The Uncertainty in Physical Measurements - An Introduction to Data Analysis in the Physics Laboratory

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.

List of contents

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.

About the author

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.

Summary

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.

Additional text

From the reviews:

"Aiming to fill the gap between tutorial-type resources and specialized treatises, this volume, which has been tested by Fornasini’s students in laboratory courses, offers a very clear, concise didactic approach to evaluating uncertainty. Actual worked examples are noted throughout the text, along with numerous figures depicting representative problems. Fornasini … addresses issues of uncertainty concerning significant digits and rounding, use of instruments, a posteriori evaluations, moments of several probability distributions, and indirect measurements. … Summing Up: Highly recommended. Upper-division undergraduates, researchers, and faculty." (D. J. Gougeon, Choice, Vol. 46 (10), June, 2009)

"The aim of this book … is to describe the nature of uncertainty in physical experiments and to provide the useful statistical tools for data analysis. … The present material is mainly addressed to the undergraduate students but could be applied by the researchers … and by the secondary school teachers as well. … we recommend this useful book for wide audience of readers without advanced knowledge of modern Mathematics." (Alexander V. Bulinski, Zentralblatt MATH, Vol. 1163, 2009)

“This is a book that arose from the author’s ‘long-lasting teaching experience’ in the Department of Physics of the University of Trento … . the author found a gap between the elementary texts used … and the more sophisticated books written for those with an extensive background in higher mathematics. This book attempts to fill that gap. … helpful to many students and indeed researchers. … many of us involved in radiation dosimetry would find much of help in this volume in our day-to-day work.” (Ralph H. Thomas, Radiation Protection Dosimetry, Vol. 140 (1), 2010)

Report

From the reviews:
"Aiming to fill the gap between tutorial-type resources and specialized treatises, this volume, which has been tested by Fornasini's students in laboratory courses, offers a very clear, concise didactic approach to evaluating uncertainty. Actual worked examples are noted throughout the text, along with numerous figures depicting representative problems. Fornasini ... addresses issues of uncertainty concerning significant digits and rounding, use of instruments, a posteriori evaluations, moments of several probability distributions, and indirect measurements. ... Summing Up: Highly recommended. Upper-division undergraduates, researchers, and faculty." (D. J. Gougeon, Choice, Vol. 46 (10), June, 2009)
"The aim of this book ... is to describe the nature of uncertainty in physical experiments and to provide the useful statistical tools for data analysis. ... The present material is mainly addressed to the undergraduate students but could be applied by the researchers ... and by the secondary school teachers as well. ... we recommend this useful book for wide audience of readers without advanced knowledge of modern Mathematics." (Alexander V. Bulinski, Zentralblatt MATH, Vol. 1163, 2009)
"This is a book that arose from the author's 'long-lasting teaching experience' in the Department of Physics of the University of Trento ... . the author found a gap between the elementary texts used ... and the more sophisticated books written for those with an extensive background in higher mathematics. This book attempts to fill that gap. ... helpful to many students and indeed researchers. ... many of us involved in radiation dosimetry would find much of help in this volume in our day-to-day work." (Ralph H. Thomas, Radiation Protection Dosimetry, Vol. 140 (1), 2010)

Product details

• Authors: Paolo Fornasini
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 15.11.2010
• EAN: 9781441926944
• ISBN: 978-1-4419-2694-4
• No. of pages: 289
• Dimensions: 159 mm x 17 mm x 235 mm
• Weight: 457 g
• Illustrations: XII, 289 p.
• Subjects: Natural sciences, medicine, IT, technology > Technology > General, dictionaries; B, engineering, Complex systems, Measurement, Theoretical, Mathematical and Computational Physics, Physics and Astronomy, Measurement Science and Instrumentation, Physical measurements, Dynamical systems, Engineering: general, Engineering, general, Technology and Engineering, Dynamics & statics, Statistical physics, Statistical Physics and Dynamical Systems