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Principles of Statistical Inference

D. R. Cox
Cambridge University Press
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The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Sarah Boslaugh
, on

Statistical analysis is fundamental to many fields of endeavour today, from wildlife biology to fraud detection. People who use statistics in support of research and decision-making in applied fields are often concerned primarily with learning the specific techniques for data analysis and interpretation which are most common in their field. Yet without an understanding of statistical theory this type of statistical practice may easily become a collection of tricks and procedures without intellectual foundation. A basic understanding of statistical inference is therefore fundamental to intelligent use of statistics as well as the ability to assess the merits of different types of analysis to a given research problem or situation.

D.R. Cox, one of the most influential statisticians of the 20th century, provides in Principles of Statistical Inference a concise summary of the basic ideas regarding statistical inference as they are currently understood. He begins with basic concepts such as likelihood, sufficiency and significance, discusses uncertainty in detail, and continues to more specialized topics including prediction, decision analysis, point estimation, and study design. Each chapter includes notes and a select bibliography. Throughout, Cox presents both the frequentist and Bayesian approaches to statistics and clarifies their differences. In Appendix A, he sets forth a brief history of mathematical statistics, concentrating on the 20th century. In Appendix B, he presents a personal view of the strengths and weakness of the Bayesian approach.

Principles of Statistical Inference is based on a series of lectures Cox delivered to doctoral students at the Institute of Mathematics, Chalmers/Gothenburg University. While the author describes the mathematical level required to understand his text as “as elementary as feasible” and similar to that acquired in an undergraduate mathematics education, it will be beyond many applied statisticians educated in other fields such as the social sciences. The explanations of key concepts are written so clearly, however, that they may be understood even if the mathematical details are skipped. Hence, Principles of Statistical Inference may serve as a resource even for those without the necessary mathematical background to understand all the details.

D. R. Cox is one of the leading statisticians of the twentieth century and is the author or co-author of approximately 300 papers and 16 books. He served as editor of Biometrika in the years 1966–1991, was elected Fellow of the Royal Society of London in 1973, was twice awarded the Guy medal of the Royal Statistical Society (1961 and 1973) and was knighted in 1985. Cox formally retired as Warden of Nuffield College and as a member of the Department of Statistics of Oxford University in 1994; he previously held posts at Imperial College, London, Birkbeck College, London, the Statistical Laboratory of the University of Cambridge, the Wool Industries Research Association and the Royal Aircraft Establishment.

Sarah Boslaugh ( is a Performance Review Analyst for BJC HealthCare and an Adjunct Instructor in the Washington University School of Medicine, both in St. Louis, MO. Her books include An Intermediate Guide to SPSS Programming: Using Syntax for Data Management (Sage, 2004), Secondary Data Sources for Public Health: A Practical Guide (Cambridge , 2007), and Statistics in a Nutshell (O'Reilly, forthcoming), and she is Editor-in-Chief of The Encyclopedia of Epidemiology (Sage, forthcoming).

 Preface; 1. Preliminaries; 2. Some concepts and simple applications; 3. Significance tests; 4. More complicated situations; 5. Some interpretational issues; 6. Asymptotic theory; 7. Further aspects of maximum likelihood; 8. Additional objectives; 9. Randomization-based analysis; Appendix A. A brief history; Appendix B. A personal view; References; Author index; Index.