# Dealing with Uncertainties: A Guide to Error Analysis

Springer Science & Business Media, Mar 6, 2007 - Science - 190 pages

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 Copyright