Statistical Methods for Groundwater Monitoring

In order to assess the effectiveness of groundwater monitoring devices and their end results, statistical techniques must be employed. Thoroughly updated and expanded, the Second Edition examines the multiple problems inherent in the analysis of groundwater monitoring data and illustrates their application and interconnections. Both comprehensive and accessible, the new edition provides environmental scientists, engineers, policy makers, public health officials, waste facility managers, industrial hygienists, statisticians, and analytical chemists with the statistical methods used to analyze the huge volume of data that groundwater monitoring wells produce.

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.

Preface	p. xv
Acknowledgments	p. xxiii
Acronyms	p. xxv
Normal Prediction Intervals	p. 1
Overview	p. 1
Prediction Intervals for the Next Single Measurement from a Normal Distribution	p. 2
Prediction Limits for the Next k Measurements from a Normal Distribution	p. 4
Normal Prediction Limits with Resampling	p. 8
Simultaneous Normal Prediction Limits for the Next k Samples	p. 11
Simultaneous Normal Prediction Limits for the Next r of m Measurements at Each of k Monitoring Wells	p. 15
Normal Prediction Limits for the Mean(s) of m>1 Future Measurements at Each of k Monitoring Wells	p. 27
Summary	p. 32
Nonparametric Prediction Intervals	p. 35
Overview	p. 35
Pass 1 of m Samples	p. 36
Pass m-1 of m Samples	p. 48
Pass First or All m-1 Resamples	p. 51
Nonparametric Prediction Limits for the Median of m Future Measurements at Each of k Locations	p. 64
Summary	p. 65
Prediction Intervals For Other Distributions	p. 67
Overview	p. 67
Lognormal Distribution	p. 68
UPL for a Single Future Observation	p. 68
Prediction Limits for m=1 Future Measurement at Each of k Locations	p. 69
Lognormal Prediction Limits for the Median of m Future Measurements	p. 70
Lognormal Prediction Limits for the Mean of m Future Measurements	p. 71
Poisson Distribution	p. 72
Poisson Prediction Limits	p. 74
Discussion	p. 75
Summary	p. 76
Gamma Prediction Intervals and Some Related Topics	p. 77
Overview	p. 77
Gamma Distribution	p. 77
Prediction Limits for a Single Measurement from a Gamma Distribution	p. 78
Simultaneous Gamma Prediction Limits for the Next r of m Measurements at Each of k Monitoring Wells	p. 80
Comparison of the Gamma Mean to a Regulatory Standard	p. 94
Summary	p. 95
Tolerance Intervals	p. 97
Overview	p. 97
Normal Tolerance Limits	p. 98
Poisson Tolerance Limits	p. 103
Gamma Tolerance Limits	p. 105
Nonparametric Tolerance Limits	p. 109
Summary	p. 109
Method Detection Limits	p. 111
Overview	p. 111
Single Concentration Designs	p. 112
Kaiser-Currie Method	p. 112
USEPA-Glaser et al. Method	p. 118
Calibration Designs	p. 120
Confidence Intervals for Calibration Lines	p. 120
Tolerance Intervals for Calibration Lines	p. 121
Prediction Intervals for Calibration Lines	p. 122
Hubaux and Vos Method	p. 122
The Procedure Due to Clayton and Co-Workers	p. 124
A Procedure Based on Tolerance Intervals	p. 125
MDLs for Calibration Data with Nonconstant Variance	p. 128
Experimental Design of Detection Limit Studies	p. 128
Obtaining the Calibration Data	p. 130
Summary	p. 136
Practical Quantitation Limits	p. 137
Overview	p. 137
Operational Definition	p. 138
A Statistical Estimate of the PQL	p. 138
Derivation of the PQL	p. 140
A Simpler Alternative	p. 142
Uncertainty in Y?*	p. 142
The Effect of the Transformation	p. 143
Selecting N	p. 144
Summary	p. 144
Interlaboratory Calibration	p. 147
Overview	p. 147
General Random-Effects Regression Model for the Case of Heteroscedastic Measurement Errors	p. 148
Rocke and Lorenzato Model	p. 148
Estimation of Model Parameters	p. 149
Iteratively Reweighted Maximum Marginal Likelihood	p. 149
Method of Moments	p. 151
Computing a Point Estimate for an Unknown True Concentration	p. 152
Confidence Region for an Unknown Concentration	p. 153
Applications of the Derived Results	p. 154
Summary	p. 159
Contaminant Source Analysis	p. 161
Overview	p. 161
Statistical Classification Problems	p. 162
Classical Discriminant Function Analysis	p. 162
Parameter Estimation	p. 164
Nonparametric Methods	p. 164
Kernel Methods	p. 165
The k-Nearest-Neighbor Method	p. 166
Summary	p. 189
Intra-Well Comparison	p. 191
Overview	p. 191
Shewhart Control Charts	p. 192
CUSUM Control Charts	p. 193
Combined Shewhart-CUSUM Control Charts	p. 193
Assumptions	p. 193
Procedure	p. 194
Detection of Outliers	p. 195
Existing Trends	p. 196
A Note on Verification Sampling	p. 196
Updating the Control Chart	p. 197
Statistical Power	p. 197
Prediction Limits	p. 200
Pooling Variance Estimates	p. 201
Summary	p. 204
Trend Analysis	p. 205
Overview	p. 205
Sen Test	p. 206
Mann-Kendall Test	p. 208
Seasonal Kendall Test	p. 211
Some Statistical Properties	p. 214
Summary	p. 215
Censored Data	p. 217
Conceptual Foundation	p. 218
Simple Substitution Methods	p. 219
Maximum Likelihood Estimators	p. 220
Restricted Maximum Likelihood Estimators	p. 224
Linear Estimators	p. 225
Alternative Linear Estimators	p. 231
Delta Distributions	p. 234
Regression Methods	p. 236
Substitution of Expected Values of Order Statistics	p. 238
Comparison of Estimators	p. 240
Some Simulation Results	p. 242
Summary	p. 244
Normal Prediction Limits For Left-Censored Data	p. 245
Prediction Limit for Left-Censored Normal Data	p. 246
Construction of the Prediction Limit	p. 246
Simple Imputed Upper Prediction Limit (SIUPL)	p. 247
Improved Upper Prediction Limit (IUPL)	p. 248
Modified Upper Prediction Limit (MUPL)	p. 248
Modified Average Upper Prediction Limit (MAUPL)	p. 248
Simulation Study	p. 249
Summary	p. 253
Tests For Departure From Normality	p. 257
Overview	p. 257
A Simple Graphical Approach	p. 258
Shapiro-Wilk Test	p. 262
Shapiro-Francia Test	p. 264
D'Agostino Test	p. 267
Methods Based on Moments of a Normal Distribution	p. 267
Multiple Independent Samples	p. 272
Testing Normality in Censored Samples	p. 276
Kolmogorov-Smirov Test	p. 277
Summary	p. 277
Variance Component Models	p. 281
Overview	p. 281
Least-Squares Estimators	p. 282
Maximum Likelihood Estimators	p. 285
Summary	p. 288
Detecting Outliers	p. 289
Overview	p. 289
Rosner Test	p. 291
Skewness Test	p. 295
Kurtosis Test	p. 295
Shapiro-Wilk Test	p. 295
Em statistic	p. 296
Dixon Test	p. 296
Summary	p. 301
Surface Water Analysis	p. 303
Overview	p. 303
Statistical Considerations	p. 305
Normal LCL for a Percentile	p. 306
Sampling Frequency	p. 307
Lognormal LCL for a Percentile	p. 308
Nonparametric LCL for a Percentile	p. 309
Statistical Power	p. 309
Summary	p. 314
Assessment And Corrective Action Monitoring	p. 317
Overview	p. 317
Strategy	p. 318
LCL or UCL?	p. 322
Normal Confidence Limits for the Mean	p. 323
Lognormal Confidence Limits for the Median	p. 324
Lognormal Confidence Limits for the Mean	p. 324
The Exact Method	p. 324
Approximating Land's Coefficients	p. 324
Approximate Lognormal Confidence Limit Methods	p. 329
Nonparametric Confidence Limits for the Median	p. 331
Confidence Limits for Other Percentiles of the Distribution	p. 332
Normal Confidence Limits for a Percentile	p. 332
Lognormal Confidence Limits for a Percentile	p. 333
Nonparametric Confidence Limits for a Percentile	p. 334
Summary	p. 335
Regulatory Issues	p. 337
Regulatory Statistics	p. 337
Methods to Be Avoided	p. 338
Analysis of Variance (ANOVA)	p. 338
Risk-Based Compliance Determinations: Comparisons to ACLs and MCLs	p. 339
Cochran's Approximation to the Behrens Fisher t-Test	p. 342
Control of the False Positive Rate by Constituents	p. 344
USEPA's 40 CFR Computation of MDLs and PQLs	p. 344
Verification Resampling	p. 345
Inter-Well versus Intra-Well Comparisons	p. 346
Computer Software	p. 347
More Recent Developments	p. 348
Summary	p. 351
Topic Index	p. 366
Table of Contents provided by Ingram. All Rights Reserved.

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Statistical Methods for Groundwater Monitoring

Summary

Author Biography

Table of Contents

Supplemental Materials