Statistics and Chemometrics for Analytical Chemistry

297 Pages·2011·2.55 MB·English

by  Manoj Chaudhary

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James N Miller & Jane C Miller
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This popular textbook gives a clear account of the principles of
Professor James Miller m
is Emeritus Professor of the main statistical methods used in modern analytical laboratories. e
Analytical Chemistry at Such methods underpin high-quality analyses in areas such as the t
Loughborough University. r for Analytical
safety of food, water and medicines, environmental monitoring, i
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analytical techniques sises the underlying statistical ideas, and no detailed knowledge of f
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including the use of Microsoft Excel and Minitab, and a large
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A past President of the Features of the new edition ic Sixth edition
Analytical Division of a
the RSC, he is a former l
• introduction to Bayesian methods
member of the Society’s C
James N Miller
Council and has served on • additions to cover method validation and sampling uncertainty h
the editorial boards of many e
• extended treatment of robust statistics
analytical and spectroscopic m Jane C Miller
journals. • new material on experimental design i
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Dr Jane Miller completed • additions to sections on regression and calibration methods t
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a PhD at Cambridge Univer- • updated Instructor’s Manual y
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and is an experienced • improved website including further exercises for lecturers and
teacher of mathematics and students at www.pearsoned.co.uk/Miller Si
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physics at higher education t
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and 6th form levels. She This book is aimed at undergraduate and graduate courses
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www.pearson-books.com
CVR_MILL0422_06_SE_CVR.indd 1 26/3/10 16:11:58
Statistics and Chemometrics
for Analytical Chemistry
Sixth Edition
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James N. Miller
Jane C. Miller
Statistics and Chemometrics
for Analytical Chemistry
Sixth Edition
Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England
and Associated Companies throughout the world
Visit us on the World Wide Web at:
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Third edition published under the Ellis Horwood imprint 1993
Fourth edition 2000
Fifth edition 2005
Sixth edition 2010
© Ellis Horwood Limited 1993
© Pearson Education Limited 2000, 2010
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.
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ISBN: 978-0-273-73042-2
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data
A catalog record of this book is available from the Library of Congress
10 9 8 7 6 5 4 3 2 1
14 13 12 11 10
Typeset in 9.25/12pt Stone Serifby 73
Printed by Ashford Colour Press Ltd., Gosport, UK.
1 Head v
Contents
Preface to the sixth 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 and resources 15
Exercises 16
2 Statistics o f repeated measurements 17
2.1 Mean and standard deviation 17
2.2 The distribution of repeated measurements 19
2.3 Log-normal distribution 23
2.4 Definition of a ‘sample’ 24
2.5 The sampling distribution of the mean 25
2.6 Confidence limits of the mean for large samples 26
2.7 Confidence limits of the mean for small samples 27
2.8 Presentation of results 29
2.9 Other uses of confidence limits 30
2.10 Confidence limits of the geometric mean for a
log-normal distribution 30
2.11 Propagation of random errors 31
2.12 Propagation of systematic errors 34
Bibliography 35
Exercises 35
vi Contents
3 Significance tests 37
3.1 Introduction 37
3.2 Comparison of an experimental mean with a known value 38
3.3 Comparison of two experimental means 39
3.4 Paired t-test 43
3.5 One-sided and two-sided tests 45
3.6 F-test for the comparison of standard deviations 47
3.7 Outliers 49
3.8 Analysis of variance 52
3.9 Comparison of several means 53
3.10 The arithmetic of ANOVA calculations 56
3.11 The chi-squared test 59
3.12 Testing for normality of distribution 61
3.13 Conclusions from significance tests 65
3.14 Bayesian statistics 66
Bibliography 69
Exercises 69
4 The quality of analytical measurements 74
4.1 Introduction 74
4.2 Sampling 75
4.3 Separation and estimation of variances using ANOVA 76
4.4 Sampling strategy 77
4.5 Introduction to quality control methods 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 91
4.12 Method performance studies (collaborative trials) 94
4.13 Uncertainty 98
4.14 Acceptance sampling 102

4.15 Method validation 104
Bibliography 106
Exercises 107
5 Calibration methods in instrumental analysis:
regression and correlation 110
5.1 Introduction: instrumental analysis 110
5.2 Calibration graphs in instrumental analysis 112
5.3 The product–moment correlation coefficient 114
5.4 The line of regression of yon x 118
5.5 Errors in the slope and intercept of the regression line 119
5.6 Calculation of a concentration and its random error 121
5.7 Limits of detection 124
Contents vii
5.8 The method of standard additions 127
5.9 Use of regression lines for comparing analytical methods 130
5.10 Weighted regression lines 135
5.11 Intersection of two straight lines 140
5.12 ANOVA and regression calculations 141
5.13 Introduction to curvilinear regression methods 142
5.14 Curve fitting 145
5.15 Outliers in regression 149
Bibliography 151
Exercises 151
6 Non-parametric and robust methods 154
6.1 Introduction 154
6.2 The median: initial data analysis 155
6.3 The sign test 160
6.4 The Wald–Wolfowitz runs test 162
6.5 The Wilcoxon signed rank test 163
6.6 Simple tests for two independent samples 166
6.7 Non-parametric tests for more than two samples 169
6.8 Rank correlation 171
6.9 Non-parametric regression methods 172
6.10 Introduction to robust methods 175
6.11 Simple robust methods: trimming and winsorisation 176
6.12 Further robust estimates of location and spread 177
6.13 Robust ANOVA 179
6.14 Robust regression methods 180
6.15 Re-sampling statistics 181
6.16 Conclusions 183
Bibliography and resources 184
Exercises 185
7 Experimental design and optimisation 186
7.1 Introduction 186

7.2 Randomisation and blocking 188
7.3 Two-way ANOVA 189
7.4 Latin squares and other designs 192
7.5 Interactions 193
7.6 Identifying the important factors: factorial designs 198
7.7 Fractional factorial designs 203
7.8 Optimisation: basic principles and univariate methods 206
7.9 Optimisation using the alternating variable search method 208
7.10 The method of steepest ascent 210
7.11 Simplex optimisation 213
7.12 Simulated annealing 216
Bibliography and resources 217
Exercises 218
viii Contents
8 Multivariate analysis 221
8.1 Introduction 221
8.2 Initial analysis 222
8.3 Principal component analysis 224
8.4 Cluster analysis 228
8.5 Discriminant analysis 231
8.6 K-nearest neighbour method 235
8.7 Disjoint class modelling 236
8.8 Regression methods 237
8.9 Multiple linear regression 238
8.10 Principal component regression 241
8.11 Partial least-squares regression 243
8.12 Natural computation methods: artificial neural networks 245
8.13 Conclusions 247
Bibliography and resources 248
Exercises 248
Solutions to exercises 251
Appendix 1: Commonly used statistical significance tests 261
Appendix 2: Statistical tables 264
Index 273
Supporting resources
Visit www.pearsoned.co.uk/millerto find valuable online resources
For students
• Further exercises
For instructors

• Further exercises
• Complete Instructor’s Manual
• PowerPoint slides of figures from the book
For more information please contact your local Pearson Education sales
representative or visit www.pearsoned.co.uk/miller
Preface to the sixth edition
Since the publication of the fifth edition of this book in 2005 the use of elemen-
tary and advanced statistical methods in the teaching and the practice of the ana-
lytical sciences has continued to increase in extent and quality. This new edition
attempts to keep pace with these developments in several chapters, while retain-
ing the basic approach of previous editions by adopting a pragmatic and, as far as
possible, non-mathematical approach to statistical calculations.
The results of many analytical experiments are conventionally evaluated using
established significance testing methods. In recent years, however, Bayesian
methods have become more widely used, especially in areas such as forensic sci-
ence and clinical chemistry. The basis and methodology of Bayesian statistics have
some distinctive features, which are introduced in a new section of Chapter 3. The
quality of analytical results obtained when different laboratories study identical
sample materials continues, for obvious practical reasons, to be an area of major
importance and interest. Such comparative studies form a major part of the
process of validating the use of a given method by a particular laboratory. Chap-
ter 4 has therefore been expanded to include a new section on method validation.
The most popular form of inter-laboratory comparison, proficiency testing schemes,
often yields suspect or unexpected results. The latter are now generally treated
using robust statistical methods, and the treatment of several such methods in

Chapter 6 has thus been expanded. Uncertainty estimates have become a widely
accepted feature of many analyses, and a great deal of recent attention has been
focused on the uncertainty contributions that often arise from the all-important
sampling process: this topic has also been covered in Chapter 4. Calibration
methods lie at the core of most modern analytical experiments. In Chapter 5 we
have expanded our treatments of the standard additions approach, of weighted
regression, and of regression methods where both x- and y-axes are subject to errors
or variations.
A topic that analytical laboratories have not, perhaps, given the attention it
deserves has been the proper use of experimental designs. Such designs have
distinctive nomenclature and approaches compared with post-experiment data
analysis, and this perhaps accounts for their relative neglect, but many experi-
mental designs are relatively simple, and again excellent software support is avail-
able. This has encouraged us to expand significantly the coverage of experimental
designs in Chapter 7. New and ever more sophisticated multivariate analysis