Statistical Methods in Analytical Chemistry Second Edition Statistical Methods in Analytical Chemistry CHEMICAL ANALYSIS A SERIES OF MONOGRAPHS ON ANALYTICAL CHEMISTRY AND ITS APPLICATIONS Editor J. D. WINEFORDNER VOLUME 153 A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto Statistical Methods in Analytical Chemistry Second Edition PETER C. MEIER CILAG A.G. (A Johnson & Johnson Company) Schaffhausen, Switzerland RICHARD E. ZUND TERANOL A.G. (A Hoffmann-LaRoche Company) Visp, Switzerland A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto This book is printed on acid-free paper. @ Copyright 0 2000 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. 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, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written pemiission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax (508) 7504744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: [email protected]. For ordering and customer service, call I-800-CALL-WILEY. Library of Congress Cataloging-in-Publication Data Meier, Peter C., 1945- Statistical methods in analytical chemistry / Peter C. Meier, Richard E. Zund. - 2nd ed. p. cm. - (Chemical analysis ; v. 153) “A Wiley-Interscience publication.” Includes bibliographical references and index. ISBN 0-47 1-29363-6 (cloth : alk. paper) 1, Chemistry, Analytic-Statistical methods. 1. Zund, Richard E. 11. Title. 111. Series. QD75.4.S8M45 2000 543’.007’2-dc2 I 99-25291 CIP Printed in the United States of America. 10 9 8 7 6 5 4 To our wives, Therese and Edith, respectively, who granted us the privilege of "book" time, and spurred us on when our motivation flagged. To our children, Lukas and Irhe, respectively, and Sabrina and Simona, who finally have their fathers back. CONTENTS PREFACE xiii CHEMICAL ANALYSIS SERIES xvii INTRODUCTION 1 CHAPTER 1: UNIVARIATE DATA 13 1.1 Mean and Standard Deviation 13 1.1.1 The Most Probable Value 14 1.1.2 The Dispersion 15 1.1.3 Independency of Measurements 21 1.1.4 Reproducibility and Repeatibility 23 1.1. 5 Reporting the Results 25 1.1.6 Interpreting the Results 27 1.2 Distributions and the Problem of Small Numbers 29 1.2.1 The Normal Distribution 29 1.2.2 Student’s &Distribution 34 1.3 Confidence Limits 35 1.3.1 Confidence Limits of the Distribution 37 1.3.2 Confidence Limits of the Mean 39 1.4 The Simulation of a Series of Measurements 41 1.5 Testing for Deviations 44 1. 5. 1 Examining Two Series of Measurements 47 1.5.2 The t-Test 48 1.5.3 Extension of the t-Test to More Than Two Series of Measurements 54 1S .4 Multiple-Range Test 56 1S .5 Outlier Tests 57 1.5.6 Analysis of Variance (ANOVA) 61 1.6 Number of Determinations 65 vii ... Vlll CONTENTS 1.7 Width of a Distribution 69 1.7.1 The F-Test 69 I .7.2 Confidence Limits for a Standard Deviation 72 1.7.3 Bartlett Test 73 1.8 Charting a Distribution 74 1.8.1 Histograms 74 1.8.2 X2-Test 76 1.8.3 Probability Charts 80 1.8.4 Conventional Control Charts (Shewhart Charts) 81 1.8.5 Cunisum Charts 8.5 1.9 Errors of the First and Second Kind 87 CHAPTER 2: BJ- AND MULTIVARIATE DATA 91 2.1 Correlation 92 2.2 Linear Regression 94 2.2.1 The Standard Approach 96 2.2.2 Slope and Intercept 97 2.2.3 Residual Variance 99 2.2.4 Testing Linearity and Slope 102 2.2.5 Inteipolating Y(x) 104 2.2.6 Interpolating X( y) 108 2.2.7 Limit of Detection 115 2.2.8 Minimizing the Costs of a Calibration 118 2.2.9 Standard Addition 120 2.2.10 Weighted Regression 122 2.2.11 The Intersection of Two Linear Regression Lines 127 2.3 Nonlinear Regression 127 2.3.1 Linearization 129 2.3.2 Nonlinear Regression and Modeling 131 2.4 Multidimensional Data/Visualizing Data 132 CHAPTER 3: RELATED TOPICS 137 3.1 GMP Background: Selectivity and Interference/Linearity/ Considerations 137 Accuracy/Precision/Reliability/Economic CONTENTS ix 3.2 Development, Qualification, and Validation; Installation Qualification, Operations Qualification, Performance Qualification/Method Development/Method Validation 140 3.3 Data Treatment Scheme: Data Acquisition/Acceptance Criteria/Data Assembly and Clean-up/Data Evaluation/ Presentation of Results/Specifications/Records Retention 145 3.4 Exploratory Data Analysis (EDA) 148 3.5 Optimization Techniques 149 3.5.1 Full Factorial vs. Classical Experiments 150 3.5.2 Simplex-Guided Experiments 156 3.5.3 Optimization of the Model: Curve Fitting 157 3.5.4 Computer Simulation 160 3.5.5 Monte Carlo Technique (MCT) 163 3.6 Smoothing and Filtering Data/Box-Car Averaging/Moving Average/Savitzky-Golay Filtering/CUSUM 167 3.7 Error Propagation and Numerical Artifacts 169 3.8 Programs 17 1 CHAPTER 4: COMPLEX EXAMPLES 175 4.1 To Weigh or Not to Weigh 175 4.2 Nonlinear Fitting 180 4.3 UV-Assay Cost Structure 185 4.4 Process Validation 190 4.5 Regulations and Realities 193 4.6 Diffusing Vapors 199 4.7 Stability h la Carte 202 4.8 Secret Shampoo Switch 203 4.9 Tablet Press Woes 205 4.10 Sounding Out Solubility 208 4.11 Exploring a Data Jungle 210 4.12 Sifting Through Sieved Samples 215 4.13 Controlling Cyanide 22 1 4.14 Ambiguous Automation 225 4.15 Mistrusted Method 229