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

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).<

The book targets scientists and researchers focused on experimentation in the fields of physics, chemistry and engineering, as well as graduate-level students studying these sciences in an applied way. The central point is the uncertainty in measurements: what are the causes of uncertainty and how do we deal with it? The possible causes of uncertainty are at first phenomenologically explored, leading to understand the necessity of a formal treatment based on probability theory and statistical tools. The basics of probability and statistics are then introduced, in order to support the most relevant data analysis procedures, which are introduced in the last part of the book: uncertainty in indirect measurements, least squares fits, chi square test, confidence intervals.

The pedagogical goal is to introduce the treatment of uncertainty in a phenomenological way, based on examples taken from laboratory experience and distinguishing the different causes of uncertainty (there is more than just random errors and gaussian distributions to consider in laboratory practice). This approach naturally leads to the idea of limiting distributions and the necessity of a probabilistic treatment. Only then is probability theory introduced in a formal way (Part 2) and data analysis procedures are developed on the basis of probability and statistics (Part 3). Examples taken from laboratory experience facilitate the understanding of the concepts of Part 2 and 3. Some heavy demonstrations and some mathematical complements are grouped in one Appendix, to facilitate the smooth reading of the main chapters.