An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements

by Taylor, John R.

• ISBN13: 9780935702750
• ISBN10: 093570275X
• Edition: 2nd
• Format: Paperback
• Copyright: 1996-08-01
• Publisher: UNIVERSITY SCIENCE BOOKS

Table of Contents

Preface to the Second Edition	xi	(4)
Preface to the First Edition	xv
Part I	3	(162)
Chapter 1. Preliminary Description of Error Analysis	3	(10)
1.1 Errors as Uncertainties	3	(1)
1.2 Inevitability of Uncertainty	3	(2)
1.3 Importance of Knowing the Uncertainties	5	(1)
1.4 More Examples	6	(2)
1.5 Estimating Uncertainties When Reading Scales	8	(2)
1.6 Estimating Uncertainties in Repeatable Measurements	10	(3)
Chapter 2. How to Report and Use Uncertainties	13	(32)
2.1 Best Estimate + Uncertainty	13	(1)
2.2 Significant Figures	14	(2)
2.3 Discrepancy	16	(2)
2.4 Comparison of Measured and Accepted Values	18	(2)
2.5 Comparison of Two Measured Numbers	20	(4)
2.6 Checking Relationships with a Graph	24	(4)
2.7 Fractional Uncertainties	28	(2)
2.8 Significant Figures and Fractional Uncertainties	30	(1)
2.9 Multiplying Two Measured Numbers	31	(4)
Problems for Chapter 2	35	(10)
Chapter 3. Propagation of Uncertainties	45	(48)
3.1 Uncertainties in Direct Measurements	46	(2)
3.2 The Square-Root Rule for a Counting Experiment	48	(1)
3.3 Sums and Differences; Products and Quotients	49	(5)
3.4 Two Important Special Cases	54	(3)
3.5 Independent Uncertainties in the Sum	57	(3)
3.6 More About Independent Uncertainties	60	(3)
3.7 Arbitrary Functions of One Variable	63	(3)
3.8 Propagation Step by Step	66	(2)
3.9 Examples	68	(3)
3.10 A More Complicated Example	71	(2)
3.11 General Formula for Error Propagation	73	(6)
Problems for Chapter 3	79	(14)
Chapter 4. Statistical Analysis of Random Uncertainties	93	(28)
4.1 Random and Systematic Errors	94	(3)
4.2 The Mean and Standard Deviation	97	(4)
4.3 The Standard Deviation as the Uncertainty in a Single Measurement	101	(1)
4.4 The Standard Deviation of the Mean	102	(2)
4.5 Examples	104	(2)
4.6 Systematic Errors	106	(4)
Problems for Chapter 4	110	(11)
Chapter 5. The Normal Distribution	121	(44)
5.1 Histograms and Distributions	122	(4)
5.2 Limiting Distributions	126	(3)
5.3 The Normal Distribution	129	(6)
5.4 The Standard Deviation as 68% Confidence Limit	135	(2)
5.5 Justification of the Mean as Best Estimate	137	(4)
5.6 Justification of Addition in Quadrature	141	(6)
5.7 Standard Deviation of the Mean	147	(2)
5.8 Acceptability of a Measured Answer	149	(5)
Problems for Chapter 4	154	(11)
Part II	165	(120)
Chapter 6. Rejection of Data	165	(8)
6.1 The Problem of Rejecting Data	165	(1)
6.2 Chauvenet's Criterion	166	(3)
6.3 Discussion	169	(1)
Problems for Chapter 6	170	(3)
Chapter 7. Weighted Averages	173	(8)
7.1 The Problem of Combining Separate Measurements	173	(1)
7.2 The Weighted Average	174	(2)
7.3 An Example	176	(2)
Problems for Chapter 7	178	(3)
Chapter 8. Least-Squares Fitting	181	(28)
8.1 Data That Should Fit a Straight Line	181	(1)
8.2 Calculation of the Constants A and B	182	(4)
8.3 Uncertainty in the Measurements of y	186	(2)
8.4 Uncertainty in the Constants A and B	188	(2)
8.5 An Example	190	(3)
8.6 Least-Squares Fits to Other Curves	193	(6)
Problems for Chapter 8	199	(10)
Chapter 9. Covariance and Correlation	209	(18)
9.1 Review of Error Propagation	209	(2)
9.2 Covariance in Error Propagation	211	(4)
9.3 Coefficient of Linear Correlation	215	(3)
9.4 Quantitative Significance of r	218	(2)
9.5 Examples	220	(2)
Problems for Chapter 9	222	(5)
Chapter 10. The Binomial Distribution	227	(18)
10.1 Distributions	227	(1)
10.2 Probabilities in Dice Throwing	228	(1)
10.3 Definition of the Binomial Distribution	228	(3)
10.4 Properties of the Binomial Distribution	231	(4)
10.5 The Gauss Distribution for Random Errors	235	(1)
10.6 Applications; Testing of Hypotheses	236	(5)
Problems for Chapter 10	241	(4)
Chapter 11. The Poisson Distribution	245	(16)
11.1 Definition of the Poisson Distribution	245	(4)
11.2 Properties of the Poisson Distribution	249	(3)
11.3 Applications	252	(2)
11.4 Subtracting a Background	254	(2)
Problems for Chapter 11	256	(5)
Chapter 12. The Chi-Squared Test for a Distribution	261	(24)
12.1 Introduction to Chi Squared	261	(4)
12.2 General Definition of Chi Squared	265	(3)
12.3 Degrees of Freedom and Reduced Chi Squared	268	(3)
12.4 Probabilities of Chi Squared	271	(3)
12.5 Examples	274	(4)
Problems for Chapter 12	278	(7)
Appendixes	285	(16)
Appendix A. Normal Error Integral, I	286	(2)
Appendix B. Normal Error Integral, II	288	(2)
Appendix C. Probabilities for Correlation Coefficients	290	(2)
Appendix D. Probabilities of Chi Squared	292	(2)
Appendix E. Two Proofs Concerning Sample Standard Deviations	294	(5)
Bibliography	299	(2)
Answers to Quick Checks and Odd-Numbered Problems	301	(22)
Index	323