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