Statistical methods for groundwater monitoring

Thoroughly updated to provide current research findings, Statistical Methods for Groundwater Monitoring, Second Edition continues to provide a comprehensive overview and accessible treatment of the statistical methods that are useful in the analysis of environmental data. This new edition expands focus on statistical comparison to regulatory standards that are a vital part of assessment, compliance, and corrective action monitoring in the environmental sciences.

The book explores quantitative concepts useful for surface water monitoring as well as soil and air monitoring applications while also maintaining a focus on the analysis of groundwater monitoring data in order to detect environmental impacts from a variety of sources, such as industrial activity and waste disposal. The authors introduce the statistical properties of alternative approaches, such as false positive and false negative rates, that are associated with each test and the factors related to these error rates. The Second Edition also features:

An introduction to Intra-laboratory Calibration Curves and random-effects regression models for non-constant measurement variability Coverage of statistical prediction limits for a gamma-distributed random variable, with a focus on estimation and testing of parameters in environmental monitoring applications A unified treatment of censored data with the computation of statistical prediction, tolerance, and control limits Expanded coverage of statistical issues related to laboratory practice, such as detection and quantitation limits An updated chapter on regulatory issues that outlines common mistakes to avoid in groundwater monitoring applications as well as an introduction to the newest regulations for both hazardous and municipal solid waste facilities

Each chapter provides a general overview of a problem, followed by statistical derivation of the solution and a relevant example complete with computational details that allow readers to perform routine application of the statistical results. Relevant issues are highlighted throughout, and recommendations are also provided for specific problems based on characteristics such as number of monitoring wells, number of constituents, distributional form of measurements, and detection frequency.

Statistical Methods for Groundwater Monitoring, Second Edition is an excellent supplement to courses on environmental statistics at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the fields of biostatistics, engineering, and the environmental sciences who work with statistical methods in their everyday work.

Author Notes

Robert D. Gibbons, PhD , is Director of the Center for Health Statistics and Professor of Biostatistics and Psychiatry at the University of Illinois at Chicago. A Fellow of the American Statistical Association and member of the Institute of Medicine of the National Academy of Sciences, Dr. Gibbons has written more than 200 journal articles in the areas of statistics and psychometrics. He is the coauthor of Longitudinal Data Analysis and Statistical Methods for Detection and Quantification of Environmental Contamination , both published by Wiley.

DULAL K. BHAUMIK, PhD , is Professor of Biostatistics, Psychiatry, and Bioengineering at the University of Illinois at Chicago. A Fellow of the American Statistical Association, Dr. Bhaumik has published more than fifty journal articles in his areas of research interest, which include environmental statistics, statistical problems in psychiatry, biostatistics, design of experiments, and statistical inference.

SUBHASH ARYAL, PhD , is Assistant Professor of Biostatistics at the University of North Texas Health Science Center at Fort Worth. He has coauthored numerous published articles on statistics in the environmental sciences.

Reviews 1

Choice Review

Over the past 20 years, the environmental aspect of groundwater has become a primary concern in the US and throughout the world. Both quantitative and qualitative groundwater monitoring are of paramount importance in the field of civil and environmental engineering. A special branch of statistics may be necessary in modeling groundwater behavior that involves many heterogeneous and nondeterministic properties. Based on his extensive experience, Gibbons has compiled a valuable collection of statistical techniques in this area. He covers many topics, including statistical predication intervals, tolerance limits, censored data, and variance component models. There is also a short chapter, "Applications to Regulatory Issues," that implements statistical rules as they apply towards US EPA subtitle C and D regulations. Gibbons hopes that "statistically rigorous detection monitoring programs will become the rule, not the exception." This would, of course, require further efforts by groundwater engineers/scientists as well as statisticians. Some advanced topics such as time series or Markov chains related to more complex issues in stochastic modeling are not addressed here. Rather than a traditional preface, there is an introduction with a summary. Overall, the book is well written and well organized, a useful and unique book on groundwater monitoring. Advance undergraduate through professional. P. C. Chan; New Jersey Institute of Technology

Preface	p. xv
Acknowledgments	p. xxiii
Acronyms	p. xxv
1 Normal Prediction Intervals	p. 1
1.1 Overview	p. 1
1.2 Prediction Intervals for the Next Single Measurement from a Normal Distribution	p. 2
1.3 Prediction Limits for the Next k Measurements from a Normal Distribution	p. 4
1.4 Normal Prediction Limits with Resampling	p. 8
1.5 Simultaneous Normal Prediction Limits for the Next k Samples	p. 11
1.6 Simultaneous Normal Prediction Limits for the Next r of m Measurements at Each of k Monitoring Wells	p. 15
1.7 Normal Prediction Limits for the Mean(s) of m> 1 Future Measurements at Each of k Monitoring Wells	p. 27
1.8 Summary	p. 32
2 Nonparametric Prediction Intervals	p. 35
2.1 Overview	p. 35
2.2 Pass 1 of m Samples	p. 36
2.3 Pass m-1 of m Samples	p. 48
2.4 Pass First or All m-1 Resamples	p. 51
2.5 Nonparametric Prediction Limits for the Median of m Future Measurements at Each of k Locations	p. 64
2.6 Summary	p. 65
3 Prediction Intervals For Other Distributions	p. 67
3.1 Overview	p. 67
3.2 Lognormal Distribution	p. 68
3.2.1 UPL for a Single Future Observation	p. 68
3.2.2 Prediction Limits for m=1 Future Measurement at Each of k Locations	p. 69
3.3 Lognormal Prediction Limits for the Median of m Future Measurements	p. 70
3.4 Lognormal Prediction Limits for the Mean of m Future Measurements	p. 71
3.5 Poisson Distribution	p. 72
3.5.1 Poisson Prediction Limits	p. 74
3.5.2 Discussion	p. 75
3.6 Summary	p. 76
4 Gamma Prediction Intervals and Some Related Topics	p. 77
4.1 Overview	p. 77
4.2 Gamma Distribution	p. 77
4.2.1 Prediction Limits for a Single Measurement from a Gamma Distribution	p. 78
4.2.2 Simultaneous Gamma Prediction Limits for the Next r of m Measurements at Each of k Monitoring Wells	p. 80
4.3 Comparison of the Gamma Mean to a Regulatory Standard	p. 94
4.4 Summary	p. 95
5 Tolerance Intervals	p. 97
5.1 Overview	p. 97
5.2 Normal Tolerance Limits	p. 98
5.3 Poisson Tolerance Limits	p. 103
5.4 Gamma Tolerance Limits	p. 105
5.5 Nonparametric Tolerance Limits	p. 109
5.6 Summary	p. 109
6 Method Detection Limits	p. 111
6.1 Overview	p. 111
6.2 Single Concentration Designs	p. 112
6.2.1 Kaiser-Currie Method	p. 112
6.2.2 USEPA-Glaser et al. Method	p. 118
6.3 Calibration Designs	p. 120
6.3.1 Confidence Intervals for Calibration Lines	p. 120
6.3.2 Tolerance Intervals for Calibration Lines	p. 121
6.3.3 Prediction Intervals for Calibration Lines	p. 122
6.3.4 Hubaux and Vos Method	p. 122
6.3.5 The Procedure Due to Clayton and Co-Workers	p. 124
6.3.6 A Procedure Based on Tolerance Intervals	p. 125
6.3.7 MDLs for Calibration Data with Nonconstant Variance	p. 128
6.3.8 Experimental Design of Detection Limit Studies	p. 128
6.3.9 Obtaining the Calibration Data	p. 130
6.4 Summary	p. 136
7 Practical Quantitation Limits	p. 137
7.1 Overview	p. 137
7.2 Operational Definition	p. 138
7.3 A Statistical Estimate of the PQL	p. 138
7.4 Derivation of the PQL	p. 140
7.5 A Simpler Alternative	p. 142
7.6 Uncertainty in Y?*	p. 142
7.7 The Effect of the Transformation	p. 143
7.8 Selecting N	p. 144
7.9 Summary	p. 144
8 Interlaboratory Calibration	p. 147
8.1 Overview	p. 147
8.2 General Random-Effects Regression Model for the Case of Heteroscedastic Measurement Errors	p. 148
8.2.1 Rocke and Lorenzato Model	p. 148
8.3 Estimation of Model Parameters	p. 149
8.3.1 Iteratively Reweighted Maximum Marginal Likelihood	p. 149
8.3.2 Method of Moments	p. 151
8.3.3 Computing a Point Estimate for an Unknown True Concentration	p. 152
8.3.4 Confidence Region for an Unknown Concentration	p. 153
8.4 Applications of the Derived Results	p. 154
8.5 Summary	p. 159
9 Contaminant Source Analysis	p. 161
9.1 Overview	p. 161
9.2 Statistical Classification Problems	p. 162
9.2.1 Classical Discriminant Function Analysis	p. 162
9.2.2 Parameter Estimation	p. 164
9.3 Nonparametric Methods	p. 164
9.3.1 Kernel Methods	p. 165
9.3.2 The k-Nearest-Neighbor Method	p. 166
9.4 Summary	p. 189
10 Intra-Well Comparison	p. 191
10.1 Overview	p. 191
10.2 Shewhart Control Charts	p. 192
10.3 CUSUM Control Charts	p. 193
10.4 Combined Shewhart-CUSUM Control Charts	p. 193
10.4.1 Assumptions	p. 193
10.4.2 Procedure	p. 194
10.4.3 Detection of Outliers	p. 195
10.4.4 Existing Trends	p. 196
10.4.5 A Note on Verification Sampling	p. 196
10.4.6 Updating the Control Chart	p. 197
10.4.7 Statistical Power	p. 197
10.5 Prediction Limits	p. 200
10.6 Pooling Variance Estimates	p. 201
10.7 Summary	p. 204
11 Trend Analysis	p. 205
11.1 Overview	p. 205
11.2 Sen Test	p. 206
11.3 Mann-Kendall Test	p. 208
11.4 Seasonal Kendall Test	p. 211
11.5 Some Statistical Properties	p. 214
11.6 Summary	p. 215
12 Censored Data	p. 217
12.1 Conceptual Foundation	p. 218
12.2 Simple Substitution Methods	p. 219
12.3 Maximum Likelihood Estimators	p. 220
12.4 Restricted Maximum Likelihood Estimators	p. 224
2.5 Linear Estimators	p. 225
12.6 Alternative Linear Estimators	p. 231
12.7 Delta Distributions	p. 234
12.8 Regression Methods	p. 236
12.9 Substitution of Expected Values of Order Statistics	p. 238
12.10 Comparison of Estimators	p. 240
12.11 Some Simulation Results	p. 242
12.12 Summary	p. 244
13 Normal Prediction Limits For Left-Censored Data	p. 245
13.1 Prediction Limit for Left-Censored Normal Data	p. 246
13.1.1 Construction of the Prediction Limit	p. 246
13.1.2 Simple Imputed Upper Prediction Limit (SIUPL)	p. 247
13.1.3 Improved Upper Prediction Limit (IUPL)	p. 248
13.1.4 Modified Upper Prediction Limit (MUPL)	p. 248
13.1.5 Modified Average Upper Prediction Limit (MAUPL)	p. 248
13.2 Simulation Study	p. 249
13.3 Summary	p. 253
14 Tests For Departure From Normality	p. 257
14.1 Overview	p. 257
14.2 A Simple Graphical Approach	p. 258
14.3 Shapiro-Wilk Test	p. 262
14.4 Shapiro-Francia Test	p. 264
14.5 D'Agostino Test	p. 267
14.6 Methods Based on Moments of a Normal Distribution	p. 267
14.7 Multiple Independent Samples	p. 272
14.8 Testing Normality in Censored Samples	p. 276
14.9 Kolmogorov-Smirov Test	p. 277
14.10 Summary	p. 277
15 Variance Component Models	p. 281
15.1 Overview	p. 281
15.2 Least-Squares Estimators	p. 282
15.3 Maximum Likelihood Estimators	p. 285
15.4 Summary	p. 288
16 Detecting Outliers	p. 289
16.1 Overview	p. 289
16.2 Rosner Test	p. 291
16.3 Skewness Test	p. 295
16.4 Kurtosis Test	p. 295
16.5 Shapiro-Wilk Test	p. 295
16.6 Em statistic	p. 296
16.7 Dixon Test	p. 296
16.8 Summary	p. 301
17 Surface Water Analysis	p. 303
17.1 Overview	p. 303
17.2 Statistical Considerations	p. 305
17.2.1 Normal LCL for a Percentile	p. 306
17.2.2 Sampling Frequency	p. 307
17.2.3 Lognormal LCL for a Percentile	p. 308
17.2.4 Nonparametric LCL for a Percentile	p. 309
17.3 Statistical Power	p. 309
17.4 Summary	p. 314
18 Assessment And Corrective Action Monitoring	p. 317
18.1 Overview	p. 317
18.2 Strategy	p. 318
18.3 LCL or UCL?	p. 322
18.4 Normal Confidence Limits for the Mean	p. 323
18.5 Lognormal Confidence Limits for the Median	p. 324
18.6 Lognormal Confidence Limits for the Mean	p. 324
18.6.1 The Exact Method	p. 324
18.6.2 Approximating Land's Coefficients	p. 324
18.6.3 Approximate Lognormal Confidence Limit Methods	p. 329
18.7 Nonparametric Confidence Limits for the Median	p. 331
18.8 Confidence Limits for Other Percentiles of the Distribution	p. 332
18.8.1 Normal Confidence Limits for a Percentile	p. 332
18.8.2 Lognormal Confidence Limits for a Percentile	p. 333
18.8.3 Nonparametric Confidence Limits for a Percentile	p. 334
18.9 Summary	p. 335
19 Regulatory Issues	p. 337
19.1 Regulatory Statistics	p. 337
19.2 Methods to Be Avoided	p. 338
19.2.1 Analysis of Variance (ANOVA)	p. 338
19.2.2 Risk-Based Compliance Determinations: Comparisons to ACLs and MCLs	p. 339
19.2.3 Cochran's Approximation to the Behrens Fisher t-Test	p. 342
19.2.4 Control of the False Positive Rate by Constituents	p. 344
19.2.5 USEPA's 40 CFR Computation of MDLs and PQLs	p. 344
19.3 Verification Resampling	p. 345
19.4 Inter-Well versus Intra-Well Comparisons	p. 346
19.5 Computer Software	p. 347
19.6 More Recent Developments	p. 348
20 Summary	p. 351
Topic Index	p. 366

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