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Title: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by John R. Taylor ISBN: 0-935702-75-X Publisher: University Science Books Pub. Date: 01 August, 1996 Format: Paperback Volumes: 1 List Price(USD): $36.50 |
Average Customer Rating: 4.82 (11 reviews)
Rating: 4
Summary: A gentle introduction to data and error analysis
Comment: Taylor's book is simply amazing.
In little more than three hundred pages it manages to explain in a crystal clear manner concepts such as the propagation of errors (starting from simple cases and moving to the general treatment), the meaning of the standard deviation of the population, of the sample and of the mean, the maximum likelihood principle, hypothesis test and confidence levels, the chi squared test and the meaning of correlation.
True, this is not a textbook on mathematical statistic, so you won't find elaborate proofs here: much is left to the reader's intuition. But as the saying goes, 'is not a bug, it's a feature!'. This text makes you understand what all those books on statistics and probability are about (or at least some of their most important applications) and it does it so well that you will reach the end of each chapter asking yourself "oh, that was it?".
Part of the book is devoted to application of error analysis and you will find chapters on weighted means, on the rejection of data, plus linear and nonlinear regression. The exercises are intriguing and all in all this is a very well written book.
Even if you plan to study the matter deeper, on tougher textbooks, please consider preparing yourself to the tougher mathematical stuff by reading this wonderful book. You won't regret it. And possibly, you will come back to it from time to time.
Rating: 5
Summary: Easy-To-Read Text on Error Analysis
Comment: Many undergraduate students in sciences and engineering must have encountered this experience: You conduct an experiment and collect the relevant data. You are asked to fit your data into a straight line by performing one or multiple linear regression. You are also to present any uncertainty and error in your data as well as calculation. You panic and scratch your head and don't know what's the appropriate procedure to carry out these analysis.
Here comes John Taylor's "An Introduction to Error Analysis", which introduces the study of uncertainties to students. The book assumes no prior knowledge and uses a plethora of pertinent examples (drawn from chemistry, physics, and engineering) to illustrate topics like propagation of uncertainties, random uncertainties, rejection of data, least-squares fitting, and distribution.
This book will save hours of studying and researching on error analysis method. It is very well-written and reader-friendly that lower division students will find it useful.
Rating: 5
Summary: A little off the top, please...
Comment: But how much is 'a little'?
I first encountered this book when I was a physics and astronomy major in college, a major that changed over time to include mathematics proper, then political science, then other humanities such as religious studies, history and philosophy. Strange as it may seem, this text has been one of the few constants that has been helpful in almost every field. For physics and any of the natural sciences, the content of this book is highly necessary - be in chemistry, physics, astronomy, geology, or biology, all sciences depend upon observation and analysis, both of which are far from perfect. The task of ever-increasing observational and analytical precision is both an art and a science in and of itself, and one of the tasks of any scientist is to discover where errors might lie.
Interestingly, this also occurs in political science and sociology, economics and history, and even philosophy (logic can incorporate ideas from error analysis, as can epistemology). Error analysis is primarily a statistical tool, and those who have had statistics will find this very familiar. The first part of the book is very simple - Taylor assumes no background, so gives an introduction to the simple reading of charts, graphs, scales and other such things, with plenty of examples. He talks about estimating, significant figures, fractional uncertainties, and how uncertainties can accumulate. How can 2 + 2 = 5? Well, if you round to the highest or lowest whole number, 2.49 and 2.49 will both be rounded down to 2 (under many normal rounding procedures), yet if the underlying calculation or data include the 'real' information, 2.49 + 2.49 in fact equals 4.98, very close to 5. If you think that's confusing, you ain't seen nothing yet...
Taylor's first part concludes by looking at the basics of simple statistical analysis - standard deviations, normal distributions, justification of the mean as best estimate, and a brief introduction to the concept of confidence. Part two gets into more detailed analysis, including least-squares fitting, correlation coefficients, binomial distributions, Poission distributions, and the chi-squared test. The mathematics requirement goes up as the chapters progress - the early chapters only require an elementary knowledge of algeba; as the text continues, knowledge of differentiation, integration and exponential functions are necessary. A first-year course in calculus should be sufficient for easy understanding here; it is possible to get through the material without this background, but it will be more difficult.
This text is designed to be a self-study for the students; it can be introduced in lectures prior to lab work, but can also be used easily for the independent reader to understand. This book is really intended for the physical scientist - most of the examples come from problems in optics or mechanics (physics problems). Useful, helpful, and a good introduction to error analysis.
Read and understand.
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Title: Data Reduction and Error Analysis for the Physical Sciences by Philip R. Bevington, D. Keith Robinson, Philip Bevington ISBN: 0072472278 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 23 July, 2002 List Price(USD): $58.25 |
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Title: The Statistical Analysis of Experimental Data by John Mandel ISBN: 0486646661 Publisher: Dover Publications Pub. Date: 01 October, 1984 List Price(USD): $16.95 |
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Title: Measurement Errors and Uncertainties: Theory and Practice by S. G. Rabinovich, Seymon Rabinovich, M. E. Alferieff ISBN: 0387988351 Publisher: AIP Press Pub. Date: 01 December, 1999 List Price(USD): $54.95 |
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Title: Experimentation and Uncertainty Analysis for Engineers by Hugh W. Coleman, W. Glenn Steele ISBN: 0471121460 Publisher: Wiley-Interscience Pub. Date: 08 January, 1999 List Price(USD): $99.00 |
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Title: Data Analysis for Scientists and Engineers by Stuart L. Meyer ISBN: 0963502700 Publisher: Peer Management Consultants Ltd Pub. Date: 01 September, 1992 List Price(USD): $55.00 |
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