This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering. It assumes no prior knowledge of statistics. It introduces the necessary concepts where needed, with key points illustrated with worked examples and graphic illustrations. In contrast to traditional mathematical treatments it uses a combination of spreadsheet and calculus-based approaches, suitable as a quick and easy on-the-spot reference. The emphasis throughout is on practical strategies to be adopted in the laboratory.
Error analysis is introduced at a level accessible to school leavers, and carried through to research level. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computer analysis. The general approach uses the chi-square statistic extensively. Particular attention is given to hypothesis testing and extraction of parameters and their uncertainties by fitting mathematical models to experimental data. Routines implemented by most contemporary data analysis packages are analysed and explained. Measurements and Their Uncertainties finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.
1. Errors in the physical sciences
2. Random errors in measurement
3. Uncertainties as probabilities
4. Error propagation
5. Data visualisation and reduction
6. Least-squares fitting of complex functions
7. Computer minimisation and the error matrix
8. Hypothesis testing - how good are our models
9. Topics for further summary
"With the shift from analytic methods to spreadsheet-based techniques, this book will enable students simultaneously to (a) become fluent in the choice and application of appropriate methods (b) understand the underlying principles. "
– David Saxon, University of Glasgow
"This is a rather beautiful little book."
– David J. Hand, International Statistical Review