A Practical Guide to Data Analysis for Physical Science Students

by Louis Lyons

• ISBN13: 9780521424639
• ISBN10: 0521424631
• Format: Paperback
• Copyright: 1991-11-29
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	xi	(2)
Glossary and Conventions	xiii
1 Experimental errors	1	(43)
1.1 Why estimate errors?	1	(3)
1.2 Random and systematic errors	4	(5)
1.2.1 What they are	4	(3)
1.2.2 Estimating random errors	7	(1)
1.2.3 Worrying about systematic errors	8	(1)
1.3 Distributions	9	(3)
1.4 Mean and variance	12	(4)
1.5 Gaussian distribution	16	(2)
1.6 The meaning of Sigma	18	(3)
1.7 Combining errors	21	(6)
1.7.1 Linear situations	22	(3)
1.7.2 Products	25	(1)
1.7.3 The general case	26	(1)
1.8 Systematic errors	27	(2)
1.9 An example including random and systematic errors	29	(2)
1.10 Combining results of different experiments	31	(2)
1.11 Worked examples	33	(4)
1.11.1 Mean and variance	33	(1)
1.11.2 Using a Gaussian distribution	34	(1)
1.11.3 Central Limit Theorem	34	(1)
1.11.4 Combining errors	35	(1)
1.11.5 Combining results	36	(1)
1.12 Does it feel right?	37	(3)
Problems	40	(4)
2 Least squares fitting	44	(29)
2.1 What are we trying to do?	44	(2)
2.2 Weighted sum of squares	46	(3)
2.3 Determining the parameters	49	(2)
2.4 The error on the gradient and intercept	51	(4)
2.4.1 Using the errors Sigma(i)	51	(2)
2.4.2 Using the scatter of points	53	(2)
2.5 Other examples	55	(1)
2.6 y^(obs) as numbers	56	(1)
2.7 Parameter testing	57	(1)
2.8 Distribution testing	58	(5)
2.9 Worked example of straight line fit	63	(6)
2.10 Summary of straight line fitting	69	(2)
Problems	71	(2)
Appendix 1 Useful formulae	73	(2)
Appendix 2 Partial differentiation	75	(3)
Appendix 3 The binomial distribution	78	(4)
Appendix 4 The Poisson distribution	82	(4)
Appendix 5 Student's distribution	86	(3)
Appendix 6 Statistical tables	89	(3)
Appendix 7 Random numbers	92	(2)
Index	94