Measurements and Their Uncertainties

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. The book finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.

ISBN 019956633X   Pages 152 ISBN13 9780199566334 (What's this?)   Weight (grammes) 352 Publisher Oxford University Press   Published in Oxford Imprint Oxford University Press   Height (mm) 247 Format Paperback   Width (mm) 189 Publication date 01 Jul 2010   Spine width (mm) 9 DEWEY 511.43   Academic level Undergraduate DEWEY edition DC22

1		Errors in the physical sciences		1
1.1		The importance of error analysis		1
1.2		Uncertainties in measurement		2
1.2.1		Terminology		3
1.2.2		Random errors		3
1.2.3		Systematic errors		4
1.2.4		Mistakes		4
1.3		Precision of measurements		5
1.3.1		Precision of an analogue device		5
1.3.2		Precision of a digital device		6
1.4		Accuracy of measurements		6
		Chapter summary		7
2		Random errors in measurements		9
2.1		Analysing distributions: some statistical ideas		9
2.2		The mean		9
2.3		The width of the distribution: estimating the precision		10
2.3.1		Rough-and-ready approach to estimating the width		10
2.3.2		Statistical approach to estimating the width		11
2.4		Continuous distributions		12
2.5		The normal distribution		13
2.6		Sample and parent distribution		13
2.7		The standard error		14
2.7.1		The error in the error		16
2.8		Reporting results		17
2.8.1		Rounding and significant figures		18
2.9		The five golden rules		19
		Chapter summary		19
		More...

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