An Introduction to Error Analysis

An Introduction to Error Analysis

The Study of Uncertainties in Physical Measurements

By: John R. Taylor

Publication date: August 2022
ISBN: 9781940380148

John R. Taylor’s best-selling text has now been released in a new third edition that features Bayesian statistics and updated new chapter-ending problems throughout. Previously translated into nine languages, this brilliant little text introduces the study of uncertainties to lower division science students using familiar examples.

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Title information

This remarkable text by John R. Taylor has been a non-stop best-selling international hit since it was first published forty years ago. However, the two-plus decades since the second edition was released have seen two dramatic developments; the huge rise in popularity of Bayesian statistics, and the continued increase in the power and availability of computers and calculators. In response to the former, Taylor has added a full chapter dedicated to Bayesian thinking, introducing conditional probabilities and Bayes’ theorem. The several examples presented in the new third edition are intentionally very simple, designed to give readers a clear understanding of what Bayesian statistics is all about as their first step on a journey to become practicing Bayesians. In response to the second development, Taylor has added a number of chapter-ending problems that will encourage readers to learn how to solve problems using computers. While many of these can be solved using programs such as Matlab or Mathematica, almost all of them are stated to apply to commonly available spreadsheet programs like Microsoft Excel. These programs provide a convenient way to record and process data and to calculate quantities like standard deviations, correlation coefficients, and normal distributions; they also have the wonderful ability – if students construct their own spreadsheets and avoid the temptation to use built-in functions – to teach the meaning of these concepts.

Pages: 392
Language: English
Publisher: University Science Books
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Preface to the Third Edition

Part I.

Chapter 1. Preliminary Description of Error Analysis

Chapter 2. How to Report and Use Uncertainties

Chapter 3. Propagation of Uncertainties

Chapter 4. Statistical Analysis of Random Uncertainties

Chapter 5. The Normal Distribution


Part II.

Chapter 6. Rejection of Data

Chapter 7. Weighted Averages

Chapter 8. Least-Square Fitting

Chapter 9. Covariance and Correlation

Chapter 10. The Binomial Distribution

Chapter 11. The Poisson Distribution

Chapter 12. The Chi-Squared Test for a Distribution

Chapter 13. Bayesian Statistics


Appendix A. Normal Error Integral, I

Appendix B. Normal Error Integral, II

Appendix C. Probabilities for Correlation Coefficients

Appendix D. Probabilities for Chi Squared

Appendix E. Two Proofs Concerning Sample Standard Deviations

The new chapter on Bayesian statistics is extremely clear and well written, and is another one of John Taylor’s fabulous expositions. I enjoyed how Taylor develops the subject by using it to answer questions about the effectiveness of a vaccine. Before reading this chapter I wondered what assumptions are needed to derive a numerical value for a vaccine’s effectiveness, and I also wondered about the data needed and the methods used. Lo and behold, all my questions were answered in this chapter! I definitely will buy the new edition of Error Analysis and I look forward to delving into the Bayesian statistics.

-Mark Semon, Bates College

From the Second Edition

This text provides a rational, step-by-step introduction to understanding and estimating random uncertainties in physical measurements. Although the text is intended primarily for undergraduate students, I find it useful as well at the research level, to introduce graduate students to unfamiliar topics in the study of experimental uncertainties…a high-quality resource [students] can continue to learn from, even after they graduate.

-Physics Today

Score a hit! The book reveals the exceptional skill of the author as lecturer and teacher. A valuable reference work for any student (or instructor) in the sciences and engineering.

-The Physics Teacher

John R. Taylor

John Taylor received his B.A. in math from Cambridge University in 1960 and his Ph.D. in theoretical physics from Berkeley in 1963. He is professor emeritus of physics and Presidential Teaching Scholar at the University of Colorado, Boulder. He is the author of some 40 articles in research journals; a book, Classical Mechanics; and three other textbooks, one of which, An Introduction to Error Analysis, has been translated into eleven foreign languages. He received a Distinguished Service Citation from the American Association of Physics Teachers and was named Colorado Professor of the Year in 1989. His television series Physics for Fun won an Emmy Award in 1990. John is now retired and lives in South Portland, Maine.