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) 


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) 


14  (2) 


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) 


35  (10) 

Chapter 3. Propagation of Uncertainties 


45  (48) 

3.1 Uncertainties in Direct Measurements 


46  (2) 

3.2 The SquareRoot 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) 


68  (3) 

3.10 A More Complicated Example 


71  (2) 

3.11 General Formula for Error Propagation 


73  (6) 


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) 


104  (2) 


106  (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) 


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) 


169  (1) 


170  (3) 

Chapter 7. Weighted Averages 


173  (8) 

7.1 The Problem of Combining Separate Measurements 


173  (1) 


174  (2) 


176  (2) 


178  (3) 

Chapter 8. LeastSquares 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) 


190  (3) 

8.6 LeastSquares Fits to Other Curves 


193  (6) 


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) 


220  (2) 


222  (5) 

Chapter 10. The Binomial Distribution 


227  (18) 


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) 


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) 


252  (2) 

11.4 Subtracting a Background 


254  (2) 


256  (5) 

Chapter 12. The ChiSquared 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) 


274  (4) 


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 OddNumbered Problems 

301  (22) 
Index 

323  