A Practical Guide to Data Analysis for Physical Science Students

✍ Scribed by Louis Lyons

• Publisher: Cambridge University Press
• Year: 1991
• Tongue: English
• Leaves: 110
• Category: Library

✦ Synopsis

It is usually straightforward to calculate the result of a practical experiment in the laboratory. Estimating the accuracy of that result is often regarded by students as an obscure and tedious routine, involving much arithmetic. An estimate of the error is, however, an integral part of the presentation of the results of experiments. This textbook is intended for undergraduates who are carrying out laboratory experiments in the physical sciences for the first time. It is a practical guide on how to analyse data and estimate errors. The necessary formulas for performing calculations are given, and the ideas behind them are explained, although this is not a formal text on statistics. Specific examples are worked through step by step in the text. Emphasis is placed on the need to think about whether a calculated error is sensible. At first students should take this book with them to the laboratory, and the format is intended to make this convenient. The book will provide the necessary understanding of what is involved, should inspire confidence in the method of estimating errors, and enable numerical calculations without too much effort. The author's aim is to make practical classes more enjoyable. Students who use this book will be able to complete their calculations quickly and confidently, leaving time to appreciate the basic physical ideas involved in the experiments.

Intended for undergraduates who are carrying out laboratory experiments in the physical sciences for the first time, this textbook on how to analyze data and estimate errors includes the necessary formulas for performing the calculations.

✦ Table of Contents

Contents
Preface
Glossary and Conventions
1. Experimental errors
1.1 Why estimate errors
1.2 Random and systematic errors
1.2.1 What they are
1.2.2 Estimating random errors
1.2.3 Worrying about systematic errors
1.3 Distributions
1.4 Mean and variance
1.5 Gaussian distribution
1.6 The meaning of σ
1.7 Combining errors
1.7.1 Linear situations
1.7.2 Products
1.7.3 The General Case
1.8 Systematic errors
1.9 An example including random and systematic errors
1.10 Combining results of different experiments
1.11 Worked examples
1.11.1 Mean and variance
1.11.2 Using a Gaussian distribution
1.11.3 Central Limit Theorem
1.11.4 Combining errors
1.11.5 Combining results
1.12 Does it feel right?
Problems
2. Least squares fitting
2.1 What are we trying to do?
2.2 Weighted sum of squares
2.3 Determining the parameters
2.4 The error on the gradient and intercept
2.5 Other examples
2.6 y(obs) as numbers
2.7 Parameter testing
2.8 Distribution testing
2.9 Worked example of straight line fit
2.10 Summary of straight line fitting
Problems
Appendix 1: Useful formulae
Appendix 2: Partial differentiation
Appendix 3: The binomial distribution
Appendix 4: The Poisson distribution
Appendix 5: Student's t distribution
Appendix 6: Statistical tables
Appendix 7: Random numbers
Index

✦ Subjects

Data Analysis