## Dealing with Uncertainties: A Guide to Error AnalysisDealing 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

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 |

179 | |