0131291920_COVER 3/2/05 10:48 AM Page 1 Statistics This popular textbook gives a clear account of the principles of the Statistics and main statistical methods used in modern analytical laboratories. Such Chemometrics methods underpin high quality analyses in areas such as the safety of food, water and medicines, environmental monitoring, and chemical and manufacturing. The treatment throughout emphasises the underlying for Analytical statistical ideas, and no detailed knowledge of mathematics is required. Chemometrics Chemistry There are numerous worked examples, including the use of Microsoft Statistics and Excel and Minitab, and a large number of student exercises, many of them based on examples from the analytical literature. Fifth edition key features Chemometrics • expanded treatment of control charts • additions to cover single point calibration and method comparison techniques for Analytical • extended treatment of robust methods for • major additions to sections on multivariate regression • numerous worked examples, using Microsoft Excel and Minitab Analytical Chemistry Chemistry • an attractive two-colour text design • updated Instructors’ Manual • improved website, www.pearsoned.co.uk/miller, including examples for lecturers and students James N Miller This book is aimed at undergraduate and graduate courses in Analytical Chemistry and related topics. It will also be a valuable & Jane C Miller resource for researchers and chemists working in analytical chemistry. Professor James Miller – is Emeritus Professor of Analytical Chemistry at Loughborough Fifth edition University. He has published numerous reviews and papers on analytical techniques and been awarded the SAC Silver Medal, the Theophilus Redwood Lectureship and the SAC Gold Medal by the Royal Miller Miller & Society of Chemistry. A past President of the Analytical Division of the RSC, he is a member of the Society’s Council and has served on the editorial boards of many analytical and spectroscopic journals. Dr Jane Miller – completed a PhD at Cambridge University’s Cavendish Laboratory and is an experienced teacher of mathematics and physics at higher education and 6th form levels. She holds an MSc in Applied Statistics and is the author of several specialist A-level statistics texts. Fifth edition www.pearson-books.com www.pearsoned.co.uk/miller SCA_A01.qxd 4/7/05 5:32 PM Page i Statistics and Chemometrics for Analytical Chemistry Fifth Edition SCA_A01.qxd 4/7/05 5:32 PM Page ii We work with leading authors to develop the strongest educational materials in chemistry, bringing cutting-edge thinking and best learning practice to a global market. Under a range of well-known imprints, including Prentice Hall, we craft high quality print and electronic publications which help readers to understand and apply their content, whether studying or at work. To find out more about the complete range of our publishing please visit us on the World Wide Web at: www.pearsoned.co.uk SCA_A01.qxd 4/7/05 5:33 PM Page iii James N. Miller Jane C. Miller Statistics and Chemometrics for Analytical Chemistry Fifth Edition SCA_A01.qxd 4/7/05 5:33 PM Page iv 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 10987654321 09 08 07 06 05 Typeset by 68 in 9.25/12pt Stone Serif Printed in Great Britain by Ashford Colour Press, Gosport, Hants SCA_A01.qxd 4/7/05 5:33 PM Page v 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 SCA_A01.qxd 4/7/05 5:33 PM Page vi vi Contents 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 y on 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 SCA_A01.qxd 4/7/05 5:33 PM Page vii 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 SCA_A01.qxd 4/7/05 5:33 PM Page viii viii Contents 8.6 K-nearest neighbour method 227 8.7