The Uncertainty in Physical Measurements

An introduction to the treatment of uncertainty in a phenomenological way, based on examples taken from laboratory experience and distinguishing the causes of uncertainty (there are more than just random errors and Gaussian distributions to consider).

The scienti c method is based on the measurement of di erent physical qu- tities and the search for relations between their values. All measured values of physical quantities are, however, a ected by uncertainty. Understanding the origin of uncertainty, evaluating its extent, and suitably taking it into account in data analysis, are fundamental steps for assessing the global accuracy of physical laws and the degree of reliability of their technological applications. The introduction to uncertainty evaluation and data analysis procedures is generally made in laboratory courses for freshmen. During my long-lasting teaching experience, I had the feeling of some sort of gap between the ava- able tutorial textbooks, and the specialized monographs. The present work aims at lling this gap, and has been tested and modi ed through a feedback interaction with my students for several years. I have tried to maintain as much as possible a tutorial approach, that, starting from a phenomenolo- cal introduction, progressively leads to an accurate de nition of uncertainty and to some of the most common procedures of data analysis, facilitating the access to advanced monographs. This book is mainly addressed to - dergraduate students, but can be a useful reference for researchers and for secondary school teachers. The book is divided into three parts and a series of appendices. Part I is devoted to a phenomenological introduction to measurement and uncertainty. In Chap.

Contains an up-to-date introduction to uncertainty in measurements, based on a comprehensive analysis of its possible different clauses Contains mathematical topics, important for many laboratory courses, which are not thoroughly discussed in competing works The figures and worked examples included in the text are taken from real laboratory practice and will highlight strengths and limitations of statistical methods Contains worked-out problems and an appendix with descriptions of experiments so students can easily obtain realistic data on which to apply theoretical recipes Includes supplementary material: sn.pub/extras

Auteur

Since 1978, the author has worked on x-ray spectroscopy (XAFS) with Synchrotron Radiation. He participated in the realization of the PWA laboratories at Adone (Frascati) and of the italian beamline BM08-Gilda at ESRF (Grenoble). He regularly performs XAFS measurements at international synchrotron facilities, including Adone (Frascati), LURE (Orsay), ESRF (Grenoble). Prof. Fornasini has also developed a software package for the analysis of EXAFS, specifically tailored for the study of anharmonic thermal effects.

Prof. Fornasini has been a member of the International Advisory Committee on Synchrotron Radiation in Materials Science since 1996 and given several invited lectures and seminars in Chester (UK), Bonn, Regensburg, Bad Honnef, Dakar, Warsaw, Frascati, Bologna, Corvallis (Oregon), Stanford University, Hirosaki (Japan), Chiba (Japan). Since 1997, he is a lecturer at the Italian School of Synchrotron Radiation, organized every two years by the "Società Italiana di Luce di Sincrotrone". He has given lectures on x-ray techniques in various Italian and international schools (Torino 1999, Rostock 2000, Varsaw 2004, Planneralm Austria 2005, Dakar 2005).

Prof. Fornasini is the author or co-author of over 100 papers published in international journals and referees of the journals: Physical Review Letters, Physical Review B, Physics Letters, and Journal of Synchrotron Radiation.

Texte du rabat

All measurements of physical quantities are affected by uncertainty. Understanding the origin of uncertainty, evaluating its extent and suitably taking it into account in data analysis is essential for assessing the degree of accuracy of phenomenological relationships and physical laws in both scientific research and technological applications.

The Uncertainty in Physical Measurements: An Introduction to Data Analysis in the Physics Laboratory presents an introduction to uncertainty and to some of the most common procedures of data analysis. This book will serve the reader well by filling the gap between tutorial textbooks and highly specialized monographs. The book is divided into three parts. The first part is a phenomenological introduction to measurement and uncertainty: properties of instruments, different causes and corresponding expressions of uncertainty, histograms and distributions, and unified expression of uncertainty. The second part contains an introduction to probability theory, random variable distributions and basic statistical tools. The third part introduces the readers to some basic data analysis procedures: propagation of uncertainty, least squares fit, chi square test, and confidence intervals to name a few.

The introduction of probability and statistical tools is made on phenomenological grounds, as a natural response to the problems arising in the laboratory practice. The author has made a concentrated effort to guarantee both accuracy and clarity through the introduction of a large number of figures and worked examples, many of them taken from laboratory experimentations and practice. The book is enriched by the detailed proposal of several simple experiments.

Paolo Fornasini is a Professor of Physics at the University of Trento, Italy. He is the author, with Giuseppe Dalba, of Esercizi di Fisica: Meccanica e Termodinamica (Springer 2006).<

Contenu
Measurements and Uncertainty.- Physical Quantities.- Measurement Units.- Measuring Instruments.- Uncertainty in Direct Measurements.- Probability and Statistics.- Basic Probability Concepts.- Distributions of Random Variables.- Statistical Tools.- Data Analysis.- Uncertainty in Indirect Measurements.- Confidence Levels.- Correlation of Physical Quantities.- The Chi Square Test.- Appendices.- Presentation of Experimental Data.- Systems of Units.- Tables.- Mathematical Complements.- Experiments.