An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements 2nd Edition

Book Preface

I first wrote An Introduction to Error Analysis because my experience teaching introductory laboratory classes for several years had convinced me of a serious need for a book that truly introduced the subject to the college science student. Several fine books on the topic were available, but none was really suitable for a student new to the subject. The favorable reception to the first edition confirmed the exis­tence of that need and suggests the book met it.

The continuing success of the first edition suggests it still meets that need. Nevertheless, after more than a decade, every author of a college textbook must surely feel obliged to improve and update the original version. Ideas for modifica­tions came from several sources: suggestions from readers, the need to adapt the book to the wide availability of calculators and personal computers, and my own experiences in teaching from the book and finding portions that could be improved.

Because of the overwhelmingly favorable reaction to the first edition, I have maintained its basic level and general approach. Hence, many revisions are simply changes in wording to improve clarity. A few changes are major, the most important of which are as follows:
(1) The number of problems at the end of each chapter is nearly doubled to give users a wider choice and teachers the ability to vary their assigned problems from year to year. Needless to say, any given reader does not need to solve any­where near the 264 problems offered; on the contrary, half a dozen problems from each chapter is probably sufficient.
(2) Several readers recommended placing a few simple exercises regularly throughout the text to let readers check that they really understand the ideas just presented. Such exercises now appear as “Quick Checks,” and I strongly urge stu­dents new to the subject to try them all. If any Quick Check takes much longer than a minute or two, you probably need to reread the preceding few paragraphs. The answers to all Quick Checks are given in the answer section at the back of the book. Those who find this kind of exercise distracting can easily skip them.
(3) Also new to this edition are complete summaries of all the important equa­tions at the end of each chapter to supplement the first edition’s brief summaries inside the front and back covers. These new summaries list all key equations from the chapter and from the problem sets as well.
(4) Many new figures appear in this edition, particularly in the earlier chapters. The figures help make the text seem less intimidating and reflect my conscious effort to encourage students to think more visually about uncertainties. I have ob­served, for example, that many students grasp issues such as the consistency of measurements if they think visually in terms of error bars.
(5) I have reorganized the problem sets at the end of each chapter in three ways. First, the Answers section at the back of the book now gives answers to all of the odd-numbered problems. (The first edition contained answers only to selected problems.) The new arrangement is simpler and more traditional. Second, as a rough guide to the level of difficulty of each problem, I have labeled the problems with a system of stars: One star (*) indicates a simple exercise that should take no more than a couple of minutes if you understand the material. Two stars (**) indicate a somewhat harder problem, and three stars (***) indicate a really searching prob­lem that involves several different concepts and requires more time. I freely admit that the classification is extremely approximate, but students studying on their own should find these indications helpful, as may teachers choosing problems to assign to their students.

Third, I have arranged the problems by section number. As soon as you have read Section N, you should be ready to try any problem listed for that section. Although this system is convenient for the student and the teacher, it seems to be currently out of favor. I assume this disfavor stems from the argument that the system might exclude the deep problems that involve many ideas from different sections. I consider this argument specious; a problem listed for Section N can, of course, involve ideas from many earlier sections and can, therefore, be just as gen­eral and deep as any problem listed under a more general heading.

(6) I have added problems that call for the use of computer spreadsheet pro­grams such as Lotus 123 or Excel. None of these problems is specific to a particular system; rather, they urge the student to learn how to do various tasks using whatever system is available. Similarly, several problems encourage students to learn to use the built-in functions on their calculators to calculate standard deviations and the like.
(7) I have added an appendix (Appendix E) to show two proofs that concern sample standard deviations: first, that, based on N measurements of a quantity, the best estimate of the true width of its distribution is the sample standard deviation with (N -1) in the denominator, and second, that the uncertainty in this estimate is as given by Equation (5.46). These proofs are surprisingly difficult and not easily found in the literature.

It is a pleasure to thank the many people who have made suggestions for this second edition. Among my friends and colleagues at the University of Colorado, the people who gave most generously of their time and knowledge were David Alexan­der, Dana Anderson, David Bartlett, Barry Bruce, John Cumalat, Mike Dubson, Bill Ford, Mark Johnson, Jerry Leigh, Uriel Nauenberg, Bill O’Sullivan, Bob Ristinen,Rod Smythe, and Chris Zafiratos. At other institutions, I particularly want to thank R. G. Chambers of Leeds, England, Sharif Heger of the University of New Mexico, Steven Hoffmaster of Gonzaga University, Hilliard Macomber of the University of Northern Iowa, Mark Semon of Bates College, Peter Timbie of Brown University, and David Van Dyke of the University of Pennsylvania. I am deeply indebted to all of these people for their generous help. I am also most grateful to Bruce Armbruster of University Science Books for his generous encouragement and support. Above all, I want to thank my wife Debby; I don’t know how she puts up with the stresses and strains of book writing, but I am so grateful she does.