Dealing With Uncertainties Book

Introduction     1
The Exactness of Science     2
Data Without Uncertainty     4
Basics on Data     7
What Is a Measurement?     8
Analog vs. Digital     11
Dealing With Data (Numerals)     12
Basics on Uncertainties (Errors)     15
Typical Sources of Internal Uncertainties     16
Definitions     17
Uncertainty of Data Depending on One Variable     26
Multiple Uncertainty Components (Quadratic Sum)     27
Radioactive Decay, a Model for Random Events     33
Time Interval Distribution of Radioactive Events     33
Inductive Approach to Uncertainty (Example)     39
Frequency and Probability Distributions     51
Frequency Distribution (Spectrum)     51
Probability Distributions     58
Statistical Confidence     65
Dealing with Probabilities     66
Deductive Approach to Uncertainty     71
Theoretical Situation     71
Practical Situation     71
Regression Analysis (Least-Squares Method)     81
Data Consistency Within Data Sets     87
Correlation     91
Introduction     91
Correlated (Systematic) Internal Uncertainties     93
Differentiation From "Systematic Errors"     104
Correlation in Cases of Linear Regression     108
Data Consistency Among Data Sets     113
Target Shooting as a Model for Uncertainties     118
Dealing With Internal Uncertainties     121
Calculations With Both Types of Uncertainties     124
Total Uncertainty     132
Using Internal Uncertainties for Diagnosis     135
Presentation and Estimation of Uncertainties     141
Graphic Presentation, Also of Uncertainties     141
Correct Presentation of Uncertainties     145
Finding the Size of Internal Uncertainties     146
Estimating the Size of (Internal) Uncertainties     148
Feedback of Uncertainties on Experiment Design     153
Optimizing Experiments     153
Optimizing Background Measurements     155
Optimizing With Respect to Dead Time     158
Optimizing in View of the Mathematical Presentation     160
Achieving the Smallest Overall Uncertainty     162
Solutions     171
Index     179