in understanding the theory and its application. The answers to many of the exercises are given in the back of the book.

...

In summary, this book is comprehensive, concise, and well-written, and is highly recommended to the student and practitioner interested in the development and application of sampling theory to practical survey problems.

**4.11. Review by: Frederick F Stephan.**

*American Sociological Review*

**20**(4) (1955), 480-482.

Most of the modern developments in sampling surveys have come to sociology from other fields, particularly from agricultural research, from mathematical statistics, from industry, and from both public and private survey organisations. Sociologists and social statisticians have made their contributions too. For example, the establishment of the research program in the Census Bureau, one of the major centres for the development and application of modern sampling methods, was in large measure the work of sociologists like Rice, Dedrick, Stouffer, and Hauser working with mathematical statisticians like Deming, Hansen, Hurwitz, and Madow and with their colleagues in both professional and administrative positions in the Bureau. Since sociology has so much to gain from sampling surveys and has had a great part in their development, we welcome Professor Cochran's excellent exposition of the sampling techniques.

This book sets a standard of excellence in sampling procedure in company with the volumes by Yates, by Deming, and by Hansen, Hurwitz and Madow. It is written very sensibly and with great technical skill. It is not a manual on how to "do it yourself". It does not treat a great many aspects of survey practice of the kind that are considered in detail in books by Parten, Festinger and Katz, or Jahoda, Deutsch and Cook. None the less there is a fundamentally practical purpose in its thorough application of statistical theory to such problems of technique as the selection of units of sampling, modes of stratification, methods of estimation and methods of determining sampling variation or "error". It shows how these technical problems can be solved economically and efficiently. It evaluates the risks of difficulty from the use of biased methods of selection and estimation. It does not neglect errors of measurement and their effect on the results. Minor problems are not dismissed casually if there is a possibility that they will at times be of major importance. The aim of the theory and its applications is to predict how a given plan of sampling will work out in practice. It is therefore of great value beyond the field of statistical methodology both for teaching and for research.

Among the phases of sampling technique that are distinctively modern are: explicit treatment of finite populations in the theory, thorough analysis of the choice of sampling units, development of more flexible and complex designs, such as those based on subsampling or double sampling, analysis of systematic sampling, and comparison of ratio and regression estimates. It is not merely these topics but the coherence of the whole and the utilisation of mathematical statistical theory to master many important details that makes this a major advance over the discussions of sampling that were available a generation ago.

**5. Sampling Techniques (Second Edition) (1963), by William G Cochran.**

**5.1. Review by: T M Fred Smith.**

*Journal of the Royal Statistical Society. Series C (Applied Statistics)*

**13**(1) (1964), 54.

The first edition of this book was generally acclaimed by statisticians. In the second edition, Professor Cochran has retained the basic structure and the same clear exposition, but has considerably enlarged the text. The additions are representative of the main advances in sampling theory during the last ten years and blend easily with the original text. In particular, the section on stratified sampling has been enlarged and now occupies two chapters, and much more accent has been placed on sampling with unequal probabilities. The new edition should be as widely acclaimed as the first edition, and is in the reviewer's opinion the clearest exposition on sampling theory. Although essentially a theoretical book, the many sections on the optimum use of sampling schemes and the many examples cited would make it rewarding reading for the applied statistician.

**5.2. Review by: Roy G Francis.**

*Journal of Health and Human Behavior*

**6**(3) (1965), 176.

... the book makes a tremendous contribution to any researcher whose work relies on surveys. Indeed, it is a must. Those who try to estimate error in surveys and who try to relate information gathering to a notion of efficiency related to survey costs, will find this book will enable them better to plan their work. As I said before, the area of mental health research needs a book such as this. We have, too long, allowed crude estimates to stand as empirically derived final truths: Ask any physician and he'll tell you that about 40 percent of his patients need some kind of psychiatric help. It's about time we began to test notions of this kind. A serious application of the wisdom contained in Cochran's

*Sampling Techniques*is just what the doctor ordered.

**5.3. Review by: Thomas T Semon.**

*Journal of Marketing Research*

**1**(2) (1964), 88.

The second edition, coming a decade after the first, is far more than a revision. Content has been broadened, particularly in sections dealing with stratified sampling, unequal clusters, ratio estimates, and sources of error in surveys. The additions are substantial and make the present edition an even more valuable book than the original. In the Preface, the author deplores the added physical length of the second edition. He should, in fact, be commended for his brisk, clear style, thanks to which the book is still of manageable size. ... this book ... is certainly one of the two or three outstanding sampling texts currently available.

**5.4. Review by: Tore Dalenius.**

*The Annals of Mathematical Statistics*

**35**(3) (1964), 1381-1382.

The first edition of Cochran's

*Sampling Techniques*was one of several text- books which appeared in the early 1950's. It was very favourably received, both in university circles and among survey statisticians. This success is explained by the outstanding professional competence of the author, the pedagogical merits of the presentation, and also by the reasonable size of the book (some 330 pages).

The second edition, published in 1963, represents primarily a useful modernisation of the first edition. Several techniques have been included which were not presented at all in the first edition, in most cases because they were not as yet available, or only touched upon. As a result, the second edition has 413 pages; this size may still be called reasonable for a textbook.

The main novelties of the second edition are the following.

(1) Cochran has devoted several paragraphs to the problems associated with the concept of "domains of study" as coined by the U. N. Sub-Commission on Sampling; Cochran uses the term "subpopulations". A subpopulation is a part of the population for which one wants to have separate estimates; such separate estimates are called for in many, perhaps most, surveys. If such parts cannot be identified in advance and thus separate samples be selected from each part, the relevant sampling theory is more complicated than that applicable to estimates of parameters which refer to the overall population (or to separate strata).

(2) In the first edition, stratified sampling was discussed in one chapter of some 35 pages; in the second edition, close to 70 pages, divided into two chapters, are devoted to the same class of techniques. ...

(3) The discussion of ratio and regression estimation now includes unbiased ratio estimation, multivariate ratio estimation and regression estimation with preassigned coefficient of regression ("difference estimation"). ...

(4) The discussion of one-stage cluster sampling and multi-stage sampling is somewhat enlarged; it covers some 90 pages in the second edition as compared with some 75 pages in the first edition. The additional pages have largely been devoted to the presentation of recent researches on sampling without replacement, with unequal probabilities of selecting (first-stage) units. ...

(5) Finally, the discussion of sources of error in surveys has been enriched by the inclusion of some new material.

...

The second edition of Cochran's Sampling Techniques is an outstanding contribution to the field of statistics. Its influence on the improvement of sample survey theory and practice in the 1960's will no doubt parallel the influence of the first edition in the 1950's.

**5.5. Review by: William J Mehok.**

*Gregorianum*

**45**(3) (1964), 673-675.

If one had unlimited funds, access to more skilled professional and secretarial help than exists and was not pressed for time, there would be no need for sampling. Furthermore, if decisions could be made infallibly by intuition, or the toss of a coin, or the consensus of experts, there would be no need for either the complete census, or

*a fortiori*, sampling. Unfortunately, such is not the case, and persons confronted with the task of summarising large masses of data and drawing conclusions from them have arrived at a satisfactory compromise called sampling. Sampling is used almost universally in any large scale research or decision-making project. With the exception of the decennial census, surveys of the complete population are almost extinct. The volume being reviewed treats the theory and practice of this procedure.

...

Cochran succeeded eminently ... He is an acknowledged leader among theoreticians. Scarcely any major recent decisions in United States government, industry, or scientific research have been made without consulting him either personally, through his publications, or through his pupils. He headed the committee which laid the Kinsey report to rest. He was a member of a ten man team evaluating evidence on the effects of smoking on health for the report of the U. S. Surgeon General's Advisory Committee on Smoking and Health. Since it affects the personal lives of so many and is at the base of a billion dollar industry, the effect of the report will be far-reaching. The present revision has updated what was a pioneer work, filling, in many of the gaps and answering many of the questions then pending. This is a difficult hook, not because the style is not readable and clear but because the reasoning is so compact that one must go slowly. One can scarcely criticise a hook on theory for not being a good "cook book", yet this is the only objection I see. Even here, the author offers copious references to literature, especially to recent simplifications and remedial procedures, so that it does supply some of the functions of a practical manual

**5.6. Review by: Siegfried Koller.**

*Revue de l'Institut International de Statistique / Review of the International Statistical Institute*

**33**(3) (1965), 558-559.

The second edition of Cochran's

*Sampling Techniques*which appears 10 years after the first edition (1953), confirms the merits of this well approved textbook in a striking manner. The clear didactic composition is preserved in spite of many additions and supplements. The added details expand but do not confuse. Most of the new sections are devoted to problems of great practical importance even if they are minor ones in theory. It turned out to be valuable for teaching as well as for application to give more attention to these special cases in separate sections of the book. To this first kind of additions belongs e.g. the widely required estimation of averages, totals, and proportions over sub-population. Other new parts refer to recent developments in theory. The chapters on stratified sampling are worked through very carefully in order to fill possible gaps. The number and construction of strata, and two-way stratification with small samples are examples of the appositions. The problems of allocation with more than one item are mentioned in greater detail. The unsatisfactory situation due to the inevitable lack of perfect solutions is mitigated by an example showing that in practice sometimes according to the flatness of the optimum, the solutions for the different items would not differ very much. But who would not have examples of strong disagreement? The experience on the comparisons required in applications led to certain supplements e.g. comparisons between different domains in general and in the special case where strata are used as domain of study. ... This revised and enlarged edition is, owing to the clear arrangement of short and distinct sections and the concise expressions, an outstanding text-book of sampling techniques.

**5.7. Review by: Alan Stuart.**

*Econometrica*

**31**(4) (1963), 773-774.

Sample survey theory is the poor little rich girl of the statistics family: it contains few results of considerable generality and almost none which are mathematically attractive. However, it carries a large dowry for the applied statistician (especially in economics and other social sciences) who can only derive his data from samples of the population of interest. Its study needs no further justification, but the problem which its lack of charms present to the teacher and textbook-writer (in our present analogy, the matchmakers) are how best to keep the suitors awake through the display of rather prosaic accomplishments until the ultimate payoff becomes obvious.

No writer had done this better than Professor Cochran in the first edition of this book, ten years ago. The new presentation is a considerable expansion of the original - about a third of it is in the starred sections new to this edition, although some of this is rewriting rather than entirely new material. In the main, the changes reflect the new research of the past decade into the construction of strata, into domains of analysis, into unbiased ratio- and regression-type estimators, and into the theory of sampling with unequal probabilities without replacement. ... This is still the best book from which to learn the theory of sample surveys.

**5.8. Review by: Walter T Federer.**

*Biometrics*

**21**(2) (1965), 508.

The second edition of Professor Cochran's popular introductory sampling theory and techniques book is about one-third larger than the first edition. Asterisks in the table of contents denote new sections; 54 out of a total of 183 sections are so marked. Also, Chapter 5 of the first edition on stratification is split into two chapters with one of them, Chapter 5, dealing with the more general and standard results and the other, Chapter 5A, which is new, dealing with specialised topics necessary for efficient use of stratification. Also, ratio estimates have been introduced into Chapters 2 and 3 whereas they were previously not encountered until Chapter 6. The topics now covered, as denoted by the chapter headings, are: introduction, simple random sampling, sampling for proportions and percentages, the estimation of sample size, stratified random sampling, further aspects of stratified sampling, ratio estimates, regression estimates, systematic sampling, one-stage cluster sampling, subsampling with units of equal size, subsampling with units of unequal size, double sampling, and sources of error in surveys. The number of exercises has been more than doubled; exercises are included at the end of each chapter. Answers to the exercises are given in the back of the book.

...

The minimum mathematical requirement for reading this book is some knowledge of differential calculus; the minimum statistical requirement is an introductory statistics course. The book is quite appropriate as a text for a one-semester course in sampling theory although it may not be possible to cover all the material in this amount of time for groups with the minimum mathematical and statistical requirements.

**6. Sampling Techniques (Third Edition) (1977), by William G Cochran.**

**6.1. Review by: William R Buckland.**

*The Journal of the Operational Research Society*

**29**(9) (1978), 931-932.

In the statistical literature of sample surveys this book ranks as one of the handful of "great" texts. Although many of the basic statistical principles are common to the design and analysis of controlled experiments, this book deals with the broader and generally larger subject of what are sometimes called field surveys; hence it is of importance to the practice of Operational Research.

Although the topics are presented in essentially the same order, the extensive revisions for this edition have enabled the book to be re-set with a slightly wider page size and an attractively clean type-face on white paper: the well-known publishers are to be congratulated. To take up the developments of statistical methods and survey practice, nearly 40 new sections are added with half this number dropped; hence the volume is still very manageable in use. The references are generally up to 1976 ... .

Apart from the basic philosophy of "why" and "how" in the Introduction, the two chapters 4 and 13 contain the topics which are most frequently forgotten or treated with cavalier disregard (i.e. the estimation of sample size and the sources of errors in surveys). It is hereabouts that the most important questions (and answers) arise vis-a-vis the client, e.g. advice to ditch a whole survey because of massive non-response.

Following widespread successful use over two decades, this new edition will continue to provide excellent service to those who trouble to use it.

**6.2. Review by: Michael R Sampford.**

*Journal of the Royal Statistical Society. Series C (Applied Statistics)*

**27**(3) (1978), 352.

Although some chapters have been extensively reworked, this is essentially an augmented version of the second edition, rather than a completely rewritten book. Most of the new material relates to practice: the large body of work on the logic of inference from samples from finite populations, that has appeared in the 15 years since the publication of the second edition, receives for the most pan cursory mention, reinforced by references to review papers, on the grounds that "the influence of this work on sampling practice has been limited thus far [but should steadily increase]". This is a perfectly reasonable policy to pursue in a book called "Sampling Techniques", but those of us who teach sampling theory may feel a trifle disappointed. For example, I myself feel that undue stress (from the practitioner's point of view) has of recent years been laid on admissibility, but it is surprising to find the word absent from the index; "Bayesian" also is missing, and I noticed only one reference to Bayesian methods in the text (in the section already quoted from). Some results on, and references to, model unbiasedness and purposive selection have been incorporated into the chapters on ratio and regression estimation, and the sections on unequal probability sampling without replacement have been considerably extended. The use of random sampling numbers is illustrated (curiously for the first time), but there is no discussion of the problems of random selection by computer, or of the hidden perils of some "random" computer procedures.

There are numerous general improvements ; some previously cumbersome proofs have been tightened up, and more use is made of standard statistical results. The chapter on ratio estimation has been extensively rewritten, with new material on jack-knifing, and references to sampling investigations of the properties of the ratio estimator and its estimated variance. The chapter on cluster sampling has been split in two, and that on sub-sampling from unequally sized clusters is considerably improved, with more use of general formulae. Attention is paid throughout to recent developments in handling complex designs and estimators; the "design effect" is here introduced by that name, and receives frequent references, and a section has been added on techniques for use with non-linear estimators, with discussion of Taylor expansion and jack-knife methods, and the method of balanced repeated sampling. Most of the new material is introduced in short sections, with brief discussion and references 10 recent papers. Reference lists, in earlier editions given chapter by chapter, have now been usefully amalgamated into a single list.

This book will no doubt be regarded as hopelessly old-fashioned by the more extreme theoreticians, but for those who want to know what is done, and what is at present practicable, it is admirable. It should serve practitioners as well, and for as long, as has the second edition.

**6.3. Review by: J E J.**

*Technometrics*

**20**(1) (1978), 104.

The volume under review is the third edition of a book that is familiar to nearly everyone who has been engaged in sample survey work for any length of time, the first edition having appeared in 1953 and the second edition a decade later. For those not familiar with these earlier editions, Cochran's book can be classified as one which is primarily concerned with estimation procedures associated with the various types of sampling used in survey work and as such makes an excellent reference book for workers in the field. There are proofs but not enough to classify it as a theoretical book; similarly, there are numerous sections devoted to sampling techniques but again, this is not the principal goal of the book either.

In comparison with the second edition, one notices that the new edition has only 13 more pages; however, the pages are five-eighths of an inch wider in the new edition and this results in print lines which are a half-inch longer so that considerable new material has been added reflecting some of the new developments in the field. The basic format of the book is the same and a few of the chapters have been changed very little. An average of two to three problems have been added to those at the end of each chapter. The answers to many of them are in the back of the book. The references which appeared at the end of each chapter have now been combined in the back of the book instead.

...

While a change from one edition to another is not usually all that dramatic, those in particular who are still using the first edition might consider the fact that a lot of new results have been presented since that book first saw the light of day.

**6.4. Review by: Michael R Sampford.**

*Biometrics*

**34**(2) (1978), 332-333.

The second edition of

*Sampling Techniques*has been for the last fourteen years an invaluable guide to those methods commonly used in survey sampling. Although the years since its publication have seen an explosion o interest in the logic of statistical inference from samples drawn from finite populations, the proposed methods resulting from this interest have not yet greatly affected survey sampling practice, so it is perhaps natural that this third edition offers few surprises. Considerable sections and some whole chapters of the two editions are identical, except for minor modifications such as some repartitioning into sections, increased numbering of formulae, the consolidation of references into a single list, the addition of a few more exercises, and the (fairly) consistent replacement of 'estimate' by 'estimator' in referring to the random variable. Some of the more cumbersome proofs have been streamlined, greater use being made of results from general statistical theory, and Lagrange multiplier arguments being replaced, where practicable, by appeals to the Cauchy-Schwarz inequality. All these features rank as improvements though it is a pity that section numbers no longer agree entirely with those in the second edition. New material has been added for the most part in the form of short sections with useful references on developments in practical survey analysis, relating particularly to complex designs and estimators. The 'design effect', though not a new concept in this book, is here given that name, with numerous brief references, and there is a new section on techniques for non-linear estimators in which recent work on Taylor expansion methods, balanced repeated replication, and the jack-knife is discussed. Discussions of efficiencies of various estimators are supplemented where possible, by references to recent sampling investigations on small-sample efficiency.

Some chapters have been extensively rewritten, including that on ratio estimation, which now contains many new references, as well as short new sections on ratios of ratios and the product estimator. In this chapter, and that on regression estimation, the discussion of population models has been extended. The chapter on cluster analysis has been split in two, for equal and unequal sizes. The discussion of with-replacement sampling has been modified, and the section on unequal-probability sampling without replacement has been considerably extended. The chapter on sub-sampling from unequally-sized clusters has been substantially modified and improved, with more use of general formulae. There is a new section on double sampling in analytical surveys.

Some readers may regret the absence of all but very brief references to recent fundamental work on finite-population inference, but Professor Cochran's view that such material is as yet out of place in a practical treatise will find many sympathisers. Much more to be regretted by the biometrician is the continued absence of any treatment of sampling problems peculiar to biology (apart from the applications in forestry of systematic sampling, dating back to the first edition). There is no reference to any of the work on estimation of natural population parameters by repeated catches, nor of methods for sampling botanical populations. With this exception, the book continues to live up to its title, and should continue to give valuable service for many years

**7. Statistical Problems of the Kinsey Report (1954), by William G Cochran, Frederick Mosteller and John W Tukey.**

**7.1. Review by: Paul Hanly Furfey.**

*The American Catholic Sociological Review*

**16**(3) (1955), 219.

Cochran and his co-authors have tried to be severely objective in their judgments. They believe that Kinsey's work stands as superior to the work of others with which it is compared. On the other hand, it had some grave defects. Kinsey's sample does not appear to have been very representative; there is reason to fear that it may have been biased in some respects. Some findings are questionable because of possible errors of memory by the subjects and inaccuracies in their reports. The work needed better statistical analysis. Finally, Kinsey and his associates "should have indicated which of their statements were undocumented or undocumentable and should have been more cautious in boldly drawing highly precise conclusions from their limited sample." The volume under review was written by statisticians and they stick to their specialty pretty consistently. They discuss the Kinsey report from the standpoint of statistical logic, and from that standpoint alone.

**7.2. Review by: Quinn McNemar.**

*Science, New Series*

**122**(3161) (1955), 206.

This volume contains a critique, by a committee of the American Statistical Association, of the methodological aspects of Kinsey's

*Sexual Behavior in the Human Male*. A 42-page concise summary of the issues is followed by a series of appendixes in which are found detailed accounts. Appendix A (110 pages) is a reproduction and evaluation of six leading reviews (in journals) of Kinsey's book. In general, these three mathematical statisticians agree with the previous critics, who had pointed out many serious shortcomings in Kinsey's methods. In Appendix B, prepared by W 0 Jenkins (a psychologist), one finds that by comparison with the eight other most important sex studies the work of Kinsey is superior, even though far from perfect. The remaining five appendixes are concerned primarily with the problems of sampling and statistical treatment of results.

**8. Statistical Methods (6th Edition) (1967), by William G Cochran and George W Snedecor.**

**8.1. Review by: Owen L Davies.**

*Journal of the Royal Statistical Society. Series C (Applied Statistics)*

**17**(3) (1968), 294.

The authors have kept in mind the two purposes the book has served during the past thirty years - as texts for introductory courses in Statistics and as reference sources of statistical techniques helpful to research.

The book rightly makes extensive use of experimental sampling both to familiarise the reader with the basic sampling distributions that underlie modern statistical practice, and as a technique in its own right for solving problems which are intractable mathematically. Indeed experimental sampling methods are nowadays used extensively in computer simulation of processes involving a stochastic element, often in preference to a mathematical treatment. There has been some re-arrangement in this new edition of the book resulting in improvement in the presentation, and some new topics are included which make the treatment more complete. Some of the new topics arc: linear calibration, linear regression when both variables arc subject to error, an introduction to probability, selection of variates for prediction in multiple regression, non-linear regression and applications to asymptotic regressions, discriminant functions.

The treatment of the subject is classical and conventional. It is also elementary and does not require a knowledge of mathematics beyond A-level. The methods arc fully explained and liberally illustrated with practical examples which should make the book easily understood by students undertaking a first course in statistics. There is a distinct biological bias in the practical illustrations.

The treatment of sampling, which covers five chapters in all, is particularly good and the book deals adequately, at the level intended, with most of the techniques of statistical analysis required by an experimental scientist.

**8.2. Review by: Tore Dalenius.**

*Revue de l'Institut International de Statistique / Review of the International Statistical Institute*

**36**(3) (1968), 361-362.

In the last few decades, the body of knowledge conceived of as "statistical methods" has undergone a development that has meant a quantitative as well as a qualitative revolution. As a consequence, most textbooks which appeared in the 1930s or even later, were soon out of date; today they have, at the very best, a purely historic value. But a few old-timers among the old textbooks have survived. To some extent this may be due to a series of revisions; but this explanation does not seem to suffice - the quality of the original version is obviously of a decisive importance. "Statistical Methods" by Snedecor and Cochran is an example of this. The first edition - prepared by the senior author - appeared in 1937. The present edition is the sixth! ... The authors have aimed at retaining the well proved features of the previous editions. Especially, the mathematical level required involves only elementary algebra; the exposition makes an extensive use of simple examples. On the other hand, the authors have introduced new material, e.g. a discussion of remedial measures for the effects of failures in the assumptions underlying the analysis of variance, and the discriminant function. In conclusion, I may add that the 30th anniversary of a classic textbook has been adequately dignified by the appearance of the present edition.

**8.3. Review by: William R Buckland.**

*Journal of the Royal Statistical Society. Series D (The Statistician)*

**18**(4) (1968), 414-415.

The appearance of a new edition (almost decennially) of Snedecor is a distinct event in the standard textbook literature of statistical methods. When the new edition is coupled with a second well-known name as co-author, the occasion must be drawn to the attention of readers of this journal; hence, the somewhat unusual procedure of devoting a full measure of space to the sixth edition of a standard work.

This book has served well many generations of students and a wide variety of research workers who need a basic reference book to help collect, analyse and interpret their data. The level of mathematical difficulty is relatively low by many current views since only elementary algebra is required. This, however, has enabled the book to make the very wide appeal that it has and, in one way, contributed to the distinctive tone of the drafting. In order to help the reader's understanding of principles the algebraic proofs of formulae are supplemented or complemented by common-sense explanations of the role played by the different parts of the formula. This "down-to-earth" and "let me help you" approach is extended by the, use of experimental sampling procedures, a good basis for using computers, extensive fully-worked illustrations in the text into which are inserted many groups of examples for the reader's own participation. In order to encourage the student into wider fields, each chapter is provided with a full list of references: these also give valuable background to the research worker in another basic discipline who may wish to follow a particular topic at some length. The book now concludes with a standard collection of statistical tables and an index of the examples analysed in the text as well as the usual author and subject indexes.

...

This book cannot be too highly commended to the Institute's students at the appropriate level, their teachers and many others who come within the viewpoint of its distinguished authors.

**8.4. Review by: Agnes M Herzberg.**

*Journal of the Royal Statistical Society. Series A (General)*

**132**(3) (1969), 442.

The first edition of Professor Snedecor's book appeared in 1937. Since then the book has become so well known that a review of the sixth edition, written in collaboration with Professor Cochran, need only consider the revisions and additions. The whole text has undergone minor revisions including various changes in layout and ordering of chapters. For example, the material on large sample methods which formerly comprised Chapter 8 has now been placed in earlier chapters. Also, the chapter on multiple regression now precedes that on covariance and multiple covariance. The statistical tables, previously scattered throughout the text, now appear in an appendix.

...

This edition with its new format maintains the mathematical level of previous editions and the student with no more than a knowledge of basic algebra should find no difficulty. The book will, no doubt, continue to be widely used, as the authors say, "both as texts for introductory courses in statistics and as reference sources of statistical techniques helpful to research workers in the interpretations of their data".

**8.5. Review by: Ivan Bello.**

*Econometrica*

**38**(2) (1970), 372-373.

This book is certainly unique in the wide range of statistical methods which it presents. All subjects are fully illustrated and the mathematical models underlying each topic are provided. The small sample distributions, so important in social research, are particularly well analysed. The chapters on regression and correlation, as well as the one on analysis of variance, provide the research worker with all the important tools he needs. Even though its greatest value lies in research work, it is undoubtedly useful for teaching too.

**9. Statistical Methods (7th Edition) (1980), by William G Cochran and George W Snedecor.**

**9.1. Review by: Richard C Campbell.**

*Biometrics*

**38**(1) (1982), 292.

This edition of the long-established introductory text was nearly complete when Professor Cochran died: Professor D F Cox completed the remaining authorial work.

The preliminary material has been expanded into three chapters to allow 'a more gradual immersion into the subject matter'. Nine topics appear for the first time, and other sections have been modified to take account of recent work and of the increased importance of computers; three new tables are useful in the detection of outliers.

The new topics are:

Probability paper,

The probability of at least one success in trials,

Levene's robust test for the equality of a set of estimated variances,

Balancing the order in which treatments are given in a repeated measurements experiment,

Simultaneous study of the different effects of a transformation in the analysis of variance,

Yates's algorithm in factorial experiments,

Experiments with repeated measurements,

Mallows $C_{p}$ criterion for choosing a subset of predictor variables in multiple regression,

Nonsampling errors in sample surveys.

The main modifications are concerned with (i) the expected values of mean squares in the analysis of variance and (ii) the calculations and uses of multiple regression, in particular the sweep operation and the use of dummy variables to bring analyses of variance and covariance into multiple regression form. With these alterations the book, including Appendix Tables and Index, makes 507 pages; the scope is described in the Preface as 'ample material for a course extending throughout the academic year'. To this reviewer, that is an understatement. Indeed the book is a remarkably complete exposition of elementary statistical methods for the user, covering a wide range of topics, with some elementary algebra to help formalise the structure, plenty of working examples and a good supply of exercises for the reader to work. It would be a very diligent reader who really did cover all this material in one academic year! This has been a successful text for nearly 45 years: the new edition should have at least as many years of useful life as that preceding.

**9.2. Review by: John A Cornell.**

*Technometrics*

**23**(3) (1981), 312-313.

Upon agreeing to review this book, it occurred to me that there is probably little I can add to what has already been said about a book that has served for several generations as a classroom text and as a reference for users of statistical methods. K A Brownlee said it very well in his 1957 review of the fifth edition when he wrote, "

*Statistical Methods*has been beloved by users of statistics in biology, and also other sciences, for talking to them in a language that they can understand, without committing conceptual errors that bring down the wrath and scorn of the theoretical statistician." This edition follows the example set by the earlier editions. ... As a text, the book contains ample material for an introductory one-year course on statistical methods for graduate students. Students with only limited mathematical training can work the computations in the exercises. ... In summary, this book is outstanding in terms of coverage of traditional methods. Here is a text that, in my opinion, will continue to be the standard against which all other texts on statistical methods are compared

**10. Statistical Methods (8th Edition) (1989), by William G Cochran and George W Snedecor.**

**10.1. Review by: William A Williams.**

*Journal of the American Statistical Association*

**86**(415) (1991), 834.

This venerable textbook, authored by two past presidents of the American Statistical Association, has now been published in its eighth edition. It continues to be the leading general statistical text in the fields of biology and agriculture because of its clearness of exposition and sensitivity to the needs of student users as well as postgraduate researchers. The excellence of the eighth edition will serve to further enhance its favourable image.

As a student I was exposed to the fourth edition under the tutelage of Waiter Federer, Cornell University. shortly after I returned from army duty in World War II. He had just finished leading our class through R A Fisher's

*Statistical Methods for Research Workers*and

*The Design of Experiments*, and we found Snedecor's style of presentation to be stimulating. That well-thumbed copy has remained on my desk-side bookshelf ever since, along with two more recent editions.

The first edition was written by Snedecor and published in 1937. Subsequent editions appeared in 1938, 1940, 1946, 1956, 1967, 1980, and 1989. They were published under the title S

*tatistical Methods Applied to Experiments in Agriculture and Biology*through the fifth edition, and excellent reviews were provided by C H Goulden, D J Finney, W J Youden, and K A Brownlee in this journal. Cochran's collaboration began with providing a chapter on sampling in the fifth edition. David F Cox, of Iowa State University, coordinated the revision of the seventh and eighth editions "guided by the principle that the work should remain the work of the original authors; thus much of the material remains as previously published." However, the seventh edition was substantially reworked, with the addition of four chapters but a reduction of 80 pages of text. It was reviewed comprehensively by J A Cornell in

*Technometrics*in 1981.

Little change in content or style occurred between the seventh and the eighth edition, and roughly 90 percent of the pages are almost exactly the same. The chapter on multiple regression has had a matrix treatment of the subject explicitly added, and an eight-page introduction to matrix notation was appended. About ten pages of text apportioned among seven locations were deleted in a "tightening-up." The total number of pages remains almost the same. A major improvement in physical readability results from a larger page size and the use of a bigger font.

A few questions occurred to me about the choice of topics and the amount of explanation provided in the treatment of regression analysis. I felt that the discussion of variable selection methods was unduly brief (three pages) in view of the increasing importance of modelling applications in data analysis. References to modem response-surface methodology literature were omitted. Problems of coefficient instability and multicollinearity were not addressed. Path analysis received only passing reference, though it is rapidly gaining in usage for ecological and agricultural research. In view of the popularity of fitting nonlinear functions with the newly available, powerful graphics and estimation programs on PC's further amplification regarding the functions requiring iterative solutions may be in order. Robust regression methods, so important to detecting outliers in a multivariate context, were not included. Principal components, cluster analysis, discriminant analysis, and spatial statistical methods were not presented, as perhaps is appropriate in a general text. In the area of experimental design, the topic of confounding, with discussions of incomplete block designs and fractional factorials, are not included, as has been indicated in previous reviews.

These comments regarding a few areas are not intended to detract from recognition of the overall excellence of this long-lived exposition of statistical methods and applications using real data. Surely this text is one of the "great books" of statistics and continues to set a high standard for other authors to try to measure up to in the future.

**10.2. Review by: Douglas H Jones.**

*Journal of Educational and Behavioral Statistics*

**19**(3) (1994), 304-307.

Snedecor and Cochran published the first edition of Statistical Methods in 1937. Over the intervening years, the authors have added various statistical topics to bring the volume up to date. The eighth edition differs from the seventh edition, primarily, by the inclusion of the matrix approach to multiple regression with an appendix on matrix algebra.

The original

*Statistical Methods*targeted established research workers who were novices in applying statistics to data. Whereas its intended audience has dwindled considerably, the book still remains a solid introduction to applied statistics. It makes available much wisdom and insight into why sound statistical methods work.

...

This book represents a traditional approach to introducing applied statistics with emphasis on computational statistics that can be done by hand with a simple calculator. Over the years, the authors have attempted to modernise this aspect. However, because of the progress in speed and power of computers since the seventies, the book is seriously behind in giving information on practical computation. Thus, material on testing portions of a model appears only intermittently throughout the book, and this results in a hard-to-follow treatise of this important statistical topic. In the 1930s, the authors targeted the intended audience of the book, established researchers unfamiliar with statistical methods. Although there were many researchers in this category from the 1930s to the 1970s, it is unlikely there remain many individuals in this category today, especially with the advent of powerful statistical packages running on personal computers. However, this book contains many gems of statistical advice that make this edition worth owning. This edition should be a successful reference book if its library usage follows the pattern of past editions. Indeed, I checked the Rutgers libraries and found that out of five copies of the seventh edition, three were on loan. Out of five copies of the sixth edition, three were on loan, and one was missing.

**11. Contributions to Statistics (1982), by William G Cochran.**

**11.1. Review by: Alan Stuart.**

*Journal of the Royal Statistical Society. Series A (General)*

**147**(3) (1984), 515.

This volume contains all the 116 known publications by the author, alone or in collaboration. Some of them (like the very first, containing the eponymous theorem) are strictly theoretical, but many are concerned with applications - Paper Number 60 is on the estimation of the rat population of Baltimore. Between these we find two well-known papers (Nos 49 and 59) on chi-squared tests and the two collaborative ones with Mosteller and Tukey (Nos 51 and 55) on the Kinsey Report. Other applications include experimentation, sample surveys, clinical trials and bio-assay, while theoretical topics include experiment designs, analysis of variance and covariance, discrimination and classification problems and survey theory. The range of the author's work is remarkable. He had a special Scottish canniness in assessing the applicability of statistical theory to practical problems, and his modest unfussy attitude made it a pleasure to discuss them with him. This collection is expensive, but it costs only 50 pence per ounce for a lifetime's wisdom. This reviewer will use it as long as he has the strength to lift it.

**11.2. Review by: Lynne Billard.**

*Journal of the American Statistical Association*

**78**(384) (1983), 991.

This volume contains the collected publications of William G Cochran. The work was begun by Cochran himself and completed by his wife, Belly I M Cochran, soon after his death in March 1980. Frederick Mosteller provides a comprehensive foreword in which he leads the reader on a journey through the highlights of Cochran's career. ... Cochran made substantial and significant contributions in statistics, most notably in sampling, biostatistics, design and analysis of complex experiments, and observational studies. While his general aura and stature were wen-known to this reviewer, a reading of this volume was nevertheless overwhelming. The reader cannot escape the feeling that he is treading a historical path, one on which with each step (paper) he is repeatedly amazed as to how much of today's standard familiar material has been associated with Cochran somehow. This path is fascinating as the reader is lured on and on with the intrigue of wondering just what else Cochran had done! Obviously, if one were interested only in the contents of the papers themselves, one need only go to the original sources. However, these sources in and of themselves cannot capture the spirit of Cochran and his contributions to statistics that is achieved by this volume. Most statisticians would no doubt enjoy this collection.

**11.3. Review by: David J Finney.**

*Biometrics*

**39**(1) (1983), 297.

When Bill Cochran died in 1980, he had nearly completed a collection of all his papers. His wife, Betty, has finished the task; with a foreword by his colleague Frederick Mosteller, this collection of 116 items now appears in one enormous volume. A short review cannot do more than outline main themes. This personal choice does not pretend to be an objective assessment of values.

Cochran's first paper, on the theorem that was to bear his name, was a foretaste of a long involvement with covariance analysis that led to a 1957 classic on the uses of covariance and aided later contributions to the analysis of observational data. Also worth re-reading is the 1936 paper on counts of diseased plants; others were to pursue the problems of runs and patterns, but here was the start of Cochran's interest in $\chi^{2}$ and related discrete problems. We owe much to him, not only for general exposition of theory (e.g. 1952) but for his studies of matching, of the consequences of small expectations, and of devices for making more powerful tests for particular types of departure from a null hypothesis.

Cochran's name has been most strongly associated with the design and analysis of experiments and with sampling. Four of the earliest papers on experiments (two on the analysis of series of experiments, long-term agricultural experiments, and special difficulties in certain analyses) already display his mastery in clear exposition and in blending sound theory with thorough understanding of the practical problem; the mark of his mentor, Frank Yates (co-author of one paper), is evident to anyone who also enjoyed the same early guidance, but so also are the signs of an independent style. Later papers did much to establish the procedures for analysis of lattice designs, and thus to encourage the use of orthogonal contrasts and the synthesis of variance components that underlie so much of any modem general computational approach.

Contributions to sampling are numerous; as is general in Cochran's work, they include both advances in theory and discussions of very practical issues, with the latter often the reason for the former. A 1940 paper, describing how sampling for the ratio of grain to total produce (in combination with full weighing of total produce) can be used for estimating grain yields, illustrates his thorough grasp of a practical issue and the associated questions of efficiency and bias. In 1942 came an important early contribution to the theory of sampling when units differ in size. The 1946 paper on systematic and stratified sampling did much to bring reason into what was too often a heated but uninformed controversy. With two colleagues, in 1953 he was author of a very thorough study of the strengths and weaknesses of the Kinsey report on male sexual behaviour; the manner in which he set rigorous sampling requirements alongside a more informal pattern of data collection, and produced reasoned conclusions, must have had much to do with his own subsequent interest in interpreting observational data and his frequent calls to assist large official and semi-official inquiries.

Another important series of papers is that on the estimation of median effective doses by stochastic approximation, several in collaboration with M Davis.

**11.4. Review by: I Richard Savage.**

*Technometrics*

**25**(2) (1983), 207.

Professor Cochran contributed to many statistical activities. His even-handed work as an advisor to the Surgeon General's study of smoking and health helped to make the report acceptable. Cochran's extensively used texts on sampling, design (with G. Cox), and methods (later editions of the book of G. Snedecor) have provided a base for studying statistical techniques. His many research publications covered a great variety of topics including design, analysis of variance, surveys, categorical data, biometry, and observational studies. These papers helped to shape the development of statistics and they remain as a valuable source of ideas. To get an overall glimpse of the variety of work done by Cochran as well as a view of the person, we now have available the biographical sketches done by R L Anderson (Biometrics, 36 (1980), 574-578), G S Watson (Annals of Statistics, 10 (1982), 1-10), and Frederick Mosteller (vii- xiii of the book under review). Cochran began the assembly of his papers, and his widow, Betty I M Cochran, completed the publication process. The volume contains about 120 papers, a list of their titles, a photograph of Cochran, a compiler's note (B.I.M.C.), and a forward (F.M.). Some editorial judgment has been used so that the photographically reproduced articles do not appear in strictly chronological order. Further, the Watson list contains 121 papers but the volume appears to list only 116 items. This discrepancy is perhaps resolved by noting that title 16 corresponds to 6 different published papers.

**12. Planning and Analysis of Observational Studies (1983), by William G Cochran, Lincoln E Moses and Frederick Mosteller.**

**12.1. Review by: Nigel C Smeeton.**

*Journal of the Royal Statistical Society. Series D (The Statistician)*

**33**(3) (1984), 321-322.

Much has been written on the subject of controlled experiments in which the investigator designs the study and selects the individuals appropriately. Sometimes, however, one is restricted to taking observations that have already been selected or measurements that seem appropriate for the objectives, as, for instance, in a study of smokers who are self-selected. With this in mind, Cochran set out to write a Monograph all Non-Experimental Studies, which he almost completed before his death. The editors then prepared the text for final publication.

The detection and reduction of bias is considered as an important issue. Advice on the execution of observational studies is given on a stage-by-stage basis. Initially, the objectives of the study should be stated and the sample and target populations defined. The investigator is encouraged to write down reservations about his methodology. Problems with pilot studies and non-response are also covered. A sensible suggestion made is that a colleague should inspect the study for weaknesses before it is finally carried out. Many examples of suitable areas of application are given. Cochran illustrated his advice with anecdotes from his own experience. I was particularly amused by the doctor's comment in Chapter 2, "I would never have rated that patient 'Much improved' if I had known he was on placebo".

To complement this work, methods of statistical analysis are also developed. A general introduction to tests of significance is given and the problem of determining a suitable size is tackled. The reduction of bias, by matching elements in different treatment groups for several variables and by other types of adjustment such as regression, is given particular emphasis. These procedures are seen to be useful, in some instances, even when assumptions such as that of a linear relationship between variables, break down. Some introduction to sampling techniques and statistical inference in controlled trials would assist the reader here.

The final chapter, which describes some simple studies, has been left unfinished by the editors. On the subject of editorial intervention, it is generally sparing and unobtrusive. However, one is left with the impression that the author would eventually have extended the scope of the references. Some of the chapters contain relatively few and only a small proportion of them are very recent.

Another slight criticism is the sometimes unpredictable manner in which the style changes between the conversational and analytical, as in Chapter 4. Cochran himself, however, did speak of the difficulty in choosing an order for this work and perhaps this style is due to the circumstances under which the text finally appeared.

This work should be of value to all who use statistics since it challenges the acceptance of commonly made assumptions. At the price, it will probably not gain the audience it deserves. However, it should cause all who read it to look at their own work more critically - and that cannot be a bad thing.

**12.2. Review by: Norman T J Bailey.**

*Biometrics*

**40**(3) (1984), 870-871.

This is an important and eminently readable book, and in spite of being relatively short it is very nearly in the form that Bill Cochran intended. Before his death in 1980 he had more or less completed six and a half of the seven chapters planned, and he had already taught a course on the subject of observational studies at Harvard. Using his notes, Lincoln Moses and Frederick Mosteller subsequently edited the posthumous manuscript, making only minor corrections, additions, revisions and rearrangements. The result, therefore, is almost entirely Bill's own book presented in the format and style in which he would have published it himself.

As described in the opening paragraph, the book deals with a class of investigations, whose objective is to study the causal effects of certain agents, procedures, treatments or programs, subject to the constraint that for 'one reason or another, the investigator cannot use controlled experimentation ... '. Reference is made to a wide range of such studies 'in government, medicine, public health, education, social science, and operations research', citing specific examples involving 'studies of the effects of habit-forming drugs, of contraceptive devices, of welfare or educational programs, of immunisations programmes, of air pollution, and so forth'. It is easy to prolong this list indefinitely.

The contrast between 'observational studies' and 'controlled experiments' is a crucial one, and. as is well known, has led to a good deal of acrimonious argumentation, There is a school of thought that seems to believe that secure knowledge can come only through carefully controlled experiments based on rigid statistical principles of design. Take, for example, the hard-core view that randomised clinical trials are essential in assessing alternative medical or surgical treatments. Unfortunately, new treatments are increasingly brought forward at a far faster rate than standard trials can be designed, implemented and concluded. Moreover, many vital social issues have to do with large complexes of interacting factors-classical experimental investigation may well be impossible. Indeed, the highest-priority issues involving our very survival, e.g. rapid environmental degradation and the policy of nuclear deterrence, not only entail complex technical issues but by their very nature exclude careful long-term experimental research.

Bill Cochran squarely faced the urgent requirement to focus more strongly on the methodology of observational studies, and to emphasise the use of scientifically and statistically respectable techniques for dealing with unavoidable constraints and biases. Carefully distinguishing this fundamental area of study from the broader observational class of analytical surveys, whose objectives are exploratory and hypothesis-seeking, Cochran concentrated on discussing a small number of key aspects dealing with the reduction or elimination of bias due to the failure of various mathematical assumptions; for example, regressions may not be linear or parallel, matching may be far from perfect, variances may be unequal, non-responses excessive in number, etc. Not only are the relevant technical aspects all clearly dealt with in detail, providing a wide range of theoretical insights. but there is everywhere in the book a major emphasis on practical applications to problems arising in the fields of science, health, human behaviour and social activities.

Bill Cochran's book should be of great interest and practical value to all those who are concerned with the planning and analysis of observational studies, whether in the role of statisticians handling the technical details of data collection, parameter estimation, hypothesis testing etc., ...

**12.3. Review by: Richard E Sykes.**

*Contemporary Sociology*

**13**(5) (1984), 581-582.

From long experience in applied statistics, William G Cochran, late professor emeritus of statistics at Harvard, knew that applied sociologists must make causal evaluations of data from subjects who are not randomly assigned or chosen, in projects over which the investigator has little control. Cochran terms these "observational studies." This book was written for investigators rather than statisticians, and much of it consists of apt advice to investigators whose data collection or analysis options, or both, are constrained by limited budgets or by the prior decisions of others. Cochran distinguishes between sampled and target populations, noting that while policy is made in regard to the latter, data are drawn from the former. Such samples are often too narrow to be representative. How can investigators remedy this deficiency? Among methods to control variation he treats refinements of measurement, blocking (matching), and control during statistical analysis. He discusses the use both of significance tests to measure whether a treatment has had any effect and of confidence intervals to estimate the upper and lower bounds of the size of the effect when bias is present. He offers a number of useful suggestions to those confronting such problems. Throughout the book Cochran offers useful advice on many problems of research planning, not limiting himself only to statistics. Although investigators may not be able to draw a sample of adequate size, he advises them to discover what sample sizes would be desirable and thereby to diagnose what effects such deficiencies as bias and nonresponse might have on their conclusions....

*Planning and Analysis of Observational Studies*was planned to aid investigators working under difficult circumstances who wish to take bias or the effects of confounding variables into account, so they can make the very best judgment about the effects of the treatment variable they are evaluating. Parts of it are rather technical, but it is filled with advice based on a lifetime's experience and ideas useful to anyone contemplating such a study, either at the data collection or analysis stage. Applied social scientists with a quantitative bent should find it intriguing. The title is deceptive; no literal observation is involved. Data, the author assumes, are from surveys or other records. It does seem unfortunate that social scientists still are looking for significant differences rather than predicting the specific value a variable should take on theoretical or law-based grounds. Lincoln E Moses and Frederick Mosteller performed a service in editing the book for publication after the author's death.

**12.4. Review by: K L.**

*Science, New Series*

**223**(4633) (1984), 277.

This is a posthumous work that has been prepared for publication by two of the author's associates. The class of studies it is concerned with is those in which controlled experimentation is impossible, as in the assessment of a given medical treatment or public health hazard when "the groups of people whom the investigator wishes to compare are already selected by some means not chosen by the investigator." The presentation is "addressed not to statisticians but to subject-matter people who do or may do" such studies. It is arranged according to concepts of methodology rather than of "subject matter," with chapters on sources of variation in responses, statistical techniques involved in drawing conclusions from data, the planning of studies, the matching of populations and adjustments in the statistical analysis as ways of dealing with the problem of confounding variables, and studies in which there is no external comparison group. Some examples from actual studies are cited, and short lists of references to other literature dealing with issues of methodology are included.

**12.5. Review by: David Holt.**

*Journal of the American Statistical Association*

**80**(391) (1985), 772-773.

The planning and analysis of observational studies is central to many area s of the social sciences and medicine, and yet compared to the design and analysis of both experiments and surveys, the statistical literature on the subject is comparatively slight. The reason for this is almost certainly that the central problem is intractable, has not yielded to systematic advances, and lacks a framework for statistical inference comparable to both experiments and surveys. Although those who analyse data from observational studies will always be left with the possibility of incorrect inference due to uncontrolled sources of influence on the variables of interest, this fact should strengthen the case for a thorough methodology and appropriate statistical practice, not diminish it.

Throughout his career W G Cochran made contributions to the design and analysis of observational studies, and this volume was edited by L E Moses and F Mosteller from Cochran's almost-completed manuscript after his death. From the editors' introduction it is clear that much of the material is just as Cochran wrote it and the book is characterised by the clear, lucid style that we associate with Cochran's writing. There are, however, disadvantages in making as little change as possible. The two that are the most conspicuous are the incomplete Chapter 7 on simple study structures and the lack of references to the most recent developments. (There are very few references to work after 1973.) The lack of recent references presumably occurred because the manuscript was written over a number of years, and as Cochran's health failed there were few additions.

...

In total the book is more a framework for thinking about observational studies rather than a comprehensive text. There are gaps and deficiencies, some because of recent developments and some because more research is yet required. It is possible to imagine a much larger text with many more sets of data and examples of entire studies or specific statistical methods.

The choice of material is difficult if one tries to write a general text in monograph length. Nevertheless there are some topics and developments (some of them perhaps too recent for Cochran's writing) that could be included or given more emphasis than they are. One would expect the general area of case control studies and retrospective versus prospective trials to feature heavily in chapters on planning issues or specific study designs. In fact little coverage is given to this area at all. In comparatively recent years renewed emphasis has been given to selection bias in the areas of economics (Heckman 1979), transportation (Manski and MacFadden 1979), and sample surveys (Holt et al. 1980). This new research ought to have direct relevance to the question of inferences from observational studies. In a related vein, the work of Rubin (1976), Little (1982), and Smith (1983) on inferences from non-random samples could also contribute to a framework for thinking about observational studies. Although the chapters on "Matching" and "Adjustments in Analysis" are the core of the book, they do not take account of the developments in the 1970s by Rubin of methods of matching and multivariate auxiliary variables. While there are interesting results for both matching and covariate adjustment on model misspecification and assumption failures, insufficient emphasis is, perhaps, given to objectives beyond simple comparisons of treatment and control group means.

Furthermore, since the methods of analysis are even more suspect than in other types of studies, one would expect a greater emphasis on diagnostics and verification of assumptions. Throughout the text useful suggestions are made, but there is clearly a need for further advances. A brief review of the published literature on the results of observational studies reveals that many do not depend on individual level analysis (perhaps because data do not exist) even though the purpose of inference is at that level. Instead much analysis takes place using aggregated data, such as death rates for cities or examination pass rates for schools. The relationship between the level of sampled data and the target for inference deserves space in an expanded text. Finally, a suggestion that I am sure would be close to Cochran's heart is inclusion of a chapter on the aftermath of the observational study. Because of the essential uncertainty about the validity of inferences, it is, perhaps, as important to take stock after the study as it is to plan before. Efforts should be made to propose hypotheses based on the results of the observational study, hypotheses that could then be targets for future studies. Such future studies should ideally take account of the most likely sources of invalidity in the completed observational study, and would be an attempt to inject an element of scientific method that has been eliminated by the lack of experimental control. The point is that more surely than for other studies, it is never the single observational study but rather the accumulated weight of evidence from a number of observational studies that supports inferences.

In summary this is a well-written, stimulating book on an important topic. It is full of insight and clues to where further work is needed. Because of its length and the circumstances in which it was written, it will probably become outdated at a faster rate than most new books. Nevertheless it makes a useful contribution, and for anyone interested in this field, it is a very good place to start.

Last Updated September 2020