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

by
Edition:
2nd
ISBN13:

9780935702750

ISBN10:
093570275X
Format:
Paperback
Pub. Date:
8/1/1996
Publisher(s):
UNIVERSITY SCIENCE BOOKS
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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


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