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 2.8 Real CMSs, Part 1 17 2.

9 Random Error 19 2.10 Real CMSs, Part 2 21 2.11 Measurements and PDFs 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 ;;? 106 10.5 Is There a Viable Way of Estimating ;;? 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 ;;0 is Unknown, How may it be Estimated? 114 11.3 What Happens if ;;0 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 ;; 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 15.3 Experimental 153 15.

4 Results and Discussion 161 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 ;; 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 17.4 The Clayton, Hines, and Elkins Method (1987-2008) 189 17.5 No Valid Extension for Heteroscedastic Systems 191 17.6 Hypothesis Testing for the ;;critical Method 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 18.3 Hazards with ad hoc Procedures 206 18.4 The HS ("Hockey Stick") NPM 207 18.5 Closed-Fo.