Preface.

Acknowledgments.

Acronyms.

**1 NORMAL PREDICTION INTERVALS.**

1.1 Overview.

1.2 Prediction Intervals for the Next Single Measurement from a Normal Distribution.

1.3 Prediction Limits for the Next *k* Measurements from a Normal Distribution.

1.4 Normal Prediction Limits with Resampling.

1.5 Simultaneous Normal Prediction Limits for the Next *k* Samples.

1.6 Simultaneous Normal Prediction Limits for the Next *r* of *m* Measurements at Each of k Monitoring Wells.

1.7 Normal Prediction Limits for the Mean(s) of *m* > 1 Future Measurements at Each of *k* Monitoring Wells.

1.8 Summary.

**2 NONPARAMETRIC PREDICTION INTERVALS.**

2.1 Overview.

2.2 Pass 1 of *m* Samples.

2.3 Pass *m* - 1 of *m* Samples.

2.4 Pass First or all *m* - 1 Resamples.

2.5 Nonparametric Prediction Limits for the Median of *m* Future Measurements at each of *k* Locations.

2.6 Summary.

**3 PREDICTION INTERVALS FOR OTHER DISTRIBUTIONS.**

3.1 Overview.

3.2 Lognormal Distribution.

3.3 Lognormal Prediction Limits for the Median of m Future Measurements.

3.4 Lognormal Prediction Limits for the Mean of *m* Future Measurements.

3.5 Poisson Distribution.

3.6 Summary.

**4 GAMMA PREDICTION INTERVALS AND SOME RELATED TOPICS.**

4.1 Overview.

4.2 Gamma Distribution.

4.3 Comparison of Gamma mean to a Regulatory Standard.

4.4 Summary.

**5 TOLERANCE INTERVALS.**

5.1 Overview.

5.2 Normal Tolerance Limits.

5.3 Poisson Tolerance Limits.

5.4 Gamma Tolerance Limits.

5.5 Nonparametric Tolerance Limits.

5.6 Summary.

**6 METHOD DETECTION LIMITS.**

6.1 Overview.

6.2 Single Concentration Designs.

6.3 Calibration Designs.

6.4 Summary.

**7 PRACTICAL QUANTITATION LIMITS.**

7.1 Overview.

7.2 Operational Definition.

7.3 A Statistical Estimate of the PQL.

7.4 Derivation of the PQL.

7.5 A Simpler Alternative.

7.6 Uncertainty in Y_{α}^{*}.

7.7 The Effect of the Transformation.

7.8 Selecting *N*.

7.9 Summary.

**8 INTERLABORATORY CALIBRATION.**

8.1 Overview.

8.2 General Random Effects Regression Model for the Case of Heteroscedastic Measurement Errors.

8.3 Estimation of Model Parameters.

8.4 Applications of the Derived Results.

8.5 Summary.

**9 CONTAMINANT SOURCE ANALYSIS.**

9.1 Overview.

9.2 Statistical Classification Problems.

9.3 Nonparametric Methods.

9.4 Summary.

**10 INTRA-WELL COMPARISON.**

10.1 Overview.

10.2 Shewart Control Charts.

10.3 (CUSUM) Control Charts.

10.4 Combined Shewart-CUSUM Control Charts.

10.5 Prediction Limits.

10.6 Pooling Variance Estimates.

10.7 Summary.

**11 TREND ANALYSIS.**

11.1 Overview.

11.2 Sen Test.

11.3 Mann-Kendall Test.

11.4 Seasonal Kendall Test.

11.5 Some Statistical Properties.

11.6 Summary.

**12 CENSORED DATA.**

12.1 Conceptual Foundation.

12.2 Simple Substitution Methods.

12.3 Maximum Likelihood Estimators.

12.4 Restricted Maximum Likelihood Estimators.

12.5 Linear Estimators.

12.6 Alternative Linear Estimators.

12.7 Delta Distributions.

12.8 Regression Methods.

12.9 Substitution of Expected Values of Order Statistics.

12.10 Comparison of Estimators.

12.11 Some Simulation Results.

12.12 Summary.

**13 NORMAL PREDICTION LIMITS FOR LEFT-CENSORED DATA.**

13.1 Prediction Limit for Left-Censored Normal Data.

13.2 Simulation Study.

13.3 Summary.

**14 TESTS FOR DEPARTURE FROM NORMALITY.**

14.1 Overview.

14.2 A Simple Graphical Approach.

14.3 The Shapiro-Wilk Test.

14.4 Shapiro-Francia Test.

14.5 D'Agostino Test.

14.6 Methods Based on Moments of a Normal Distribution.

14.7 Multiple Independent Samples.

14.8 Testing Normality in Censored Samples.

14.9 The Kolmogorov-Smirnov Test.

14.10 Summary.

**15 VARIANCE COMPONENT MODELS.**

15.1 Overview.

15.2 Least-Squares Estimators.

15.3 Maximum Likelihood Estimators.

15.4 Summary.

**16 DETECTING OUTLIERS.**

16.1 Overview.

16.2 Rosner Test.

16.3 Skewness Test.

16.4 Kurtosis Test.

16.5 Shapiro-Wilk Test.

16.6 *E*_{m} statistic.

16.7 Dixon Test.

16.8 Summary.

**17 SURFACE WATER ANALYSIS.**

17.1 Overview.

17.2 Statistical Considerations.

17.3 Statistical Power.

17.4 Summary.

**18 ASSESSMENT AND CORRECTIVE ACTION MONITORING.**

18.1 Overview.

18.2 Strategy.

18.3 LCL or UCL?

18.4 Normal Confidence Limits for the Mean.

18.5 Lognormal Confidence Limits for the Median.

18.6 Lognormal Confidence Limits for the Mean.

18.7 Nonparametric Confidence Limits for the Median.

18.8 Confidence Limits for Other Percentiles of the Distribution.

18.9 Summary.

**19 REGULATORY ISSUES.**

19.1 Regulatory Statistics.

19.2 Methods to be Avoided.

19.3 Verification Resampling.

19.4 Interwell versus Intrawell Comparisons.

19.5 Computer Software.

19.6 More Recent Developments.

**20 SUMMARY.**

Topic Index.