# An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, Third Edition

**Forthcoming in Spring of 2022**

John R. Taylor’s best-selling text will be 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.

*"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."*

-Mark Semon, Bates College

### Summary

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.

Copyright 2022

### Table of Contents

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

### Reviews

*“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