## Measurement Uncertainty and ProbabilityA measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science. |

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### Contents

Components of error or uncertainty | 21 |

The randomization of systematic errors | 56 |

Beyond the ordinary conﬁdence interval | 72 |

Evaluation of uncertainty | 83 |

Evaluation using the linear approximation | 98 |

Evaluation without the linear approximation | 125 |

Uncertainty information ﬁt for purpose | 152 |

Related topics | 173 |

Why take part in a measurement comparison? | 192 |

Other philosophies | 204 |

An assessment of objective Bayesian statistics | 220 |

Guide to the Expression of Uncertainty in Measurement | 237 |

Measurement near a limit an insoluble problem? | 245 |

Appendix A The weak law of large numbers | 259 |

Appendix F An alternative to a symmetric beta distribution | 264 |

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### Common terms and phrases

applied approach attributed Bayesian statistics calculated calibration Chapter coefﬁcient of excess components of error concept conditional conﬁdence interval conﬁdence interval conﬁdence region consider corresponding covariance covariance matrix credible interval deﬁned Deﬁnition 3.1 degree of belief described difﬁculty distribution with mean experimental ﬁducial ﬁgure ﬁnd ﬁnite ﬁrst ﬁxed error frequentist frequentist statistics hypothesis idea improper prior independent interval obtained involves JCGM known least 95 linear approximation mean zero measurand equation measurement error measurement problems measurement result measurement uncertainty method Monte Carlo normal distribution notation outcome parent distribution parent variance Pearson distribution posterior distribution prior distribution probability density function probability distribution probability statements procedure quantiles random error random interval random variable realized 95 relevant sample scientiﬁc Section simulation situation speciﬁed standard deviation standard uncertainty success rate sufﬁcient Suppose symmetric systematic errors target value Type B error Uncertainty in Measurement uncertainty interval variance 02 Willink