An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements

Even if you have achieved a high level of mathematical sophistication, this book is a great read. I find myself gaining great new insights to basic principles due to Taylor's logical developments. This is simply the best available introductory text on error analysis.

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.

I had to get this book because it was one of the texts required for an undergradute physics course in data analysis. It turns out to have been a very useful book. I've used it as reference, for among other things, analyzing data collected for a port development project in Pusan, South Korea, developing software used for medical diagnostics equipment, and, most recently, in developing financial software.

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.

Students in our cell biology laboratory use this book frequently to help us analyze our data. For example there is an excellent discussion about the difference between standard error and standard error of the mean. While it is aimed at undergraduate physicists and engineers, it will be practical for (and easily digested by) biologists as well.