Statistical Methods for Detection and Quantification of Environmental Contamination

by Gibbons, Robert D.; Coleman, David E.

• ISBN13: 9780471255321
• ISBN10: 0471255327
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-07-13
• Publisher: Wiley-Interscience

Summary

Comprehensive coverage, state-of-the-art methods This groundbreaking volume describes the statistical theory that underlies the detection and quantification of environmental pollution both in the laboratory and in the field. It presents the foundation of relating measured concentrations to true concentrations and the development of intervals of uncertainty for true concentrations, and it presents a comprehensive review of the problem of estimating thresholds at which detection and quantification decisions can be made reliably. The authors demonstrate the use of analytical measurements in making environmental impact decisions and in comparing environmental data to regulatory standards and naturally occurring background concentrations. Taking the next step in a major evolution in the way environmental impact decisions are made, Statistical Methods for Detection and Quantification of Environmental Contamination: Presents statistical methods that allow the earliest possible detection and quantification of contaminants Describes procedures applicable to all environmental constituents Covers numerous state-of-the-art approaches Includes case studies demonstrating practical applications of these approaches An indispensable handbook for scientists and engineers involved in environmental monitoring programs, this book is also an important resource for public health officials, waste facility managers, regulators, statisticians, and analytical chemists. "Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. "Statistical Methods for Detection and Quantification of Environmental Contamination was among those chosen.

Author Biography

ROBERT D. GIBBONS, PhD, is Professor of Biostatistics and Director of the Center for Health Statistics at the University of Illinois at Chicago

Table of Contents

Acknowledgments	xv
Introduction	1	(6)
PART I DETECTION AND QUANTIFICATION IN THE LABORATORY	7	(122)
Conceptual Foundations	9	(12)
Chemical Measurement Process	9	(2)
Calibration and Evaluation Functions	11	(1)
Sensitivity	12	(1)
Accuracy and Precision	12	(2)
Detection and Quantification (Quantitation)	14	(3)
Conceptual Definitions of the Three Limits	14	(2)
Interpretation of the Intervals Defined by the Critical Level, Detection Limit, and Quantitation Limit	16	(1)
Between-Laboratory Environment	17	(4)
Bias and Variation Within a Single Laboratory	17	(1)
Bias and Variation Between Laboratories	18	(1)
Currie's Schematic	18	(3)
Statistical Foundations and Review	21	(13)
Hypothesis Testing	21	(6)
Truth and Certainty of Belief	22	(2)
Statistical Yardstick for Hypothesis Testing	24	(2)
Statistical Significance and Practical Importance	26	(1)
Interval Estimation	27	(7)
Confidence Intervals	27	(3)
Prediction Intervals	30	(2)
Statistical Tolerance Intervals	32	(2)
Calibration-Based Regression Models	34	(14)
Calibration Designs	34	(1)
Ordinary Least-Squares Estimation	34	(1)
Weighted Least-Squares Estimation	35	(1)
Estimating the Weights	36	(3)
Rocke and Lorenzato Model	36	(2)
Exponential Model	38	(1)
Linear Model	39	(1)
Iteratively Reweighted Least-Squares Estimation	39	(1)
OLS Prediction Intervals	40	(1)
OLS Tolerance Intervals	40	(1)
WLS Prediction Intervals	41	(1)
WLS Tolerance Intervals	42	(1)
Illustration	42	(6)
Single-Concentration-Based Detection Limit Methods	48	(9)
Introduction	48	(1)
Kaiser-Currie Method	49	(1)
U.S. EPA 40CFR, Part 136 (GLASER et al.)	50	(2)
Prediction Limits	52	(1)
Tolerance Limits	52	(1)
Simultaneous Control of False Positive and False Negative Rates	53	(1)
Limitations	54	(2)
Illustration	56	(1)
Single-Concentration-Based Quantification Limit Methods	57	(4)
Introduction	57	(1)
Currie's Determination Limit	58	(1)
ACS Limit of Quantitation	58	(1)
EPA Practical Quantification Limit	58	(1)
EPA Minimum Level	59	(1)
Illustration	59	(1)
Discussion	60	(1)
Calibration-Based Detection Limit Methods	61	(18)
Introduction	61	(1)
Models for Constant Variance (Hubaux and Vos)	62	(2)
Procedure Due to Clayton and Co-workers	64	(1)
Generalization to Multiple Future Detection Decisions	65	(1)
Nonconstant Variance	66	(1)
Variance Proportional to Concentration	66	(1)
Modeling Observed Variance	67	(1)
Iteratively Reweighted Least Squares	68	(1)
Illustration	69	(1)
Between-Laboratory Detection Estimate	70	(9)
Interlaboratory Detection Estimate and the ASTM	72	(1)
IDE Approach	73	(6)
Calibration-Based Quantification Limit Methods	79	(11)
Introduction	79	(1)
Alternative Minimum Level	79	(3)
Alternative Formulations	82	(2)
Estimator Due to Gibbons and Co-workers	84	(1)
Interlaboratory Quantitation Estimate	85	(5)
IQE Approach	86	(4)
Significant Digits	90	(14)
Introduction	90	(1)
Measurement Uncertainty Intervals from Calibration	90	(2)
Common Use of Significant Digits	92	(1)
Pair of Problems Due to Having Ten Fingers and Their Solutions	92	(4)
Order-of-Magnitude Uncertainty Range: Fractions of Significant Digits	93	(1)
Order-of-Magnitude Relative Uncertainty: Bounding Relationship	94	(2)
Definition of Detection: At Least Zero Significant Digits	96	(2)
Definition of Quantitation: At Least One Significant Digit	98	(3)
Use of QL1D	99	(1)
Development of QL1D	99	(1)
Graphical Example of Computing QL1D	100	(1)
Reporting Measurement and Uncertainty	101	(3)
Adorning a Measurement with Uncertainty	101	(1)
Measurement, Standard Deviation, Radical, and Degrees of Freedom: MRDS Format	102	(2)
Experimental Design of Detection and Quantification Limit Studies and Related Studies	104	(13)
Introduction	104	(1)
Basic Considerations and Recommendations	105	(3)
Variance Components	108	(3)
Youden Pairs	111	(2)
Matrix Effects and Blanks	113	(3)
Matrix Effects	113	(2)
Blanks	115	(1)
Blind Studies	116	(1)
Between-Laboratory Detection and Quantification Limit Estimators	117	(12)
Introduction	117	(1)
Naive Estimators	118	(1)
Approximate Estimator	118	(1)
More Sophisticated Approach	118	(4)
Random-Effects Model for Homogeneous Errors	119	(1)
Random-Effects Model for Heterogenous Errors	120	(2)
Applications	122	(1)
Illustration	123	(6)
PART II DETECTION AND QUANTIFICATION IN THE FIELD	129	(154)
Comparison of a Single Measurement to a Regulatory Standard	131	(5)
Introduction	131	(1)
Determining Regulatory Compliance	132	(2)
Case I: STD = 0	132	(1)
Case II: 0 < STD < LQ	132	(1)
Case IIa: 0 < STD ≤ LC	133	(1)
Case IIb: 0 < LC < STD < LQ	133	(1)
Case III: LQ ≤ STD	133	(1)
Confidence Interval for True Concentration	134	(1)
Illustration	134	(2)
Censored Data	136	(28)
Introduction	136	(1)
Conceptual Foundation	137	(2)
Simple Substitution Methods	139	(1)
Maximum Likelihood Estimators	139	(4)
Restricted Maximum Likelihood Estimators	143	(1)
Linear Estimators	144	(1)
Alternative Linear Estimators	145	(8)
Delta Distributions	153	(2)
Regression Methods	155	(2)
Substitution of Expected Values of Order Statistics	157	(1)
Comparison of Estimators	158	(3)
Further Simulation Results	161	(1)
Summary	162	(2)
Testing Distributional Assumptions	164	(19)
Introduction	164	(1)
Simple Graphical Approach	165	(1)
Shapiro-Wilk Test	166	(5)
Shapiro-Francia Test	171	(1)
D'Agostino's Test	171	(2)
Methods Based on Moments of a Normal Distribution	173	(2)
Multiple Independent Samples	175	(2)
Testing Normality in Censored Samples	177	(4)
Kolmogorov-Smirnov Test	181	(1)
Summary	182	(1)
Testing for Outliers	183	(11)
Introduction	183	(1)
Rosner's Test	184	(3)
Skewness Test	187	(1)
Kurtosis Test	188	(1)
Shapiro-Wilk Test	188	(1)
Em-statistic	188	(2)
Dixon's Test	190	(1)
Illustration	191	(2)
Summary	193	(1)
Detecting Trend	194	(10)
Introduction	194	(1)
Sen's Test	195	(2)
Mann-Kendall Test	197	(3)
Seasonal Kendall Test	200	(3)
Statistical Properties	203	(1)
Summary	203	(1)
Detection Monitoring	204	(14)
Introduction	204	(1)
Groundwater Detection Monitoring	204	(2)
Statistical Prediction Intervals	206	(5)
Single Location and Constituent	206	(1)
Multiple Locations	207	(1)
Verification Resampling	208	(1)
Multiple Constituents	209	(1)
Problem of Nondetects	209	(1)
Nonparametric Prediction Limits	210	(1)
Intrawell Comparisons	211	(1)
Illustration	212	(1)
Methods to be Avoided	213	(4)
Analysis of Variance	213	(2)
Cochran's Approximation to the Behrens-Fisher t-Test	215	(2)
Summary	217	(1)
Assessment and Corrective Action Monitoring: Overview	218	(11)
Introduction	218	(1)
Strategy	219	(4)
Application to Specific Media	223	(5)
Soils: Evaluation of Individual Source Areas (PAOCs)	223	(1)
Soils: Area- or Site-wide Evaluations	224	(1)
Groundwater: Aquifer	224	(2)
Groundwater: Groundwater-Surface Water Interface	226	(1)
Groundwater: Long-Term Monitoring	226	(1)
Groundwater: Natural Attenuation Evaluation	227	(1)
Waste Stream Sampling	228	(1)
Summary	228	(1)
Assessment and Corrective Action Monitoring: Comparison to a Standard	229	(23)
Introduction	229	(1)
LCL or UCL?	230	(1)
Normal Confidence Limits for the Mean	231	(1)
Lognormal Confidence Limits for the Median	232	(1)
Lognormal Confidence Limits for the Mean	232	(10)
Exact Method	232	(1)
Approximating Land's Coefficients	233	(5)
Approximate Lognormal Confidence Limit Methods	238	(4)
Nonparametric Confidence Limits for the Median	242	(1)
Confidence Limits for Other Percentiles of the Distribution	243	(9)
Normal Confidence Limits for a Percentile	243	(1)
Lognormal Confidence Limits for a Percentile	244	(1)
Nonparametric Confidence Limits for a Percentile	244	(8)
Assessment and Corrective Action Monitoring: Comparison to Background	252	(21)
Introduction	252	(1)
Normal Prediction Limits for m = 1 Future Measurements at Each of k Locations	253	(5)
Normal Prediction Limits for the Mean(s) of m > 1 Future Measurements at Each of k Locations	258	(4)
Lognormal Prediction Limits for m = 1 Future Measurements at Each of k Locations	262	(2)
Lognormal Prediction Limits for the Median of m > 1 Future Measurements at Each of k Locations	264	(1)
Lognormal Prediction Limits for the Mean of m > 1 Future Measurements at Each of k Locations	265	(2)
Nonparametric Prediction Limits for m = 1 Future Measurements in Each of k Locations	267	(1)
Nonparametric Prediction Limits for the Median of m > 1 Future Measurements at Each of k Locations	267	(6)
Assessment and Corrective Action Monitoring: Case Studies	273	(7)
Long-Term Monitoring	273	(1)
Soil PAOC and Soil Phase III Evaluation	274	(3)
PAOC 2	274	(2)
PAOC 18	276	(1)
Results	276	(1)
Site-wide Groundwater Evaluation	277	(3)
Review of Available Computer Software	280	(1)
Summary	281	(2)
Appendix: Land's Tables	283	(40)
Glossary of Measurement Terminology	323	(16)
Mathematical Symbols	339	(2)
Web References	341	(2)
Annotated Bibliography	343	(38)
Index	381