{"product_id":"limits-of-detection-in-chemical-analysis-isbn-9781119188971","title":"Limits of Detection in Chemical Analysis","description":"\u003cp\u003eDetails methods for computing valid limits of detection.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eClearly explains analytical detection limit theory, thereby mitigating incorrect detection limit concepts, methodologies and results\u003c\/li\u003e \u003cli\u003eExtensive use of computer simulations that are freely available to readers\u003c\/li\u003e \u003cli\u003eCurated short-list of important references for limits of detection\u003c\/li\u003e \u003cli\u003eVideos, screencasts, and animations are provided at an associated website, to enhance understanding\u003c\/li\u003e \u003cli\u003eIllustrated, with many detailed examples and cogent explanations\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eAcknowledgment xix\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xx\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Background 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 1\u003c\/p\u003e \u003cp\u003e1.2 A Short List of Detection Limit References 2\u003c\/p\u003e \u003cp\u003e1.3 An Extremely Brief History of Limits of Detection 2\u003c\/p\u003e \u003cp\u003e1.4 An Obstruction 3\u003c\/p\u003e \u003cp\u003e1.5 An Even Bigger Obstruction 3\u003c\/p\u003e \u003cp\u003e1.6 What Went Wrong? 4\u003c\/p\u003e \u003cp\u003e1.7 Chapter Highlights 5\u003c\/p\u003e \u003cp\u003eReferences 5\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Chemical Measurement Systems and their Errors 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 9\u003c\/p\u003e \u003cp\u003e2.2 Chemical Measurement Systems 9\u003c\/p\u003e \u003cp\u003e2.3 The Ideal CMS 10\u003c\/p\u003e \u003cp\u003e2.4 CMS Output Distributions 12\u003c\/p\u003e \u003cp\u003e2.5 Response Function Possibilities 12\u003c\/p\u003e \u003cp\u003e2.6 Nonideal CMSs 15\u003c\/p\u003e \u003cp\u003e2.7 Systematic Error Types 15\u003c\/p\u003e \u003cp\u003e2.7.1 What Is Fundamental Systematic Error? 16\u003c\/p\u003e \u003cp\u003e2.7.2 Why Is an Ideal Measurement System Physically Impossible? 16\u003c\/p\u003e \u003cp\u003e2.8 Real CMSs, Part 1 17\u003c\/p\u003e \u003cp\u003e2.8.1 A Simple Example 18\u003c\/p\u003e \u003cp\u003e2.9 Random Error 19\u003c\/p\u003e \u003cp\u003e2.10 Real CMSs, Part 2 21\u003c\/p\u003e \u003cp\u003e2.11 Measurements and PDFs 22\u003c\/p\u003e \u003cp\u003e2.11.1 Several Examples of Compound Measurements 22\u003c\/p\u003e \u003cp\u003e2.12 Statistics to the Rescue 23\u003c\/p\u003e \u003cp\u003e2.13 Chapter Highlights 24\u003c\/p\u003e \u003cp\u003eReferences 24\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Response, Net Response, and Content Domains 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 25\u003c\/p\u003e \u003cp\u003e3.2 What is the Blank’s Response Domain Location? 27\u003c\/p\u003e \u003cp\u003e3.3 False Positives and False Negatives 28\u003c\/p\u003e \u003cp\u003e3.4 Net Response Domain 29\u003c\/p\u003e \u003cp\u003e3.5 Blank Subtraction 29\u003c\/p\u003e \u003cp\u003e3.6 Why Bother with Net Responses? 31\u003c\/p\u003e \u003cp\u003e3.7 Content Domain and Two Fallacies 31\u003c\/p\u003e \u003cp\u003e3.8 Can an Absolute Standard Truly Exist? 33\u003c\/p\u003e \u003cp\u003e3.9 Chapter Highlights 34\u003c\/p\u003e \u003cp\u003eReferences 34\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Traditional Limits of Detection 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 37\u003c\/p\u003e \u003cp\u003e4.2 The Decision Level 37\u003c\/p\u003e \u003cp\u003e4.3 False Positives Again 38\u003c\/p\u003e \u003cp\u003e4.4 Do False Negatives Really Matter? 40\u003c\/p\u003e \u003cp\u003e4.5 False Negatives Again 40\u003c\/p\u003e \u003cp\u003e4.6 Decision Level Determination Without a Calibration Curve 41\u003c\/p\u003e \u003cp\u003e4.7 Net Response Domain Again 41\u003c\/p\u003e \u003cp\u003e4.8 An Oversimplified Derivation of the Traditional Detection Limit, \u003ci\u003eX\u003csub\u003eDC\u003c\/sub\u003e \u003c\/i\u003e42\u003c\/p\u003e \u003cp\u003e4.9 Oversimplifications Cause Problems 43\u003c\/p\u003e \u003cp\u003e4.10 Chapter Highlights 43\u003c\/p\u003e \u003cp\u003eReferences 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Modern Limits of Detection 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 45\u003c\/p\u003e \u003cp\u003e5.2 Currie Detection Limits 46\u003c\/p\u003e \u003cp\u003e5.3 Why were p and q Each Arbitrarily Defined as 0.05? 48\u003c\/p\u003e \u003cp\u003e5.4 Detection Limit Determination Without Calibration Curves 49\u003c\/p\u003e \u003cp\u003e5.5 A Nonparametric Detection Limit Bracketing Experiment 49\u003c\/p\u003e \u003cp\u003e5.6 Is There a Parametric Improvement? 51\u003c\/p\u003e \u003cp\u003e5.7 Critical Nexus 52\u003c\/p\u003e \u003cp\u003e5.8 Chapter Highlights 53\u003c\/p\u003e \u003cp\u003eReferences 53\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Receiver Operating Characteristics 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 55\u003c\/p\u003e \u003cp\u003e6.2 ROC Basics 55\u003c\/p\u003e \u003cp\u003e6.3 Constructing ROCs 57\u003c\/p\u003e \u003cp\u003e6.4 ROCs for Figs 5.3 and 5.4 59\u003c\/p\u003e \u003cp\u003e6.5 A Few Experimental ROC Results 60\u003c\/p\u003e \u003cp\u003e6.6 Since ROCs may Work Well, Why Bother with Anything Else? 64\u003c\/p\u003e \u003cp\u003e6.7 Chapter Highlights 65\u003c\/p\u003e \u003cp\u003eReferences 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Statistics of an Ideal Model CMS 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 67\u003c\/p\u003e \u003cp\u003e7.2 The Ideal CMS 67\u003c\/p\u003e \u003cp\u003e7.3 Currie Decision Levels in all Three Domains 70\u003c\/p\u003e \u003cp\u003e7.4 Currie Detection Limits in all Three Domains 71\u003c\/p\u003e \u003cp\u003e7.5 Graphical Illustrations of eqns 7.3–7.8 72\u003c\/p\u003e \u003cp\u003e7.6 An Example: are Negative Content Domain Values Legitimate? 74\u003c\/p\u003e \u003cp\u003e7.7 Tabular Summary of the Equations 76\u003c\/p\u003e \u003cp\u003e7.8 Monte Carlo Computer Simulations 77\u003c\/p\u003e \u003cp\u003e7.9 Simulation Corroboration of the Equations in Table 7.2 78\u003c\/p\u003e \u003cp\u003e7.10 Central Confidence Intervals for Predicted \u003ci\u003ex \u003c\/i\u003eValues 80\u003c\/p\u003e \u003cp\u003e7.11 Chapter Highlights 81\u003c\/p\u003e \u003cp\u003eReferences 81\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 If Only the True Intercept is Unknown 83\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 83\u003c\/p\u003e \u003cp\u003e8.2 Assumptions 83\u003c\/p\u003e \u003cp\u003e8.3 Noise Effect of Estimating the True Intercept 83\u003c\/p\u003e \u003cp\u003e8.4 A Simple Simulation in the Response and NET Response Domains 84\u003c\/p\u003e \u003cp\u003e8.5 Response Domain Effects of Replacing the True Intercept by an Estimate 86\u003c\/p\u003e \u003cp\u003e8.6 Response Domain Currie Decision Level and Detection Limit 88\u003c\/p\u003e \u003cp\u003e8.7 NET Response Domain Currie Decision Level and Detection Limit 88\u003c\/p\u003e \u003cp\u003e8.8 Content Domain Currie Decision Level and Detection Limit 89\u003c\/p\u003e \u003cp\u003e8.9 Graphical Illustrations of the Decision Level and Detection Limit Equations 89\u003c\/p\u003e \u003cp\u003e8.10 Tabular Summary of the Equations 90\u003c\/p\u003e \u003cp\u003e8.11 Simulation Corroboration of the Equations in Table 8.1 91\u003c\/p\u003e \u003cp\u003e8.12 Chapter Highlights 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 If Only the True Slope is Unknown 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 95\u003c\/p\u003e \u003cp\u003e9.2 Possible “Divide by Zero” Hazard 96\u003c\/p\u003e \u003cp\u003e9.3 The t Test for t\u003csub\u003eslope\u003c\/sub\u003e 96\u003c\/p\u003e \u003cp\u003e9.4 Response Domain Currie Decision Level and Detection Limit 97\u003c\/p\u003e \u003cp\u003e9.5 NET Response Domain Currie Decision Level and Detection Limit 97\u003c\/p\u003e \u003cp\u003e9.6 Content Domain Currie Decision Level and Detection Limit 97\u003c\/p\u003e \u003cp\u003e9.7 Graphical Illustrations of the Decision Level and Detection Limit Equations 98\u003c\/p\u003e \u003cp\u003e9.8 Tabular Summary of the Equations 99\u003c\/p\u003e \u003cp\u003e9.9 Simulation Corroboration of the Equations in Table 9.1 99\u003c\/p\u003e \u003cp\u003e9.10 Chapter Highlights 101\u003c\/p\u003e \u003cp\u003eReferences 101\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 If the True Intercept and True Slope are Both Unknown 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 103\u003c\/p\u003e \u003cp\u003e10.2 Important Definitions, Distributions, and Relationships 104\u003c\/p\u003e \u003cp\u003e10.3 The Noncentral t Distribution Briefly Appears 105\u003c\/p\u003e \u003cp\u003e10.4 What Purpose Would be Served by Knowing \u003ci\u003e𝛿\u003c\/i\u003e? 106\u003c\/p\u003e \u003cp\u003e10.5 Is There a Viable Way of Estimating \u003ci\u003e𝛿\u003c\/i\u003e? 106\u003c\/p\u003e \u003cp\u003e10.6 Response Domain Currie Decision Level and Detection Limit 107\u003c\/p\u003e \u003cp\u003e10.7 NET Response Domain Currie Decision Level and Detection Limit 107\u003c\/p\u003e \u003cp\u003e10.8 Content Domain Currie Decision Level and Detection Limit 108\u003c\/p\u003e \u003cp\u003e10.9 Graphical Illustrations of the Decision Level and Detection Limit Equations 108\u003c\/p\u003e \u003cp\u003e10.10 Tabular Summary of the Equations 109\u003c\/p\u003e \u003cp\u003e10.11 Simulation Corroboration of the Equations in Table 10.3 109\u003c\/p\u003e \u003cp\u003e10.12 Chapter Highlights 109\u003c\/p\u003e \u003cp\u003eReferences 111\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 If Only the Population Standard Deviation is Unknown 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 113\u003c\/p\u003e \u003cp\u003e11.2 Assuming \u003ci\u003e𝜎\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e is Unknown, How may it be Estimated? 114\u003c\/p\u003e \u003cp\u003e11.3 What Happens if \u003ci\u003e𝜎\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e is Estimated by s\u003csub\u003e0\u003c\/sub\u003e? 114\u003c\/p\u003e \u003cp\u003e11.4 A Useful Substitution Principle 116\u003c\/p\u003e \u003cp\u003e11.5 Response Domain Currie Decision Level and Detection Limit 116\u003c\/p\u003e \u003cp\u003e11.6 NET Response Domain Currie Decision Level and Detection Limit 117\u003c\/p\u003e \u003cp\u003e11.7 Content Domain Currie Decision Level and Detection Limit 117\u003c\/p\u003e \u003cp\u003e11.8 Major Important Differences From Chapter 7 117\u003c\/p\u003e \u003cp\u003e11.9 Testing for False Positives and False Negatives 120\u003c\/p\u003e \u003cp\u003e11.10 Correction of a Slightly Misleading Figure 121\u003c\/p\u003e \u003cp\u003e11.11 An Informative Screencast 121\u003c\/p\u003e \u003cp\u003e11.12 Central Confidence Intervals for \u003ci\u003e𝜎 \u003c\/i\u003eand s 122\u003c\/p\u003e \u003cp\u003e11.13 Central Confidence Intervals for \u003ci\u003eY\u003csub\u003eC\u003c\/sub\u003e \u003c\/i\u003eand \u003ci\u003eY\u003csub\u003eD\u003c\/sub\u003e \u003c\/i\u003e122\u003c\/p\u003e \u003cp\u003e11.14 Central Confidence Intervals for \u003ci\u003eX\u003csub\u003eC\u003c\/sub\u003e \u003c\/i\u003eand \u003ci\u003eX\u003csub\u003eD\u003c\/sub\u003e \u003c\/i\u003e123\u003c\/p\u003e \u003cp\u003e11.15 Tabular Summary of the Equations 123\u003c\/p\u003e \u003cp\u003e11.16 Simulation Corroboration of the Equations in Table 11.1 123\u003c\/p\u003e \u003cp\u003e11.17 Chapter Highlights 125\u003c\/p\u003e \u003cp\u003eReferences 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 If Only the True Slope is Known 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 127\u003c\/p\u003e \u003cp\u003e12.2 Response Domain Currie Decision Level and Detection Limit 127\u003c\/p\u003e \u003cp\u003e12.3 NET Response Domain Currie Decision Level and Detection Limit 128\u003c\/p\u003e \u003cp\u003e12.4 Content Domain Currie Decision Level and Detection Limit 128\u003c\/p\u003e \u003cp\u003e12.5 Graphical Illustrations of the Decision Level and Detection Limit Equations 128\u003c\/p\u003e \u003cp\u003e12.6 Tabular Summary of the Equations 128\u003c\/p\u003e \u003cp\u003e12.7 Simulation Corroboration of the Equations in Table 12.1 129\u003c\/p\u003e \u003cp\u003e12.8 Chapter Highlights 129\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 If Only the True Intercept is Known 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 131\u003c\/p\u003e \u003cp\u003e13.2 Response Domain Currie Decision Level and Detection Limit 132\u003c\/p\u003e \u003cp\u003e13.3 NET Response Domain Currie Decision Level and Detection Limit 132\u003c\/p\u003e \u003cp\u003e13.4 Content Domain Currie Decision Level and Detection Limit 132\u003c\/p\u003e \u003cp\u003e13.5 Tabular Summary of the Equations 133\u003c\/p\u003e \u003cp\u003e13.6 Simulation Corroboration of the Equations in Table 13.1 133\u003c\/p\u003e \u003cp\u003e13.7 Chapter Highlights 135\u003c\/p\u003e \u003cp\u003eReferences 135\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 If all Three Parameters are Unknown 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 137\u003c\/p\u003e \u003cp\u003e14.2 Response Domain Currie Decision Level and Detection Limit 137\u003c\/p\u003e \u003cp\u003e14.3 NET Response Domain Currie Decision Level and Detection Limit 138\u003c\/p\u003e \u003cp\u003e14.4 Content Domain Currie Decision Level and Detection Limit 138\u003c\/p\u003e \u003cp\u003e14.5 The Noncentral \u003ci\u003et \u003c\/i\u003eDistribution Reappears for Good 138\u003c\/p\u003e \u003cp\u003e14.6 An Informative Computer Simulation 139\u003c\/p\u003e \u003cp\u003e14.7 Confidence Interval for x\u003ci\u003e\u003csub\u003eD\u003c\/sub\u003e\u003c\/i\u003e, with a Major Proviso 142\u003c\/p\u003e \u003cp\u003e14.8 Central Confidence Intervals for Predicted \u003ci\u003ex \u003c\/i\u003eValues 143\u003c\/p\u003e \u003cp\u003e14.9 Tabular Summary of the Equations 143\u003c\/p\u003e \u003cp\u003e14.10 Simulation Corroboration of the Equations in Table 14.1 143\u003c\/p\u003e \u003cp\u003e14.11 An Example: DIN 32645 145\u003c\/p\u003e \u003cp\u003e14.12 Chapter Highlights 146\u003c\/p\u003e \u003cp\u003eReferences 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Bootstrapped Detection Limits in a Real CMS 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 150\u003c\/p\u003e \u003cp\u003e15.2 Theoretical 151\u003c\/p\u003e \u003cp\u003e15.2.1 Background 151\u003c\/p\u003e \u003cp\u003e15.2.2 Blank Subtraction Possibilities 151\u003c\/p\u003e \u003cp\u003e15.2.3 Currie Decision Levels and Detection Limits 152\u003c\/p\u003e \u003cp\u003e15.3 Experimental 153\u003c\/p\u003e \u003cp\u003e15.3.1 Experimental Apparatus 153\u003c\/p\u003e \u003cp\u003e15.3.2 Experiment Protocol 153\u003c\/p\u003e \u003cp\u003e15.3.3 Testing the Noise: Is It AGWN? 156\u003c\/p\u003e \u003cp\u003e15.3.4 Bootstrapping Protocol in the Experiments 157\u003c\/p\u003e \u003cp\u003e15.3.5 Estimation of the Experimental Noncentrality Parameter 160\u003c\/p\u003e \u003cp\u003e15.3.6 Computer Simulation Protocol 160\u003c\/p\u003e \u003cp\u003e15.4 Results and Discussion 161\u003c\/p\u003e \u003cp\u003e15.4.1 Results for Four Standards 161\u003c\/p\u003e \u003cp\u003e15.4.2 Results for 3–12 Standards 162\u003c\/p\u003e \u003cp\u003e15.4.3 Toward Accurate Estimates of X\u003ci\u003e\u003csub\u003eD\u003c\/sub\u003e \u003c\/i\u003e163\u003c\/p\u003e \u003cp\u003e15.4.4 How the X\u003ci\u003e\u003csub\u003eD\u003c\/sub\u003e \u003c\/i\u003eEstimates Were Obtained 164\u003c\/p\u003e \u003cp\u003e15.4.5 Ramifications 165\u003c\/p\u003e \u003cp\u003e15.5 Conclusion 165\u003c\/p\u003e \u003cp\u003eAcknowledgments 166\u003c\/p\u003e \u003cp\u003eReferences 166\u003c\/p\u003e \u003cp\u003e15.6 Postscript 167\u003c\/p\u003e \u003cp\u003e15.7 Chapter Highlights 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Four Relevant Considerations 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 169\u003c\/p\u003e \u003cp\u003e16.2 Theoretical Assumptions 170\u003c\/p\u003e \u003cp\u003e16.3 Best Estimation of \u003ci\u003e𝛿 \u003c\/i\u003e171\u003c\/p\u003e \u003cp\u003e16.4 Possible Reduction in the Number of Expressions? 172\u003c\/p\u003e \u003cp\u003e16.5 Lowering Detection Limits 174\u003c\/p\u003e \u003cp\u003e16.6 Chapter Highlights 178\u003c\/p\u003e \u003cp\u003eReferences 178\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Neyman–Pearson Hypothesis Testing 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 181\u003c\/p\u003e \u003cp\u003e17.2 Simulation Model for Neyman–Pearson Hypothesis Testing 181\u003c\/p\u003e \u003cp\u003e17.3 Hypotheses and Hypothesis Testing 183\u003c\/p\u003e \u003cp\u003e17.3.1 Hypotheses Pertaining to False Positives 183\u003c\/p\u003e \u003cp\u003e17.3.1.1 Hypothesis 1 183\u003c\/p\u003e \u003cp\u003e17.3.1.2 Hypothesis 2 183\u003c\/p\u003e \u003cp\u003e17.3.2 Hypotheses Pertaining to False Negatives 185\u003c\/p\u003e \u003cp\u003e17.3.2.1 Hypothesis 3 185\u003c\/p\u003e \u003cp\u003e17.3.2.2 Hypothesis 4 185\u003c\/p\u003e \u003cp\u003e17.4 The Clayton, Hines, and Elkins Method (1987–2008) 189\u003c\/p\u003e \u003cp\u003e17.5 No Valid Extension for Heteroscedastic Systems 191\u003c\/p\u003e \u003cp\u003e17.6 Hypothesis Testing for the \u003ci\u003e𝛿\u003c\/i\u003ecritical Method 192\u003c\/p\u003e \u003cp\u003e17.6.1 Hypothesis Pertaining to False Positives 192\u003c\/p\u003e \u003cp\u003e17.6.1.1 Hypothesis 5 192\u003c\/p\u003e \u003cp\u003e17.6.2 Hypothesis Pertaining to False Negatives 192\u003c\/p\u003e \u003cp\u003e17.6.2.1 Hypothesis 6 192\u003c\/p\u003e \u003cp\u003e17.7 Monte Carlo Tests of the Hypotheses 192\u003c\/p\u003e \u003cp\u003e17.8 The Other Propagation of Error 193\u003c\/p\u003e \u003cp\u003e17.9 Chapter Highlights 197\u003c\/p\u003e \u003cp\u003eReferences 197\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Heteroscedastic Noises 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 199\u003c\/p\u003e \u003cp\u003e18.2 The Two Simplest Heteroscedastic NPMs 199\u003c\/p\u003e \u003cp\u003e18.2.1 Linear NPM 201\u003c\/p\u003e \u003cp\u003e18.2.2 Experimental Corroboration of the Linear NPM 202\u003c\/p\u003e \u003cp\u003e18.2.3 Hazards with Heteroscedastic NPMs 203\u003c\/p\u003e \u003cp\u003e18.2.4 Example: A CMS with Linear NPM 204\u003c\/p\u003e \u003cp\u003e18.3 Hazards with \u003ci\u003ead hoc \u003c\/i\u003eProcedures 206\u003c\/p\u003e \u003cp\u003e18.4 The HS (“Hockey Stick”) NPM 207\u003c\/p\u003e \u003cp\u003e18.5 Closed-Form Solutions for Four Heteroscedastic NPMs 209\u003c\/p\u003e \u003cp\u003e18.6 Shot Noise (Gaussian Approximation) NPM 210\u003c\/p\u003e \u003cp\u003e18.7 Root Quadratic NPM 211\u003c\/p\u003e \u003cp\u003e18.8 Example: Marlap Example 20.13, Corrected 211\u003c\/p\u003e \u003cp\u003e18.9 Quadratic NPM 211\u003c\/p\u003e \u003cp\u003e18.10 A Few Important Points 212\u003c\/p\u003e \u003cp\u003e18.11 Chapter Highlights 212\u003c\/p\u003e \u003cp\u003eReferences 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Limits of Quantitation 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 215\u003c\/p\u003e \u003cp\u003e19.2 Theory 217\u003c\/p\u003e \u003cp\u003e19.3 Computer Simulation 219\u003c\/p\u003e \u003cp\u003e19.4 Experiment 221\u003c\/p\u003e \u003cp\u003e19.5 Discussion and Conclusion 223\u003c\/p\u003e \u003cp\u003eAcknowledgments 224\u003c\/p\u003e \u003cp\u003eReferences 224\u003c\/p\u003e \u003cp\u003e19.6 Postscript 225\u003c\/p\u003e \u003cp\u003e19.7 Chapter Highlights 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 The Sampled Step Function 227\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 227\u003c\/p\u003e \u003cp\u003e20.2 A Noisy Step Function Temporal Response 229\u003c\/p\u003e \u003cp\u003e20.3 Signal Processing Preliminaries 230\u003c\/p\u003e \u003cp\u003e20.4 Processing the Sampled Step Function Response 231\u003c\/p\u003e \u003cp\u003e20.5 The Standard t-Test for Two Sample Means When the Variance is Constant 232\u003c\/p\u003e \u003cp\u003e20.6 Response Domain Decision Level and Detection Limit 233\u003c\/p\u003e \u003cp\u003e20.7 Hypothesis Testing 233\u003c\/p\u003e \u003cp\u003e20.8 Is There any Advantage to Increasing \u003ci\u003eN\u003c\/i\u003e\u003csub\u003eanalyte\u003c\/sub\u003e? 233\u003c\/p\u003e \u003cp\u003e20.9 NET Response Domain Decision Level and Detection Limit 235\u003c\/p\u003e \u003cp\u003e20.10 NET Response Domain SNRs 235\u003c\/p\u003e \u003cp\u003e20.11 Content Domain Decision Level and Detection Limit 235\u003c\/p\u003e \u003cp\u003e20.12 The RSDB–BEC Method 236\u003c\/p\u003e \u003cp\u003e20.13 Conclusion 237\u003c\/p\u003e \u003cp\u003e20.14 Chapter Highlights 237\u003c\/p\u003e \u003cp\u003eReferences 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 The Sampled Rectangular Pulse 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 239\u003c\/p\u003e \u003cp\u003e21.2 The Sampled Rectangular Pulse Response 239\u003c\/p\u003e \u003cp\u003e21.3 Integrating the Sampled Rectangular Pulse Response 240\u003c\/p\u003e \u003cp\u003e21.4 Relationship Between Digital Integration and Averaging 242\u003c\/p\u003e \u003cp\u003e21.5 What is the Signal in the Sampled Rectangular Pulse? 243\u003c\/p\u003e \u003cp\u003e21.6 What is the Noise in the Sampled Rectangular Pulse? 243\u003c\/p\u003e \u003cp\u003e21.7 The Noise Bandwidth 244\u003c\/p\u003e \u003cp\u003e21.8 The SNR with Matched Filter Detection of the Rectangular Pulse 245\u003c\/p\u003e \u003cp\u003e21.9 The Decision Level and Detection Limit 245\u003c\/p\u003e \u003cp\u003e21.10 A Square Wave at the Detection Limit 246\u003c\/p\u003e \u003cp\u003e21.11 Effect of Sampling Frequency 247\u003c\/p\u003e \u003cp\u003e21.12 Effect of Area Fraction Integrated 247\u003c\/p\u003e \u003cp\u003e21.13 An Alternative Limit of Detection Possibility 248\u003c\/p\u003e \u003cp\u003e21.14 Pulse-to-Pulse Fluctuations 248\u003c\/p\u003e \u003cp\u003e21.15 Conclusion 249\u003c\/p\u003e \u003cp\u003e21.16 Chapter Highlights 250\u003c\/p\u003e \u003cp\u003eReferences 250\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 The Sampled Triangular Pulse 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 251\u003c\/p\u003e \u003cp\u003e22.2 A Simple Triangular Pulse Shape 251\u003c\/p\u003e \u003cp\u003e22.3 Processing the Sampled Triangular Pulse Response 253\u003c\/p\u003e \u003cp\u003e22.4 The Decision Level and Detection Limit 254\u003c\/p\u003e \u003cp\u003e22.5 Detection Limit for a Simulated Chromatographic Peak 254\u003c\/p\u003e \u003cp\u003e22.6 What Should Not be Done? 256\u003c\/p\u003e \u003cp\u003e22.7 A Bad Play, in Three Acts 256\u003c\/p\u003e \u003cp\u003e22.8 Pulse-to-Pulse Fluctuations 258\u003c\/p\u003e \u003cp\u003e22.9 Conclusion 258\u003c\/p\u003e \u003cp\u003e22.10 Chapter Highlights 259\u003c\/p\u003e \u003cp\u003eReferences 259\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 The Sampled Gaussian Pulse 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 261\u003c\/p\u003e \u003cp\u003e23.2 Processing the Sampled Gaussian Pulse Response 262\u003c\/p\u003e \u003cp\u003e23.3 The Decision Level and Detection Limit 263\u003c\/p\u003e \u003cp\u003e23.4 Pulse-to-Pulse Fluctuations 263\u003c\/p\u003e \u003cp\u003e23.5 Conclusion 264\u003c\/p\u003e \u003cp\u003e23.6 Chapter Highlights 264\u003c\/p\u003e \u003cp\u003eReferences 264\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Parting Considerations 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 267\u003c\/p\u003e \u003cp\u003e24.2 The Measurand Dichotomy Distraction 269\u003c\/p\u003e \u003cp\u003e24.3 A “New Definition of LOD” Distraction 273\u003c\/p\u003e \u003cp\u003e24.4 Potentially Important Research Prospects 274\u003c\/p\u003e \u003cp\u003e24.4.1 Extension to Method Detection Limits 274\u003c\/p\u003e \u003cp\u003e24.4.2 Confidence Intervals in the Content Domain 275\u003c\/p\u003e \u003cp\u003e24.4.3 Noises Other Than AGWN 275\u003c\/p\u003e \u003cp\u003e24.5 Summary 276\u003c\/p\u003e \u003cp\u003eReferences 277\u003c\/p\u003e \u003cp\u003eAppendix A Statistical Bare Necessities 279\u003c\/p\u003e \u003cp\u003eAppendix B An Extremely Short Lightstone\u003csup\u003e®\u003c\/sup\u003e Simulation Tutorial 299\u003c\/p\u003e \u003cp\u003eAppendix C Blank Subtraction and the \u003ci\u003e𝜂\u003c\/i\u003e\u003csup\u003e1∕2 \u003c\/sup\u003eFactor 311\u003c\/p\u003e \u003cp\u003eAppendix D Probability Density Functions for Detection Limits 321\u003c\/p\u003e \u003cp\u003eAppendix E The Hubaux and Vos Method 325\u003c\/p\u003e \u003cp\u003eBibliography 331\u003c\/p\u003e \u003cp\u003eGlossary of Organization and Agency Acronyms 335\u003c\/p\u003e \u003cp\u003eIndex 337\u003c\/p\u003e \u003cb\u003eEdward Voigtman\u003c\/b\u003e 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. \u003cp\u003e\u003cb\u003eDetails methods for computing valid limits of detection\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLimits of Detection in Chemical Analysis \u003c\/i\u003edetails 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: \u003c\/p\u003e \u003cul\u003e \u003cli\u003eClear explanations of decision level and detection limit concepts\u003c\/li\u003e \u003cli\u003eProfuse illustrations with many detailed examples and cogent explanations\u003c\/li\u003e \u003cli\u003eExtensive use of corroborating computer simulations that are freely available to readers\u003c\/li\u003e \u003cli\u003eA curated short-list of important references for limits of detection\u003c\/li\u003e \u003cli\u003eVideos, screencasts, and animations are provided at an associated website\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989530689765,"sku":"NP9781119188971","price":167.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119188971.jpg?v=1761784482","url":"https:\/\/k12savings.com\/es\/products\/limits-of-detection-in-chemical-analysis-isbn-9781119188971","provider":"K12savings","version":"1.0","type":"link"}