Water Supply and Quality Book from C.H.I.P.S.

Statistical Methods for Groundwater Monitoring
Second Edition
by Robert D. Gibbons

Statistical Methods for Groundwater Monitoring 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.

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
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.

Contents

1. Normal Prediction Intervals

• Prediction Intervals for the Next Single Measurement from a Normal Distribution
• Prediction Limits for the Next k Measurements from a Normal Distribution
• Normal Prediction Limits with Resampling
• Simultaneous Normal Prediction Limits for the Next k Samples
• Simultaneous Normal Prediction Limits for the Next r of m Measurements at Each of k Monitoring Wells
• Normal Prediction Limits for the Mean(s) of m > 1 Future Measurements at Each of k Monitoring Wells
2. Nonparametric Prediction Intervals
• Pass 1 of m Samples
• Pass m - 1 of m Samples
• Pass First or all m - 1 Resamples
• Nonparametric Prediction Limits for the Median of m Future Measurements at each of k Locations
3. Prediction Intervals for Other Distributions
• Lognormal Distribution
• Lognormal Prediction Limits for the Median of m Future Measurements
• Lognormal Prediction Limits for the Mean of m Future Measurements
• Poisson Distribution
4. Gamma Prediction Intervals and Some Related Topics
• Gamma Distribution
• Comparison of Gamma mean to a Regulatory Standard
5. Tolerance Intervals
• Normal Tolerance Limits
• Poisson Tolerance Limits
• Gamma Tolerance Limits
• Nonparametric Tolerance Limits
6. Method Detection Limits
• Single Concentration Designs
• Calibration Designs
7. Practical Quantitation Limits
• Operational Definition
• A Statistical Estimate of the PQL
• Derivation of the PQL
• A Simpler Alternative
• Uncertainty
• The Effect of the Transformation
• Selecting N
8. Interlaboratory Calibration
• General Random Effects Regression Model for the Case of Heteroscedastic Measurement Errors
• Estimation of Model Parameters
• Applications of the Derived Results
9. Contaminant Source Analysis
• Statistical Classification Problems
• Nonparametric Methods
10. Intra-Well Comparison
• Shewart Control Charts
• (CUSUM) Control Charts
• Combined Shewart-CUSUM Control Charts
• Prediction Limits
• Pooling Variance Estimates
11. Trend Analysis
• Sen Test
• Mann-Kendall Test
• Seasonal Kendall Test
• Some Statistical Properties
12. Censored Data
• Conceptual Foundation
• Simple Substitution Methods
• Maximum Likelihood Estimators
• Restricted Maximum Likelihood Estimators
• Linear Estimators
• Alternative Linear Estimators
• Delta Distributions
• Regression Methods
• Substitution of Expected Values of Order Statistics
• Comparison of Estimators
• Some Simulation Results
13. Normal Prediciton Limits for Left-Censored Data
• Prediction Limit for Left-Censored Normal Data
• Simulation Study
14. Tests for Departure from Normality
• A Simple Graphical Approach
• The Shapiro-Wilk Test
• Shapiro-Francia Test
• D'Agostino Test
• Methods Based on Moments of a Normal Distribution
• Multiple Independent Samples
• Testing Normality in Censored Samples
• The Kolmogorov-Smirnov Test
15. Variance Component Models
• Least-Squares Estimators
• Maximum Likelihood Estimators
16. Detecting Outliers
• Rosner Test
• Skewness Test
• Kurtosis Test
• Shapiro-Wilk Test
• Em statistic
• Dixon Test
17. Surface Water Analysis
• Statistical Considerations
• Statistical Power
18. Assessment and Corrective Action Monitoring
• Strategy
• LCL or UCL?
• Normal Confidence Limits for the Mean
• Lognormal Confidence Limits for the Median
• Lognormal Confidence Limits for the Mean
• Nonparametric Confidence Limits for the Median
• Confidence Limits for Other Percentiles of the Distribution
19. Regulatory Issues
• Regulatory Statistics
• Methods to be Avoided
• Verification Resampling
• Interwell versus Intrawell Comparisons
• Computer Software
• More Recent Developments
Index