Preface	6
	Preface to the First Edition	7
	Prolog. Seven Myths in Error Analysis	9
	Contents	11
	Introduction	13
	The Exactness of Science	14
	Falsification vs. Verification	16
	Data without Uncertainty	16
	Uncertainties in Every-Day Life	17
	Basics on Data	19
	Measurement Data	19
	The Best Estimate	20
	Directly Measured Data	21
	Indirectly Measured Data	21
	Counting vs. Measuring	22
	The Basic Counting Model	23
	Indirect Counting	24
	Analog vs. Digital	24
	``Analog'' Measurements	25
	Dealing with Data (Numerals)	26
	Valid Digits	26
	Truncation of Numbers	26
	Rounding	26
	Basics on Uncertainties	29
	General Characteristics of Uncertainties	31
	Shape of Uncertainty Distributions	32
	Definitions	34
	Terminology	34
	Necessary Requirements	34
	Deviations	35
	Random Uncertainties	37
	Maximum Uncertainties (Tolerances)	41
	Limits	42
	Outliers (Flyers)	43
	Uncertainty of Data Depending on One Variable	45
	Length	45
	Circular Area	45
	Multiple Uncertainty Components (Quadratic Sum)	47
	Properties of the ``Quadratic'' Sum	49
	Subtraction in Quadrature	51
	Combined Standard Uncertainty	51
	Uncertainty Evaluations (Error Analysis)	52
	Inductive Method	52
	Deductive Method	53
	Experimental Uncertainty	53
	Counting and Measurement Uncertainties	54
	Parameter Uncertainties	56
	Model Uncertainties	56
	Additional Experimental Uncertainties	60
	Radioactive Decay, a Model for Random Events	61
	Time Interval Distribution of Radioactive Events	61
	Prescaling	63
	Counting Loss (Dead Time)	64
	Direct Correction of Dead Time	65
	Direct Correction for Lost Counts	67
	Loss Correction Using a Pulse Generator	67
	Inductive Approach to Uncertainty (Example)	69
	Properties of Data Sets and Arrays	69
	Reproducibility within Data Sets	76
	Linear Regression (Least-Squares Method)	77
	Frequency and Probability Distributions	80
	Frequency Distribution (Spectrum)	80
	Characteristics of Distributions	83
	Effect of Data Uncertainty on the Distribution	85
	Probability Distributions	88
	Binomial Distribution	88
	Poisson Distribution	89
	Normal (or Gaussian) Distribution	91
	Finite Distributions	95
	Convolution of Uncertainty Distributions	97
	Statistical Confidence	98
	Dealing with Probabilities	99
	Deductive Approach to Uncertainty	104
	Theoretical Situation	104
	Practical Situation	104
	Best Estimates Using Internal Uncertainties	106
	Deductive vs. Inductive Uncertainties	109
	The Sign of an Uncertainty	110
	Benefits of Repeated Measurements	111
	Regression Analysis (Least-Squares Method)	116
	Weighted Mean	118
	Weighted Linear Regression	119
	General Regression Analysis	121
	Benefits of Regression Analysis	122
	Data Consistency within Data Sets	123
	Criterion of Chauvenet	123
	Discarding Data with Internal Uncertainties	125
	Correlation	126
	Introduction	126
	Measure of Relation	127
	Correlated (Systematic) Uncertainties	128
	Sign of a ``Systematic'' Uncertainty	129
	Differentiation from Uncorrelated Uncertainties	130
	More Examples of Correlated Uncertainties	137
	External Scale Uncertainties?	141
	Differentiation from ``Systematic Errors''	141
	Gross Mistakes	142
	Corrections	142
	Correlation in Cases of Linear Regression	148
	Weighted Linear Regression (Example)	148
	Linear Regression without Weighting (Example)	149
	Consistency among Data Sets	152
	Contradictory Data Sets	154
	Dependent (Correlated) Data Sets	156
	Target Shooting as a Model for Uncertainties	158
	Accuracy vs. Precision	160
	Dealing with Internal Uncertainties	161
	Calculations with Both Types of Uncertainties	164
	Uncertainty of a Sum	165
	Uncertainty of a Difference	166
	Uncertainty of a Product	169
	Uncertainty of a Ratio	170
	Uncertainty of a Power (Root)	171
	Uncertainty of More Exotic Functions	172
	Total Uncertainty	173
	Adding Correlated to Uncorrelated Uncertainties	173
	Combined Uncertainty of a Single Best Estimate	174
	Combined Uncertainty of Data Sets	174
	Using Internal Uncertainties for Diagnosis	176
	Quality Assurance	176
	Analogy to Bayes' Principle	178
	Chi-Squared Test	179
	Presentation and Estimation of Uncertainties	183
	Graphic Presentation, Also of Uncertainties	183
	Uncertainty Bars (Error Bars)	184
	Charts	185
	Transformations	185
	Correct Presentation of Uncertainties	190
	Finding the Size of Internal Uncertainties	192
	Ideal Situation in Measurements	193
	Pragmatic Solution for Measurements	193
	Estimating the Size of Uncertainties	194
	Finding Upper Limits	195
	Finding Lower Limits	197
	Feedback of Uncertainties on Experiment Design	198
	Optimizing Experiments	198
	Reasons For and Against Optimization	199
	Prevalent Design Criteria	200
	Optimizing Background Measurements	201
	Optimized Simple Background Measurement	201
	Optimized Complex Background Measurement	202
	Optimizing with Respect to Dead Time	204
	Optimizing in View of the Mathematical Presentation	206
	Optimizing Flat Dependences	207
	Optimizing Linear Dependences	207
	Optimum Angles for Cross Section Measurements	208
	Achieving the Smallest Overall Uncertainty	209
	The Ratio Method	209
	Solutions	218
	Index	231