Lyons L. A Practical Guide to Data Analysis for Physical Science Students

Cambridge: Cambridge University Press, 1991. — 110 p.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.Glossary and Conventions
Experimental errors
Why estimate errors
Random and systematic errors
What they are
Estimating random errors
Worrying about systematic errors
Distributions
Mean and variance
Gaussian distribution
The meaning of σ
Combining errors
Linear situations
Products
The General Case
Systematic errors
An example including random and systematic errors
Combining results of different experiments
Worked examples
Mean and variance
Using a Gaussian distribution
Central Limit Theorem
Combining errors
Combining results
Does it feel right?
Problems
Least squares fitting
What are we trying to do?
Weighted sum of squares
Determining the parameters
The error on the gradient and intercept
Other examples
y(obs) as numbers
Parameter testing
Distribution testing
Worked example of straight line fit
Summary of straight line fitting
Problems
Useful formulae
Partial differentiation
The binomial distribution
The Poisson distribution
Student's t distribution
Statistical tables
Random numbers