New York. John Wiley & Sons, Inc.
The background to the text and Cochran's aims and objectives are clearly set out in the Preface. We give an extract below:
This book was developed from a course of lectures on sample survey techniques which I gave for a few years at North Carolina State College to students who intended to make their careers in the field of statistics. The purpose of the book 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 of 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.
As an indication of the level at which the book is directed, the minimum mathematical equipment necessary for an easy understanding of the proofs is a knowledge of calculus as far as the determination of maxima and minima (using Lagrange's multipliers where required), plus a familiarity with elementary algebra, and especially with the use of summation signs. On the statistical side, the book presupposes an introductory course which includes such topics as combinatorial probabilities, expected values and their properties, means and standard deviations, the normal, binomial, and multinomial distributions, confidence limits, Student's t-test, linear regression, and the simpler types of analysis of variance. Occasionally, reference is made to more advanced statistical results, since I have tried to point out the relation between sample survey theory and the main stream of statistical theory. In the early parts of the book, each step in a proof should be readily apparent from the previous steps; towards the end, where the proofs are more condensed, most readers will find that some work with pencil and paper is necessary to follow the steps in detail.
Readers with advanced training in probability may find the arguments by which theorems are established rather pedestrian. In a sense, sample survey theory is easy, because thus far it has dealt mainly with means and variances. By the use of powerful operational methods, the bulk of the 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.
Sampling theory and practice have both grown so much in the past ten years that an adequate coverage of the two aspects of sampling now requires a lengthy volume. Although this book is not intended to contain a thorough discussion of sampling practice, it does endeavour to show how the various topics that comprise sampling theory arise from problems in sampling practice. This link is essential to an understanding of sample survey theory, whose primary aim is to make sampling practice more efficient and economical. In the same Way, the book presents some of the recommendations about sampling practice that follow from the results in theory. I have deliberately refrained, however, from making these recommendations too specific or too strong. The tendency in sampling practice, where decisions must often be made quickly on inadequate knowledge, is to develop a series of working rules, each of which has some basis in theory. There is danger, however, that working rules which have been successful in one type of sampling become entrenched, so that they are relied upon in quite different kinds of sampling for which they are not appropriate. Re-examination from time to time of the theoretical basis for any proposed working rule helps to avoid this danger.
The choice of a system of notation is a perplexing one to the writer. The chief problem is how to prevent an epidemic of subscripts, which make the results look formidable and unattractive. With multistage stratified sampling, several symbols are needed to remind the reader of the structure of the population, and, ideally, the notation adopted for an estimate computed from sample data should remind him not only of the way in which the estimate is made, but also of the way in which the sample is drawn. My approach has been to use capital letters for characteristics of the population and small letters for those of the sample, and to employ a consistent set of subscripts to denote the structure of the population. For the rest, subscripts with a mnemonic, content have been favoured, and I have not hesitated to repeat the definition of some notation in places where my guess is that the reader will have begun to forget it. Lapses from consistency occur: the alphabet soon becomes used up, and the letter m, for instance, is worked overtime. Although I hope that any inconsistencies will not be troublesome, the reader who is puzzled by them has my apologies and sympathy; the struggle to understand a theorem without knowing clearly what the symbols mean is highly exasperating.
My best thanks are due to Dr A L Finkner and Dr Emil H Jebe, who prepared a large part of the mimeographed lecture notes from which this book was developed. Dr Jebe made a painstaking reading of the present book in manuscript, and Dr Helen Abbey also read parts of the manuscript. The secretarial staff and graduate students of the Department of Biostatistics, Johns Hopkins University, gave invaluable help in the preparation of manuscript and in proofreading. For permission to use data from surveys I am indebted to Dr F C Cornell and Dr Finkner. Some theoretical investigations were facilitated by a research contract with the Office of Naval Research. While the manuscript was nearing completion, I had the advantage of reading a substantial part of the book, Sample Survey Methods and Theory, by M H Hansen, W N Hurwitz, and W G Madow, and of noting how these authors had handled the inevitable points at which a lucid exposition is hard to find. Numerous references to this fine book would have been made if it had appeared in print in sufficient time.
The present book contains more material than can be covered in the time usually devoted to a course on sample surveys. However, the sections have been prepared so that many of them can be omitted, or condensed to a brief statement of the results, without detriment to later parts of the book. There are, for instance, numerous discussions of special topics, which attempt to answer questions that have been raised by alert sampling practitioners but which are not essential to a firm understanding of the fundamentals of the subject. ...
WILLIAM G COCHRAN
The Johns Hopkins University