Dealing with Uncertainties: A Guide to Error Analysis

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Springer Science & Business Media, Mar 6, 2007 - Science - 190 pages
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Dealing with Uncertainties proposes and explains a new approach for the analysis of uncertainties. Firstly, it is shown that uncertainties are the consequence of modern science rather than of measurements. Secondly, it stresses the importance of the deductive approach to uncertainties. This perspective has the potential of dealing with the uncertainty of a single data point and of data of a set having differing weights. Both cases cannot be dealt with the inductive approach, which is usually taken. This innovative monograph also fully covers both uncorrelated and correlated uncertainties. The weakness of using statistical weights in regression analysis is discussed. Abundant examples are given for correlation in and between data sets and for the feedback of uncertainties on experiment design.

 

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Contents

Introduction
1
11 The Exactness of Science
2
12 Data Without Uncertainty
4
Basics on Data
6
21 What Is a Measurement?
8
22 Analog vs Digital
11
23 Dealing With Data Numerals
12
Basics on Uncertainties Errors
15
72 Correlated Systematic Internal Uncertainties
93
73 Differentiation From Systematic Errors
104
74 Correlation in Cases of Linear Regression
108
75 Data Consistency Among Data Sets
113
76 Target Shooting as a Model for Uncertainties
118
Dealing With Internal Uncertainties
121
81 Calculations With Both Types of Uncertainties
124
82 Total Uncertainty
132

31 Typical Sources of Internal Uncertainties
16
32 Definitions
17
33 Uncertainty of Data Depending on One Variable
26
34 Multiple Uncertainty Components Quadratic Sum
27
Radioactive Decay a Model for Random Events
33
42 Inductive Approach to Uncertainty Example
39
Frequency and Probability Distributions
50
52 Probability Distributions
58
53 Statistical Confidence
65
54 Dealing With Probabilities
66
Deductive Approach to Uncertainty
71
63 Regression Analysis LeastSquares Method
81
64 Data Consistency Within Data Sets
87
Correlation
90
83 Using Internal Uncertainties for Diagnosis
135
Presentation and Estimation of Uncertainties
140
92 Correct Presentation of Uncertainties
145
93 Finding the Size of Internal Uncertainties
146
94 Estimating the Size of Internal Uncertainties
148
Feedback of Uncertainties on Experiment Design
153
102 Optimizing Background Measurements
155
103 Optimizing With Respect to Dead Time
158
104 Optimizing in View of the Mathematical Presentation
160
105 Achieving the Smallest Overall Uncertainty
162
Solutions
170
Index
179
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