The Uncertainty in Physical Measurements

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.