Statistics and Chemometrics for Analytical Chemistry

285 Pages·2008·9.96 MB·English

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Statistics and This popular textbook gives a clear account of the principles of the t
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main statistical methods used in modern analytical laboratories. Such t
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Chemometrics methods underpin high quality analyses in areas such as the safety of c
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food, water and medicines, environmental monitoring, and chemical
for Analytical manufacturing. The treatment throughout emphasises the underlying a
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Statistics and
statistical ideas, and no detailed knowledge of mathematics is required. d
Chemistry There are numerous worked examples, including the use of Microsoft C
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Excel and Minitab, and a large number of student exercises, many of
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them based on examples from the analytical literature. m Chemometrics
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Fifth edition key features
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• expanded treatment of control charts for Analytical
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techniques
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• extended treatment of robust methods
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• major additions to sections on multivariate regression
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• numerous worked examples, using Microsoft Excel and Minitab A
• an attractive two-colour text design n
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• updated Instructors’ Manual
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• improved website, www.pearsoned.co.uk/miller, including t James N Miller
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examples for lecturers and students c
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This book is aimed at undergraduate and graduate courses in l & Jane C Miller
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Analytical Chemistry and related topics. It will also be a valuable
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resource for researchers and chemists working in analytical chemistry. e
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Fifth edition
Professor James Miller – is Emeritus Professor of Analytical Chemistry at Loughborough i
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University. He has published numerous reviews and papers on t
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analytical techniques and been awarded the SAC Silver Medal, the y
Theophilus Redwood Lectureship and the SAC Gold Medal by the Royal
Society of Chemistry. A past President of the Analytical Division of the M
RSC, he is a member of the Society’s Council and has served on the i
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editorial boards of many analytical and spectroscopic journals. e
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Dr Jane Miller – completed a PhD at Cambridge University’s Cavendish Laboratory and &

is an experienced teacher of mathematics and physics at higher M
education and 6th form levels. She holds an MSc in Applied Statistics i
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and is the author of several specialist A-level statistics texts. le
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Statistics and Chemometrics
for Analytical Chemistry
Fifth Edition
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We work with leading authors to develop the
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James N. Miller
Jane C. Miller
Statistics and Chemometrics
for Analytical Chemistry
Fifth Edition
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Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England
and Associated Companies throughout the world
Visit us on the World Wide Web at:
www.pearsoned.co.uk
Third edition published under the Ellis Horwood imprint 1993
Fourth edition 2000
Fifth edition 2005
© Ellis Horwood Limited 1993
© Pearson Education Limited 2000, 2005
The rights of J. N. Miller and J. C. Miller to be identified as authors of
this Work have been asserted by them in accordance with the Copyright,
Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored
in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without either the prior
written permission of the Publishers or a licence permitting restricted
copying in the United Kingdom issued by the Copyright Licensing Agency Ltd,
90 Tottenham Court Road, London W1T 4LP.
All trademarks used herein are the property of their respective owners. The use
of any trademark in this text does not vest in the author or publisher any
trademark ownership rights in such trademarks, nor does the use of such
trademarks imply any affiliation with or endorsement of this book by
such owners. Microsoft is a trademark of Microsoft Corporation; MINITAB is a
registered trademark of Minitab, Inc.; The Unscrambler is a trademark of Camo ASA.
ISBN 0 131 29192 0
British Library Cataloguing-in-Publication Data
A catalogue record for this book can be obtained from the British Library
Library of Congress Cataloging-in-Publication Data
Miller, J. N. (James N.), 1943–
Statistics and chemometrics for analytical chemistry / James N. Miller and Jane C.
Miller. — 5th ed.
p. cm.
Includes bibliographical references.
ISBN 0-13-129192-0 (pbk.)
1. Chemistry, Analytic — Statistical methods — Textbooks. I. Miller, J. C. (Jane Charlotte)
II. Title.
QD75.4.S8M54 2005
543'.072 — dc22
2004060168
10 9 8 7 6 5 4 3 2 1
09 08 07 06 05
Typeset by 68 in 9.25/12pt Stone Serif
Printed in Great Britain by Ashford Colour Press, Gosport, Hants
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Contents
Preface to the fifth edition ix
Preface to the first edition xi
Acknowledgements xiii
Glossary of symbols xv
1 Introduction 1
1.1 Analytical problems 1
1.2 Errors in quantitative analysis 2
1.3 Types of error 3
1.4 Random and systematic errors in titrimetric analysis 6
1.5 Handling systematic errors 9
1.6 Planning and design of experiments 12
1.7 Calculators and computers in statistical calculations 13
Bibliography 15
Exercises 16
2 Statistics of repeated measurements 18
2.1 Mean and standard deviation 18
2.2 The distribution of repeated measurements 20
2.3 Log-normal distribution 24
2.4 Definition of a ‘sample’ 24
2.5 The sampling distribution of the mean 26
2.6 Confidence limits of the mean for large samples 27
2.7 Confidence limits of the mean for small samples 28
2.8 Presentation of results 29
2.9 Other uses of confidence limits 31
2.10 Confidence limits of the geometric mean for
a log-normal distribution 31
2.11 Propagation of random errors 32
2.12 Propagation of systematic errors 35
Bibliography 37
Exercises 37
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3 Significance tests 39
3.1 Introduction 39
3.2 Comparison of an experimental mean with a known value 39
3.3 Comparison of two experimental means 41
3.4 Paired t-test 45
3.5 One-sided and two-sided tests 47
3.6 F-test for the comparison of standard deviations 49
3.7 Outliers 51
3.8 Analysis of variance 54
3.9 Comparison of several means 55
3.10 The arithmetic of ANOVA calculations 58
3.11 The chi-squared test 61
3.12 Testing for normality of distribution 63
3.13 Conclusions from significance tests 67
Bibliography 69
Exercises 69
4 The quality of analytical measurements 74
4.1 Introduction 74
4.2 Sampling 74
4.3 Separation and estimation of variances using ANOVA 76
4.4 Sampling strategy 77
4.5 Quality control methods – Introduction 78
4.6 Shewhart charts for mean values 79
4.7 Shewhart charts for ranges 81
4.8 Establishing the process capability 83
4.9 Average run length: cusum charts 86
4.10 Zone control charts (J-charts) 89
4.11 Proficiency testing schemes 90
4.12 Collaborative trials 93
4.13 Uncertainty 98
4.14 Acceptance sampling 102
Bibliography 103
Exercises 104
5 Calibration methods: regression and correlation 107
5.1 Introduction: instrumental analysis 107
5.2 Calibration graphs in instrumental analysis 108
5.3 The product–moment correlation coefficient 110
5.4 The line of regression of yon x 114
5.5 Errors in the slope and intercept of the regression line 115
5.6 Calculation of a concentration and its random error 118
5.7 Limits of detection 121
5.8 The method of standard additions 124
5.9 Use of regression lines for comparing analytical methods 126
5.10 Weighted regression lines 131
5.11 Intersection of two straight lines 135
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Contents vii
5.12 ANOVA and regression calculations 136
5.13 Curvilinear regression methods – Introduction 138
5.14 Curve fitting 141
5.15 Outliers in regression 145
Bibliography 146
Exercises 147
6 Non-parametric and robust methods 150
6.1 Introduction 150
6.2 The median: initial data analysis 151
6.3 The sign test 156
6.4 The Wald–Wolfowitz runs test 158
6.5 The Wilcoxon signed rank test 159
6.6 Simple tests for two independent samples 162
6.7 Non-parametric tests for more than two samples 165
6.8 Rank correlation 167
6.9 Non-parametric regression methods 169
6.10 Robust methods – Introduction 171
6.11 Robust estimates of location and spread 173
6.12 Robust regression methods 175
6.13 Re-sampling statistics 176
6.14 Conclusions 178
Bibliography 179
Exercises 179
7 Experimental design and optimization 181
7.1 Introduction 181
7.2 Randomization and blocking 182
7.3 Two-way ANOVA 183
7.4 Latin squares and other designs 186
7.5 Interactions 187
7.6 Factorial versus one-at-a-time design 192
7.7 Factorial design and optimization 193
7.8 Optimization: basic principles and univariate methods 197
7.9 Optimization using the alternating variable search method 200
7.10 The method of steepest ascent 202
7.11 Simplex optimization 205
7.12 Simulated annealing 209
Bibliography 209
Exercises 210
8 Multivariate analysis 213
8.1 Introduction 213
8.2 Initial analysis 214
8.3 Principal component analysis 215
8.4 Cluster analysis 220
8.5 Discriminant analysis 223
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viii Contents
8.6 K-nearest neighbour method 227
8.7 Disjoint class modelling 228
8.8 Regression methods 228
8.9 Multiple linear regression (MLR) 229
8.10 Principal components regression (PCR) 232
8.11 Partial least squares (PLS) regression 234
8.12 Artificial neural networks 236
8.13 Conclusions 237
Bibliography 238
Exercises 239
Solutions to exercises 241
Appendix 1: Commonly used statistical significance tests 251
Appendix 2: Statistical tables 254
Index 263
Supporting resources
Visit www.pearsoned.co.uk/millerto find valuable online resources
For instructors
• Complete, downloadable Instructor’s Manual
• PowerPoint slides that can be downloaded and used as OHTs
For more information please contact your local Pearson Education sales
representative or visit www.pearsoned.co.uk/miller
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Preface to the fifth edition
Since the publication of the fourth edition of this book in 2000 the use of statis-
tics and chemometrics methods in the teaching and practice of the analytical sci-
ences has continued to expand rapidly. Once again this new edition seeks to
reflect these developments while retaining the basic aims of previous editions,
which adopted a pragmatic and as far as possible non-mathematical approach to
statistical calculations. We have also continued to include in the text examples
solved with the aid of Microsoft Excel® and the familiar statistics package
Minitab®, both widely available to teachers, students and researchers, and both in
a welcome process of continuing development. Extras and macros for both pro-
grams are available through the Internet, in many cases without charge. The
graphic and other facilities offered by these programs are further exploited in the
Instructors’ Manual, which is again available to accompany this edition, and still
further updates and examples for teachers and students are provided through the
associated website. As in the last edition the solutions to the exercises given in
this book are only outline ones – full solutions are given in the Instructors’
Manual.
The main areas where new material has appeared in this edition are in
Chapters 4–8. Chapter 4 includes an expanded treatment of control charts and
additional material on uncertainty and on proficiency testing schemes. In
Chapter 5 there is more material on the use of regression lines for method com-
parisons. Chapter 6 reflects the continuing growth of importance of robust
methods, and Chapter 7 provides extra sections on factorial designs and on the
simplex optimization method. The use of multivariate methods is now very com-
mon, so Chapter 8 includes an extended discussion of the principal components
and partial least squares regression methods, and more on neural networks. In the
earlier chapters on basic statistics the main changes are the greater emphasis on
the Grubbs outlier test and a move of the section of Kolmogorov methods to
Chapter 3. The bibliographies for each chapter have been updated, with rather
more annotations than in the past, and with more emphasis on publications from
standards organizations.
As always we are very grateful to colleagues and correspondents who have
pointed out minor errors (we remain responsible for any that are still there) and
made other constructive suggestions. Once again we thank the Royal Society