Measurement Analysis: An Introduction to the Statistical Analysis of Laboratory Data in Physics, Chemistry and the Life Sciences

by Mario Caria

Overview

This book deals with the statistical treatment of experimental data. It is also meant for those who are entirely new to the field of statistics and probability calculus, and those who wish to obtain rigorous estimates of the uncertainties associated with the experimental results of any discipline, such as meteorology, engineering, physics, chemistry and the life sciences. To understand the text, only a basic understanding of differential calculus is required.As an innovative teaching approach, simple laboratory class experiments are used as the basis for developing a detailed statistical analysis. This is done by directly using the students' logbooks without re-elaboration. The approach is profitable and can be easily pursued by the layman.People have, in the past, been confused by the many statistical definitions, formulae and assumptions. This book tries to avoid any arbitrary definition by using the recently introduced ISO directives.All the concepts, parameters and test variables for the modern treatment of experimental data are included. Among them are the error, uncertainty and its estimate, the distribution functions and the associated parameters. Every concept is associated with a simple experimental situation and the data analysis is performed in numerical detail. For completeness, the correlation of uncertainties with the error matrix is dealt with in greater detail. All the tests of hypotheses are presented. They are introduced from simple arguments and developed up to the analytical details. The applications of the tests to the fitting of experimental curves of the χ2, t and F tests, as well as the one most often used in the life sciences, the ANOVA, are shown.

Product Details

ISBN-13:	9781860942310
Publisher:	Imperial College Press
Publication date:	11/28/2000
Pages:	240
Product dimensions:	6.30(w) x 8.83(h) x 0.78(d)

Table of Contents

	Preface	vii
1	Measurements, errors and estimates	1
1.1	Error and Uncertainty	1
1.1.1	Resolution and reading error	2
1.1.2	The illegitimate error	5
1.1.3	Uncertainty and systematic error	6
1.2	Uncertainty and casual error	7
1.2.1	The expression of expanded uncertainty	18
2	Distribution of data and errors	23
2.1	Probability and distributions	23
2.2	Distribution functions	24
2.2.1	The Binomial distribution function	27
2.2.2	The Poisson distribution function	40
2.2.3	The Guass distribution function	45
2.2.4	Relations between distribution functions	58
2.2.5	The constant distribution function and the reading error	65
3	Processing of data and uncertainties	73
3.1	The combination of uncertainties	73
3.1.1	Rigorous calculation for the estimate of the combined uncertainty	73
3.2	The number of significant digits	82
3.3	The problem of correlation	85
3.3.1	The error matrix or matrix of uncertainties	88
3.4	Interpolation and combination of uncertainties	99
3.5	Extrapolation and combination of uncertainties	106
3.6	Mean standard deviation and the weighted mean	110
4	Accuracy tests	117
4.1	Hypotheses and the verification of accuracy	117
4.2	Maximum likelihood	118
4.3	The x[superscript 2] parameter	122
4.4	Minimisation	126
4.5	The x[superscript 2] accuracy test	134
4.5.1	The number of degrees of freedom	135
4.5.2	The parameter x[superscript 2 subscript r]	137
4.5.3	The x[superscript 2] probability function	145
4.6	The t accuracy test	157
4.7	The F accuracy test	171
4.7.1	The F test for the analysis of one variance or ANOVA	175
4.8	The generalised x[superscript 2] accuracy test	180
4.9	Confidence, trust and expanded uncertainty	184
4.9.1	Probability intervals	185
4.9.2	The confidence or trust level	186
4.9.3	The t parameter and the confidence level	188
4.10	Exclusion of data	192
4.10.1	Limits and exclusion of data	198
A	Experiments	201
A 1	The speed of light in coaxial cables	201
A.2	The light rotation angle in a polarimeter	202
A.3	Radioactive decay counts	203
A.4	The time constant in an RC circuit	203
A.5	Photoresistance of a semiconductor	205
A.6	Magnetic induction between two solenoids	205
A.7	The characteristic curve of a semiconductor diode	207
B	Symbols used in the text	209