An Introduction to Error Analysis, 3e
The Study of Uncertainties in Physical Measurements
by Taylor
ISBN: 9781940380087 | Copyright 2022
Instructor Requests
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 _x0013_ if students construct their own spreadsheets and avoid the temptation to use built-in functions _x0013_ to teach the meaning of these concepts.
Published under the University Science Books imprint
Expand/Collapse All | |
---|---|
Front Cover (pg. 1) | |
Front Endsheets (pg. 2) | |
Contents (pg. 10) | |
Preface to the Third Edition (pg. 14) | |
Part I (pg. 1) | |
Chapter 1. Preliminary Description of Error Analysis (pg. 3) | |
1.1 “Error” versus “Uncertainty” (pg. 3) | |
1.2 Inevitability of Uncertainty (pg. 4) | |
1.3 Importance of Knowing the Uncertainties (pg. 5) | |
1.4 More Examples (pg. 7) | |
1.5 Estimating Uncertainties When Reading Scales (pg. 8) | |
1.6 Estimating Uncertainties in Repeatable Measurements (pg. 10) | |
Problems for Chapter 1 (pg. 12) | |
Chapter 2. How to Report and Use Uncertainties (pg. 13) | |
2.1 Best Estimate ± Uncertainty (pg. 13) | |
2.2 Significant Figures (pg. 15) | |
2.3 Discrepancy (pg. 17) | |
2.4 Comparison of Measured and Accepted Values (pg. 19) | |
2.5 Comparison of Two Measured Numbers (pg. 21) | |
2.6 Checking Relationships with a Graph (pg. 25) | |
2.7 Fractional Uncertainties (pg. 29) | |
2.8 Significant Figures and Fractional Uncertainties (pg. 30) | |
2.9 Multiplying Two Measured Numbers (pg. 32) | |
Principal Definitions and Equations of Chapter 2 (pg. 35) | |
Problems for Chapter 2 (pg. 35) | |
Chapter 3. Propagation of Uncertainties (pg. 45) | |
3.1 Uncertainties in Direct Measurements (pg. 46) | |
3.2 The Square-Root Rule for a Counting Experiment (pg. 48) | |
3.3 Sums and Differences; Products and Quotients (pg. 49) | |
3.4 Two Important Special Cases (pg. 54) | |
3.5 Independent Uncertainties in a Sum (pg. 57) | |
3.6 More about Independent Uncertainties (pg. 60) | |
3.7 Arbitrary Functions of One Variable (pg. 63) | |
3.8 Propagation Step by Step (pg. 66) | |
3.9 Examples (pg. 68) | |
3.10 A More Complicated Example (pg. 71) | |
3.11 General Formula for Error Propagation (pg. 73) | |
Principal Definitions and Equations of Chapter 3 (pg. 77) | |
Problems for Chapter 3 (pg. 79) | |
Chapter 4. Statistical Analysis of Random Uncertainties (pg. 95) | |
4.1 Random and Systematic Errors (pg. 96) | |
4.2 The Mean and Standard Deviation (pg. 99) | |
4.3 The Standard Deviation as the Uncertainty in a Single Measurement (pg. 103) | |
4.4 The Standard Deviation of the Mean (pg. 104) | |
4.5 Examples (pg. 106) | |
4.6 Systematic Errors (pg. 108) | |
Principal Definitions and Equations of Chapter 4 (pg. 112) | |
Problems for Chapter 4 (pg. 113) | |
Chapter 5. The Normal Distribution (pg. 123) | |
5.1 Histograms and Distributions (pg. 124) | |
5.2 Limiting Distributions (pg. 128) | |
5.3 The Normal Distribution (pg. 131) | |
5.4 The Standard Deviation as 68% Confidence Limit (pg. 137) | |
5.5 Justification of the Mean as Best Estimate (pg. 139) | |
5.6 Justification of Addition in Quadrature (pg. 143) | |
5.7 Standard Deviation of the Mean (pg. 149) | |
5.8 Acceptability of a Measured Answer (pg. 151) | |
Principal Definitions and Equations of Chapter 5 (pg. 154) | |
Problems for Chapter 5 (pg. 156) | |
Part II (pg. 165) | |
Chapter 6. Rejection of Data (pg. 167) | |
6.1 The Problem of Rejecting Data (pg. 167) | |
6.2 Chauvenet’s Criterion (pg. 168) | |
6.3 Discussion (pg. 171) | |
Principal Definitions and Equations of Chapter 6 (pg. 172) | |
Problems for Chapter 6 (pg. 172) | |
Chapter 7. Weighted Averages (pg. 175) | |
7.1 The Problem of Combining Separate Measurements (pg. 175) | |
7.2 The Weighted Average (pg. 176) | |
7.3 An Example (pg. 178) | |
Principal Definitions and Equations of Chapter 7 (pg. 179) | |
Problems for Chapter 7 (pg. 180) | |
Chapter 8. Least-Squares Fitting (pg. 183) | |
8.1 Data That Should Fit a Straight Line (pg. 183) | |
8.2 Calculation of the Constants A and B (pg. 185) | |
8.3 Uncertainty in the Measurements of y (pg. 189) | |
8.4 Uncertainty in the Constants A and B (pg. 190) | |
8.5 An Example (pg. 192) | |
8.6 Least-Squares Fits to Other Curves (pg. 195) | |
Principal Definitions and Equations of Chapter 8 (pg. 200) | |
Problems for Chapter 8 (pg. 202) | |
Chapter 9. Covariance and Correlation (pg. 211) | |
9.1 Review of Error Propagation (pg. 211) | |
9.2 Covariance in Error Propagation (pg. 213) | |
9.3 Coefficient of Linear Correlation (pg. 217) | |
9.4 Quantitative Significance of r (pg. 221) | |
9.5 Examples (pg. 223) | |
Principal Definitions and Equations of Chapter 9 (pg. 223) | |
Problems for Chapter 9 (pg. 224) | |
Chapter 10. The Binomial Distribution (pg. 229) | |
10.1 Distributions (pg. 229) | |
10.2 Probabilities in Dice Throwing (pg. 230) | |
10.3 Definition of the Binomial Distribution (pg. 231) | |
10.4 Properties of the Binomial Distribution (pg. 233) | |
10.5 The Gauss Distribution for Random Errors (pg. 237) | |
10.6 Applications; Testing of Hypotheses (pg. 238) | |
Principal Definitions and Equations of Chapter 10 (pg. 242) | |
Problems for Chapter 10 (pg. 243) | |
Chapter 11. The Poisson Distribution (pg. 247) | |
11.1 Definition of the Poisson Distribution (pg. 247) | |
11.2 Properties of the Poisson Distribution (pg. 251) | |
11.3 Applications (pg. 254) | |
11.4 Subtracting a Background (pg. 256) | |
Principal Definitions and Equations of Chapter 11 (pg. 257) | |
Problems for Chapter 11 (pg. 258) | |
Chapter 12. The Chi-Squared Test for a Distribution (pg. 265) | |
12.1 Introduction to Chi Squared (pg. 265) | |
12.2 General Definition of Chi Squared (pg. 269) | |
12.3 Degrees of Freedom and Reduced Chi Squared (pg. 273) | |
12.4 Probabilities for Chi Squared (pg. 276) | |
12.5 Examples (pg. 278) | |
Principal Definitions and Equations of Chapter 12 (pg. 282) | |
Problems for Chapter 12 (pg. 283) | |
Chapter 13. Bayesian Statistics (pg. 289) | |
13.1 Probability (pg. 289) | |
13.2 Two Basic Rules for Probabilities (pg. 290) | |
13.3 Conditional Probability and the Enhanced Product Rule (pg. 294) | |
13.4 Bayes’ Theorem (pg. 296) | |
13.5 A Pandemic Paradox (pg. 296) | |
13.6 More Poker Chips (pg. 298) | |
13.7 How Biased Is This Penny? (pg. 300) | |
13.8 More Suspect Coins (pg. 306) | |
13.9 Bayesian Solution for a Counting Experiment (pg. 308) | |
13.10 Summary So Far (pg. 310) | |
13.11 Monte Carlo and Markov Chains (pg. 311) | |
13.12 Conclusion (pg. 314) | |
Principal Definitions and Equations of Chapter 13 (pg. 314) | |
Problems for Chapter 13 (pg. 315) | |
Back Matter (pg. 321) | |
Appendix A. Normal Error Integral, I (pg. 322) | |
Appendix B. Normal Error Integral, II (pg. 324) | |
Appendix C. Probabilities for Correlation Coefficients (pg. 326) | |
Appendix D. Probabilities for Chi Squared (pg. 328) | |
Appendix E. Two Proofs Concerning Sample Standard Deviations (pg. 330) | |
Bibliography (pg. 335) | |
Answers to Quick Checks and Odd-Numbered Problems (pg. 337) | |
Index (pg. 365) | |
Back Endsheets (pg. 372) | |
Back Cover (pg. 374) |
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. He retired in 2005 and now lives in Washington, D.C.
eTextbook
Go paperless today! Available online anytime, nothing to download or install.
Features
|