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

, by Taylor, John R.

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ISBN: 9780935702750 | 093570275X
Cover: Paperback
Copyright: 8/1/1996

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Supplemental Materials

Preface to the Second Edition

(4)

Preface to the First Edition

Part I

(162)

Chapter 1. Preliminary Description of Error Analysis

(10)

1.1 Errors as Uncertainties

(1)

1.2 Inevitability of Uncertainty

(2)

1.3 Importance of Knowing the Uncertainties

(1)

1.4 More Examples

(2)

1.5 Estimating Uncertainties When Reading Scales

(2)

1.6 Estimating Uncertainties in Repeatable Measurements

(3)

Chapter 2. How to Report and Use Uncertainties

(32)

2.1 Best Estimate + Uncertainty

(1)

2.2 Significant Figures

(2)

2.3 Discrepancy

(2)

2.4 Comparison of Measured and Accepted Values

(2)

2.5 Comparison of Two Measured Numbers

(4)

2.6 Checking Relationships with a Graph

(4)

2.7 Fractional Uncertainties

(2)

2.8 Significant Figures and Fractional Uncertainties

(1)

2.9 Multiplying Two Measured Numbers

(4)

Problems for Chapter 2

(10)

Chapter 3. Propagation of Uncertainties

(48)

3.1 Uncertainties in Direct Measurements

(2)

3.2 The Square-Root Rule for a Counting Experiment

(1)

3.3 Sums and Differences; Products and Quotients

(5)

3.4 Two Important Special Cases

(3)

3.5 Independent Uncertainties in the Sum

(3)

3.6 More About Independent Uncertainties

(3)

3.7 Arbitrary Functions of One Variable

(3)

3.8 Propagation Step by Step

(2)

3.9 Examples

(3)

3.10 A More Complicated Example

(2)

3.11 General Formula for Error Propagation

(6)

Problems for Chapter 3

(14)

Chapter 4. Statistical Analysis of Random Uncertainties

(28)

4.1 Random and Systematic Errors

(3)

4.2 The Mean and Standard Deviation

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

Table of Contents

Supplemental Materials