A Student's Guide to Data and Error Analysis : Student's Guides - Herman J. C. Berendsen

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A Student's Guide to Data and Error Analysis

By: Herman J. C. Berendsen

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Hardcover | 7 April 2011

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Hardcover
238 Pages

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22.86 x 15.24 x 1.75

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All students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.

Industry Reviews

"Overall, this would be a nice text or reference to accompany a short course in statistics for undergraduate science or engineering..also useful for researchers desiring a primer or review...Recommended." - CHOICE

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Non-Fiction Engineering & Technology Technology in General Engineering in General Science Science in General Maths for Scientists Mathematics Mathematical Foundation Maths for Engineers Probability & Statistics

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Paperback

Published: 7th April 2011

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Preface	p. xi
Data and error analysis	p. 1
Introduction	p. 3
The presentation of physical quantities with their inaccuracies	p. 5
How to report a series of measurements	p. 5
How to represent numbers	p. 9
How to express inaccuracies	p. 10
Reporting units	p. 13
Graphical presentation of experimental data	p. 14
Errors: classification and propagation	p. 18
Classification of errors	p. 18
Error propagation	p. 19
Probability distributions	p. 27
Introduction	p. 27
Properties of probability distributions	p. 29
The binomial distribution	p. 32
The Poisson distribution	p. 36
The normal distribution	p. 37
The central limit theorem	p. 41
Other distributions	p. 42
Processing of experimental data	p. 53
The distribution function of a data series	p. 54
The average and the mean squared deviation of a data series	p. 57
Estimates for mean and variance	p. 58
Accuracy of mean and Student's t-distribution	p. 59
Accuracy of variance	p. 60
Handling data with unequal weights	p. 61
Robust estimates	p. 63
Graphical handling of data with errors	p. 71
Introduction	p. 71
Linearization of functions	p. 73
Graphical estimates of the accuracy of parameters	p. 77
Using calibration	p. 78
Fitting functions to data	p. 84
Introduction	p. 84
Linear regression	p. 87
General least-squares fit	p. 92
The chi-squared test	p. 95
Accuracy of the parameters	p. 98
F-test on significance of the fit	p. 106
Back to Bayes: knowledge as a probability distribution	p. 111
Direct and inverse probabilities	p. 111
Enter Bayes	p. 112
Choosing the prior	p. 114
Three examples of Bayesian inference	p. 114
Conclusion	p. 121
References	p. 123
Answers to exercises	p. 125
Appendices	p. 133
Combining uncertainties	p. 135
Systematic deviations due to random errors	p. 138
Characteristic function	p. 141
From binomial to normal distributions	p. 143
The binomial distribution	p. 143
The multinomial distribution	p. 144
The Poisson distribution	p. 145
The normal distribution	p. 146
Central limit theorem	p. 148
Estimation of the variance	p. 151
Standard deviation of the mean	p. l54
Weight factors when variances are not equal	p. 158
Least-squares fitting	p. 160
How do you find the best parameters a and b in y≈ ax+b?	p. 160
General linear regression	p. 161
SSQ as a function of the parameters	p. 162
Covariances of the parameters	p. 163
Python codes	p. 167
Scientific data	p. 197
Chi-squared distribution	p. 199
F-distribution	p. 201
Least-squares fitting	p. 203
Normal distribution	p. 205
Physical constants	p. 209
Probability distributions	p. 211
Student's t-distribution	p. 213
Units	p. 215
Index	p. 220
Table of Contents provided by Ingram. All Rights Reserved.

A Student's Guide to Data and Error Analysis

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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