Covers all the elements of statistical error analysis in measurement. A step-by-step presentation of how random errors occur when taking measurements, how these errors behave, how measurement errors can be used to determine the reliability of the values, and how to accord weights to different measurements of the same quantity. Provides several appendices including a Frequency Distribution Tabulation Sheet and Arithmetic Probability Paper—two items intended for photocopying.
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.
"Evaluating Measurement Accuracy" is intended for anyone who is concerned with measurements in any field of science or technology. It reflects the latest developments in metrology and offers new results, but is designed to be accessible to readers at different levels: meteorologists, engineers and experimental scientists who use measurements as tools in their professions, graduate and undergraduate students in the natural sciences and engineering, and technicians performing complex measurements in industry, quality control, and trade. The material of the book is presented from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements. This inclusion is a notable and unique aspect of this title as complex measurements done in industry and trade are often neglected in metrological literature, leaving the practitioners of these measurements to devise their own ad-hoc techniques.
“Evaluating Measurement Accuracy, 2nd Edition” is intended for those who are concerned with measurements in any field of science or technology. It reflects the latest developments in metrology and offers new results, but is designed to be accessible to readers at different levels: scientists who advance the field of metrology, engineers and experimental scientists who use measurements as tool in their professions, students and graduate students in natural sciences and engineering, and, in parts describing practical recommendations, technicians performing mass measurements in industry, quality control, and trade. This book presents material from the practical perspective and offers solutions and recommendations for problems that arise in conducting real-life measurements. This new edition adds a method for estimating accuracy of indirect measurements with independent arguments, whose development Dr. Rabinovich was able to complete very recently. This method, which is called the Method of Enumeration, produces estimates that are no longer approximate, similar to the way the method of reduction described in the first edition removed approximation in estimating uncertainty of indirect measurements with dependent arguments. The method of enumeration completes addressing the range of problems whose solutions signify the emergence of the new theory of accuracy of measurements. A new method is added for building a composition of histograms, and this method forms a theoretical basis for the method of enumeration.Additionally, as a companion to this book, a concise practical guide that assembles simple step-by-step procedures for typical tasks the practitioners are likely to encounter in measurement accuracy estimation is available at SpringerLink.
Errors in Practical Measurement in Science, Engineering, and Technology B. Austin Barry A step-by-step presentation of how random errors occur when taking measurements, how these errors behave, how measurement errors can be used to determine the reliability of the values, and how to accord weights to different measurements of the same quantity. Introduces the concept of percentage compliance with a demand specification, discusses practical plotting of frequency distribution curves, offers tables of areas beneath the normal curve to assist in formulating the validity of measurements, and provides basic information of the probability ellipse for two-dimensional errors. Appendices contain a review and reference of significant figures, complete information for writing a specification for a procedure, suggestions for the use of a Fortran program, and more. 1978 (0 471-03156-9) 183 pp.
This book is designed as a laboratory companion, student textbook or reference book for professional scientists. The text is for use in one-term numerical analysis, data and error analysis, or computer methods courses, or for laboratory use. It is for the sophomore-junior level, and calculus is a prerequisite. The new edition includes applications for PC use.
