Details

Limits of Detection in Chemical Analysis

Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its Applications 1. Aufl.

von: Edward Voigtman
132,99 €
Verlag:	Wiley
Format:	EPUB
Veröffentl.:	24.02.2017
ISBN/EAN:	9781119188988
Sprache:	englisch
Anzahl Seiten:	368

In den Warenkorb

Als Gutschein

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

Titelbeschreibung

Details methods for computing valid limits of detection. <ul> <li>Clearly explains analytical detection limit theory, thereby mitigating incorrect detection limit concepts, methodologies and results</li> <li>Extensive use of computer simulations that are freely available to readers</li> <li>Curated short-list of important references for limits of detection</li> <li>Videos, screencasts, and animations are provided at an associated website, to enhance understanding</li> <li>Illustrated, with many detailed examples and cogent explanations</li> </ul>

Inhaltsverzeichnis

Preface xv Acknowledgment xix About the Companion Website xx 1 Background 1 1.1 Introduction 1 1.2 A Short List of Detection Limit References 2 1.3 An Extremely Brief History of Limits of Detection 2 1.4 An Obstruction 3 1.5 An Even Bigger Obstruction 3 1.6 What Went Wrong? 4 1.7 Chapter Highlights 5 References 5 2 Chemical Measurement Systems and their Errors 9 2.1 Introduction 9 2.2 Chemical Measurement Systems 9 2.3 The Ideal CMS 10 2.4 CMS Output Distributions 12 2.5 Response Function Possibilities 12 2.6 Nonideal CMSs 15 2.7 Systematic Error Types 15 2.7.1 What Is Fundamental Systematic Error? 16 2.7.2 Why Is an Ideal Measurement System Physically Impossible? 16 2.8 Real CMSs, Part 1 17 2.8.1 A Simple Example 18 2.9 Random Error 19 2.10 Real CMSs, Part 2 21 2.11 Measurements and PDFs 22 2.11.1 Several Examples of Compound Measurements 22 2.12 Statistics to the Rescue 23 2.13 Chapter Highlights 24 References 24 3 The Response, Net Response, and Content Domains 25 3.1 Introduction 25 3.2 What is the Blank’s Response Domain Location? 27 3.3 False Positives and False Negatives 28 3.4 Net Response Domain 29 3.5 Blank Subtraction 29 3.6 Why Bother with Net Responses? 31 3.7 Content Domain and Two Fallacies 31 3.8 Can an Absolute Standard Truly Exist? 33 3.9 Chapter Highlights 34 References 34 4 Traditional Limits of Detection 37 4.1 Introduction 37 4.2 The Decision Level 37 4.3 False Positives Again 38 4.4 Do False Negatives Really Matter? 40 4.5 False Negatives Again 40 4.6 Decision Level Determination Without a Calibration Curve 41 4.7 Net Response Domain Again 41 4.8 An Oversimplified Derivation of the Traditional Detection Limit, XDC 42 4.9 Oversimplifications Cause Problems 43 4.10 Chapter Highlights 43 References 43 5 Modern Limits of Detection 45 5.1 Introduction 45 5.2 Currie Detection Limits 46 5.3 Why were p and q Each Arbitrarily Defined as 0.05? 48 5.4 Detection Limit Determination Without Calibration Curves 49 5.5 A Nonparametric Detection Limit Bracketing Experiment 49 5.6 Is There a Parametric Improvement? 51 5.7 Critical Nexus 52 5.8 Chapter Highlights 53 References 53 6 Receiver Operating Characteristics 55 6.1 Introduction 55 6.2 ROC Basics 55 6.3 Constructing ROCs 57 6.4 ROCs for Figs 5.3 and 5.4 59 6.5 A Few Experimental ROC Results 60 6.6 Since ROCs may Work Well, Why Bother with Anything Else? 64 6.7 Chapter Highlights 65 References 65 7 Statistics of an Ideal Model CMS 67 7.1 Introduction 67 7.2 The Ideal CMS 67 7.3 Currie Decision Levels in all Three Domains 70 7.4 Currie Detection Limits in all Three Domains 71 7.5 Graphical Illustrations of eqns 7.3–7.8 72 7.6 An Example: are Negative Content Domain Values Legitimate? 74 7.7 Tabular Summary of the Equations 76 7.8 Monte Carlo Computer Simulations 77 7.9 Simulation Corroboration of the Equations in Table 7.2 78 7.10 Central Confidence Intervals for Predicted x Values 80 7.11 Chapter Highlights 81 References 81 8 If Only the True Intercept is Unknown 83 8.1 Introduction 83 8.2 Assumptions 83 8.3 Noise Effect of Estimating the True Intercept 83 8.4 A Simple Simulation in the Response and NET Response Domains 84 8.5 Response Domain Effects of Replacing the True Intercept by an Estimate 86 8.6 Response Domain Currie Decision Level and Detection Limit 88 8.7 NET Response Domain Currie Decision Level and Detection Limit 88 8.8 Content Domain Currie Decision Level and Detection Limit 89 8.9 Graphical Illustrations of the Decision Level and Detection Limit Equations 89 8.10 Tabular Summary of the Equations 90 8.11 Simulation Corroboration of the Equations in Table 8.1 91 8.12 Chapter Highlights 93 9 If Only the True Slope is Unknown 95 9.1 Introduction 95 9.2 Possible “Divide by Zero” Hazard 96 9.3 The t Test for tslope 96 9.4 Response Domain Currie Decision Level and Detection Limit 97 9.5 NET Response Domain Currie Decision Level and Detection Limit 97 9.6 Content Domain Currie Decision Level and Detection Limit 97 9.7 Graphical Illustrations of the Decision Level and Detection Limit Equations 98 9.8 Tabular Summary of the Equations 99 9.9 Simulation Corroboration of the Equations in Table 9.1 99 9.10 Chapter Highlights 101 References 101 10 If the True Intercept and True Slope are Both Unknown 103 10.1 Introduction 103 10.2 Important Definitions, Distributions, and Relationships 104 10.3 The Noncentral t Distribution Briefly Appears 105 10.4 What Purpose Would be Served by Knowing 𝛿? 106 10.5 Is There a Viable Way of Estimating 𝛿? 106 10.6 Response Domain Currie Decision Level and Detection Limit 107 10.7 NET Response Domain Currie Decision Level and Detection Limit 107 10.8 Content Domain Currie Decision Level and Detection Limit 108 10.9 Graphical Illustrations of the Decision Level and Detection Limit Equations 108 10.10 Tabular Summary of the Equations 109 10.11 Simulation Corroboration of the Equations in Table 10.3 109 10.12 Chapter Highlights 109 References 111 11 If Only the Population Standard Deviation is Unknown 113 11.1 Introduction 113 11.2 Assuming 𝜎0 is Unknown, How may it be Estimated? 114 11.3 What Happens if 𝜎0 is Estimated by s0? 114 11.4 A Useful Substitution Principle 116 11.5 Response Domain Currie Decision Level and Detection Limit 116 11.6 NET Response Domain Currie Decision Level and Detection Limit 117 11.7 Content Domain Currie Decision Level and Detection Limit 117 11.8 Major Important Differences From Chapter 7 117 11.9 Testing for False Positives and False Negatives 120 11.10 Correction of a Slightly Misleading Figure 121 11.11 An Informative Screencast 121 11.12 Central Confidence Intervals for 𝜎 and s 122 11.13 Central Confidence Intervals for YC and YD 122 11.14 Central Confidence Intervals for XC and XD 123 11.15 Tabular Summary of the Equations 123 11.16 Simulation Corroboration of the Equations in Table 11.1 123 11.17 Chapter Highlights 125 References 125 12 If Only the True Slope is Known 127 12.1 Introduction 127 12.2 Response Domain Currie Decision Level and Detection Limit 127 12.3 NET Response Domain Currie Decision Level and Detection Limit 128 12.4 Content Domain Currie Decision Level and Detection Limit 128 12.5 Graphical Illustrations of the Decision Level and Detection Limit Equations 128 12.6 Tabular Summary of the Equations 128 12.7 Simulation Corroboration of the Equations in Table 12.1 129 12.8 Chapter Highlights 129 13 If Only the True Intercept is Known 131 13.1 Introduction 131 13.2 Response Domain Currie Decision Level and Detection Limit 132 13.3 NET Response Domain Currie Decision Level and Detection Limit 132 13.4 Content Domain Currie Decision Level and Detection Limit 132 13.5 Tabular Summary of the Equations 133 13.6 Simulation Corroboration of the Equations in Table 13.1 133 13.7 Chapter Highlights 135 References 135 14 If all Three Parameters are Unknown 137 14.1 Introduction 137 14.2 Response Domain Currie Decision Level and Detection Limit 137 14.3 NET Response Domain Currie Decision Level and Detection Limit 138 14.4 Content Domain Currie Decision Level and Detection Limit 138 14.5 The Noncentral t Distribution Reappears for Good 138 14.6 An Informative Computer Simulation 139 14.7 Confidence Interval for xD, with a Major Proviso 142 14.8 Central Confidence Intervals for Predicted x Values 143 14.9 Tabular Summary of the Equations 143 14.10 Simulation Corroboration of the Equations in Table 14.1 143 14.11 An Example: DIN 32645 145 14.12 Chapter Highlights 146 References 147 15 Bootstrapped Detection Limits in a Real CMS 149 15.1 Introduction 150 15.2 Theoretical 151 15.2.1 Background 151 15.2.2 Blank Subtraction Possibilities 151 15.2.3 Currie Decision Levels and Detection Limits 152 15.3 Experimental 153 15.3.1 Experimental Apparatus 153 15.3.2 Experiment Protocol 153 15.3.3 Testing the Noise: Is It AGWN? 156 15.3.4 Bootstrapping Protocol in the Experiments 157 15.3.5 Estimation of the Experimental Noncentrality Parameter 160 15.3.6 Computer Simulation Protocol 160 15.4 Results and Discussion 161 15.4.1 Results for Four Standards 161 15.4.2 Results for 3–12 Standards 162 15.4.3 Toward Accurate Estimates of XD 163 15.4.4 How the XD Estimates Were Obtained 164 15.4.5 Ramifications 165 15.5 Conclusion 165 Acknowledgments 166 References 166 15.6 Postscript 167 15.7 Chapter Highlights 167 16 Four Relevant Considerations 169 16.1 Introduction 169 16.2 Theoretical Assumptions 170 16.3 Best Estimation of 𝛿 171 16.4 Possible Reduction in the Number of Expressions? 172 16.5 Lowering Detection Limits 174 16.6 Chapter Highlights 178 References 178 17 Neyman–Pearson Hypothesis Testing 181 17.1 Introduction 181 17.2 Simulation Model for Neyman–Pearson Hypothesis Testing 181 17.3 Hypotheses and Hypothesis Testing 183 17.3.1 Hypotheses Pertaining to False Positives 183 17.3.1.1 Hypothesis 1 183 17.3.1.2 Hypothesis 2 183 17.3.2 Hypotheses Pertaining to False Negatives 185 17.3.2.1 Hypothesis 3 185 17.3.2.2 Hypothesis 4 185 17.4 The Clayton, Hines, and Elkins Method (1987–2008) 189 17.5 No Valid Extension for Heteroscedastic Systems 191 17.6 Hypothesis Testing for the 𝛿critical Method 192 17.6.1 Hypothesis Pertaining to False Positives 192 17.6.1.1 Hypothesis 5 192 17.6.2 Hypothesis Pertaining to False Negatives 192 17.6.2.1 Hypothesis 6 192 17.7 Monte Carlo Tests of the Hypotheses 192 17.8 The Other Propagation of Error 193 17.9 Chapter Highlights 197 References 197 18 Heteroscedastic Noises 199 18.1 Introduction 199 18.2 The Two Simplest Heteroscedastic NPMs 199 18.2.1 Linear NPM 201 18.2.2 Experimental Corroboration of the Linear NPM 202 18.2.3 Hazards with Heteroscedastic NPMs 203 18.2.4 Example: A CMS with Linear NPM 204 18.3 Hazards with ad hoc Procedures 206 18.4 The HS (“Hockey Stick”) NPM 207 18.5 Closed-Form Solutions for Four Heteroscedastic NPMs 209 18.6 Shot Noise (Gaussian Approximation) NPM 210 18.7 Root Quadratic NPM 211 18.8 Example: Marlap Example 20.13, Corrected 211 18.9 Quadratic NPM 211 18.10 A Few Important Points 212 18.11 Chapter Highlights 212 References 213 19 Limits of Quantitation 215 19.1 Introduction 215 19.2 Theory 217 19.3 Computer Simulation 219 19.4 Experiment 221 19.5 Discussion and Conclusion 223 Acknowledgments 224 References 224 19.6 Postscript 225 19.7 Chapter Highlights 226 20 The Sampled Step Function 227 20.1 Introduction 227 20.2 A Noisy Step Function Temporal Response 229 20.3 Signal Processing Preliminaries 230 20.4 Processing the Sampled Step Function Response 231 20.5 The Standard t-Test for Two Sample Means When the Variance is Constant 232 20.6 Response Domain Decision Level and Detection Limit 233 20.7 Hypothesis Testing 233 20.8 Is There any Advantage to Increasing Nanalyte? 233 20.9 NET Response Domain Decision Level and Detection Limit 235 20.10 NET Response Domain SNRs 235 20.11 Content Domain Decision Level and Detection Limit 235 20.12 The RSDB–BEC Method 236 20.13 Conclusion 237 20.14 Chapter Highlights 237 References 237 21 The Sampled Rectangular Pulse 239 21.1 Introduction 239 21.2 The Sampled Rectangular Pulse Response 239 21.3 Integrating the Sampled Rectangular Pulse Response 240 21.4 Relationship Between Digital Integration and Averaging 242 21.5 What is the Signal in the Sampled Rectangular Pulse? 243 21.6 What is the Noise in the Sampled Rectangular Pulse? 243 21.7 The Noise Bandwidth 244 21.8 The SNR with Matched Filter Detection of the Rectangular Pulse 245 21.9 The Decision Level and Detection Limit 245 21.10 A Square Wave at the Detection Limit 246 21.11 Effect of Sampling Frequency 247 21.12 Effect of Area Fraction Integrated 247 21.13 An Alternative Limit of Detection Possibility 248 21.14 Pulse-to-Pulse Fluctuations 248 21.15 Conclusion 249 21.16 Chapter Highlights 250 References 250 22 The Sampled Triangular Pulse 251 22.1 Introduction 251 22.2 A Simple Triangular Pulse Shape 251 22.3 Processing the Sampled Triangular Pulse Response 253 22.4 The Decision Level and Detection Limit 254 22.5 Detection Limit for a Simulated Chromatographic Peak 254 22.6 What Should Not be Done? 256 22.7 A Bad Play, in Three Acts 256 22.8 Pulse-to-Pulse Fluctuations 258 22.9 Conclusion 258 22.10 Chapter Highlights 259 References 259 23 The Sampled Gaussian Pulse 261 23.1 Introduction 261 23.2 Processing the Sampled Gaussian Pulse Response 262 23.3 The Decision Level and Detection Limit 263 23.4 Pulse-to-Pulse Fluctuations 263 23.5 Conclusion 264 23.6 Chapter Highlights 264 References 264 24 Parting Considerations 267 24.1 Introduction 267 24.2 The Measurand Dichotomy Distraction 269 24.3 A “New Definition of LOD” Distraction 273 24.4 Potentially Important Research Prospects 274 24.4.1 Extension to Method Detection Limits 274 24.4.2 Confidence Intervals in the Content Domain 275 24.4.3 Noises Other Than AGWN 275 24.5 Summary 276 References 277 Appendix A Statistical Bare Necessities 279 Appendix B An Extremely Short Lightstone® Simulation Tutorial 299 Appendix C Blank Subtraction and the 𝜂1∕2 Factor 311 Appendix D Probability Density Functions for Detection Limits 321 Appendix E The Hubaux and Vos Method 325 Bibliography 331 Glossary of Organization and Agency Acronyms 335 Index 337

Autorenportrait

Edward Voigtman is emeritus professor of chemistry at the University of Massachusetts – Amherst, having retired after 29 years as a faculty member. His interests include ultrasensitive detection techniques, applications of signal/noise theory, optical calculus-based computer simulation of spectrometric systems and analytical detection limit theory and practice.

Back cover copy

Details methods for computing valid limits of detection The limit of detection is among the most important concepts in chemical analysis. In simple terms, if a chemical analyte is present at, or above, the limit of detection, it has low a priori-specified probability of escaping detection. This is distinct from the formerly used decision level, i.e., the level above which there is low a priori-specified probability of obtaining a false positive from a true analytical blank. In some cases, qualitative detection of analyte is sufficient, but in many other cases, quantification is also desired or required, e.g., total arsenic concentration in a source of potable water. In this case, the concept of limit of quantitation is also relevant because meaningful quantification is not possible at the limit of detection. Limits of Detection in Chemical Analysis details methods for computing valid, unbiased limits of detection. It correctly and clearly explains analytical detection limit theory, thereby mitigating against incorrect detection limit concepts, methodologies and results. The book focuses exclusively on how limits of detection are correctly defined and computed for ordinary univariate chemical measurement systems (CMSs). The book features: <ul> <li>Clear explanations of decision level and detection limit concepts</li> <li>Profuse illustrations with many detailed examples and cogent explanations</li> <li>Extensive use of corroborating computer simulations that are freely available to readers</li> <li>A curated short-list of important references for limits of detection</li> <li>Videos, screencasts, and animations are provided at an associated website</li> </ul> This book is recommended for anyone wanting to learn about limits of detection. It is written at a level that makes it easily accessible to undergraduates, graduate students and researchers in both academia and industry. Readers will learn how to properly, and rather simply, compute statistically valid limits of detection and know what their limitations are.