Basic Chemometric Techniques in Atomic Spectroscopy

2nd Edition

RSC Analytical Spectroscopy Monographs

Edited by Jose M Andrade-Garda

Basic Chemometric Techniques in Atomic Spectroscopy

RSC Publishing

RSC Analytical Spectroscopy Monographs No. 13 ISBN: 978-1-84973-796-8 ISSN: 2041-9732 A catalogue record for this book is available from the British Library r The Royal Society of Chemistry 2013 All rights reserved Apart from fair dealing for the purposes of research for non-commercial purposes or for private study, criticism or review, as permitted under the Copyright, Designs and Patents Act 1988 and the Copyright and Related Rights Regulations 2003, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of The Royal Society of Chemistry or the copyright owner, or in the case of reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of the licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to The Royal Society of Chemistry at the address printed on this page. The RSC is not responsible for individual opinions expressed in this work. Published by The Royal Society of Chemistry, Thomas Graham House, Science Park, Milton Road, Cambridge CB4 0WF, UK Registered Charity Number 207890 For further information see our web site at www.rsc.org Printed in the United Kingdom by CPI Group (UK) Ltd, Croydon, CR0 4YY, UK

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Contents

2.10

Appendix 2. Comparison of Two Regression Lines Another Possibility Acknowledgements References Chapter 3

Implementing a Robust Methodology: Experimental Designs and Optimisation Xavier Toma`s-Morer, Lucinio Gonza´lez-Sabate´, Laura Ferna´ndez-Ruano and Marı´a Paz Go´mez-Carracedo 3.1

Basics of Experimental Design 3.1.1 Objectives and Strategies 3.1.2 Variables and Responses: Factors, Levels, Effects and Interactions 3.2 Analysis of Experimental Designs 3.2.1 Factorial Designs 3.2.2 2f Factorial Designs 3.2.3 Algorithms: BH2 and Yates 3.2.4 Graphical and Statistical Analysis 3.2.5 Blocking Experiments 3.2.6 Confounding: Fractional Factorial Designs 3.2.7 Saturated Designs: Plackett-Burman Designs. Use in Screening and Robustness Studies 3.3 Taguchi’s Approach to Experimental Design 3.3.1 Strategies for Robust Designs 3.3.2 Planning Experiments: Orthogonal Arrays 3.3.3 Robust Parameter Design: Reducing Variation 3.3.4 Worked Example 3.4 Optimisation 3.4.1 Experimental Optimisation 3.4.2 The Simplex Method 3.4.3 The Modified Simplex Method 3.4.4 Response Surface Designs 3.5 Examples of Practical Applications References Chapter 4

113 116 117 117 123

123 123 124 125 125 126 128 130 133 134 136 138 138 139 145 147 154 154 155 164 167 175 232

Ordinary Multiple Linear Regression and Principal Components Regression Joan Ferre´-Baldrich and Ricard Boque´-Martı´

256

4.1

256

4.2

Introduction 4.1.1 Multivariate Calibration in Quantitative Analysis 4.1.2 Notation Basics of Multivariate Regression 4.2.1 The Multiple Linear Regression Model 4.2.2 Estimation of the Model Coefficients

256 259 260 260 261

CHAPTER 3

Implementing a Robust Methodology: Experimental Designs and Optimisation XAVIER TOMA`S-MORER,*a LUCINIO GONZA´LEZ-SABATE´,a LAURA FERNA´NDEZ-RUANOa AND MARI´A PAZ GO´MEZ-CARRACEDOb a

Department of Applied Statistics, Institut Quı´ mic de Sarria`, Universitat Ramon Llull, Barcelona, Spain; b Department of Analytical Chemistry, University of A Corun˜a, A Corun˜a, Spain *Email: [email protected]

3.1 Basics of Experimental Design In this section, the basics of experimental designs are introduced. Many definitions are given to introduce the most usual nomenclature and to avoid some common misconceptions. A practical and easy-to-follow approach was preferred instead of a more formal one, and literature references are given for more advanced or interested readers.

3.1.1 Objectives and Strategies An ‘experiment’ is just a test or series of tests. Experiments are performed in all scientific disciplines and are an important part of the way we learn about how systems and processes work. The validity of the conclusions that are drawn RSC Analytical Spectroscopy Monographs No. 13 Basic Chemometric Techniques in Atomic Spectroscopy: 2nd Edition Edited by Jose´ M. Andrade-Garda r The Royal Society of Chemistry 2013 Published by the Royal Society of Chemistry, www.rsc.org

123

This was the first book for atomic spectroscopists to present the basic principies of experimenta l designs, optimization and multivariate regression, now presented in a new, revised edition. Multivariate regression is a valuable statistical method for handling complex problems (such as spectral and chemical interferences), which arise during atomic spectroscopy. However, the technique is underused as most spectroscopists do not have time to study the often complex literature on the subject. This practical introduction uses conceptual explanations and worked examples to give readers a clear understanding of the technique. This book also includes new types of experimental designs and a recently developed, promising multivariate regression method based on the so-called 'SupportVector Machines'. Mathematics is kept to a minim um but, when required, is kept at a basic level. Practical considerations, interpretations and troubleshooting are emphasized and literature surveys are included to guide the reader to further work. Noticeably, most chapters include reviews that cove r up to ten years. The same dataset is used for all chapters dealing with calibration to demonstrate the differences between the different methodologies. Readers willleam how to handle spectral and chemical interferences in atomic spectroscopy in a new, more efficient and costeffective way.

Front cover image courtesy of Shutterstock and Sabino Muiño-Varela, Alatzne Carlosena-Zubieta, Rosa Soto-Ferreiro and Jose Manuel Andrade-Garda.

RSC Analytical Spectroscopy Monographs ISBN 978-1-84973 - 796-8

Series Editor: N Barnett, Deakin University,Australia Established as a useful source of information on spectrometric and spectroscopic measurement techniques for ana lytical scientists, RSC Analytical Spectroscopy Monographs are aimed at practising analysts who need immediate guidance and advice. Each monograph provides the practical detail which working analysts need, explaining key facts and concepts in a concise and readable manner for graduates and non-specialists.

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