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E-grāmata: Limits of Detection in Chemical Analysis

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Limits of Detection in Chemical AnalysisPalielināt
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Details methods for computing valid limits of detection.

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