Statistical Applications for Environmental Analysis and Risk Assessment guides readers through real-world situations and the best statistical methods used to determine the nature and extent of the problem, evaluate the potential human health and ecological risks, and design and implement remedial systems as necessary. Featuring numerous worked examples using actual data and “ready-made” software scripts, Statistical Applications for Environmental Analysis and Risk Assessment also includes:

• Descriptions of basic statistical concepts and principles in an informal style that does not presume prior familiarity with the subject

• Detailed illustrations of statistical applications in the environmental and related water resources fields using real-world data in the contexts that would typically be encountered by practitioners

• Software scripts using the high-powered statistical software system, R, and supplemented by USEPA’s ProUCL and USDOE’s VSP software packages, which are all freely available

• Coverage of frequent data sample issues such as non-detects, outliers, skewness, sustained and cyclical trend that habitually plague environmental data samples

• Clear demonstrations of the crucial, but often overlooked, role of statistics in environmental sampling design and subsequent exposure risk assessment.

Preface

Acknowledgements

1. Introduction

1.1 Introduction and Overview

1.2 The Aim of the Book: Get in the Game!

1.3 The Approach and Style: Impossible to Misunderstand!

PART I BASIC STATISTICAL MEASURES AND CONCEPTS

2. Introduction to Software Packages used in this Book

2.1 R

2.2 ProUCL

2.3 Visual Sample Plan

2.4 DataPlot

2.5 Kendal-Thiel Robust Line

2.6 Minitab^®

2.7 Excel 2010

3. Laboratory Detection Limits, Non-Detects and Data Analysis

3.1 Introduction and Overview

3.2 Types of Laboratory Data Detection Limits

3.3 Problems with Non-Detects (NDs) in Statistical Data Samples

3.4 Options for Addressing Non-Detects in Data Analysis

4. Data Sample, Data Population and Data Distribution

4.1 Introduction and Overview

4.2 Data Sample versus Data Population or Universe

4.3 The Concept of a Distribution

4.4 Types of Distributions

EXERCISES

5. Graphics for Data Analysis and Presentation

5.1 Introduction and Overview

5.2 Graphics for Single Univariate Data Samples

5.3 Graphics for Two or more Univariate Data Samples

5.4 Graphics for Bivariate and Multivariate Data Samples

5.5 Graphics for Data Presentation

5.6 Data Smoothing

EXERCISES

6. Basic Statistical Measures: Descriptive or Summary Statistics

6.1 Introduction and Overview

6.2 Arithmetic Mean and Weighted Mean

6.3 Median and other Robust Measures of Central Tendency

6.4 Standard Deviation, Variance, and other Measures of Dispersion or Spread

6.5 Skewness and other Measures of Shape

6.6 Outliers

6.6.1 Tests for Outliers

6.7 Data Transformations

EXERCISES

PART II STATISTICAL PROCEDURES FOR UNIVARIATE DATA

7. Statistical Intervals: Confidence, Tolerance and Prediction Intervals

7.1 Introduction and Overview

7.2 Confidence Intervals

7.3 Tolerance Intervals

7.4 Prediction Intervals

7.5 Control Charts

EXERCISES

8. Tests of Hypothesis and Decision Making

8.1 Introduction and Overview

8.2 Basic Terminology and Procedures for Tests of Hypothesis

8.3 Type I and Type II Decision Errors, Statistical Power, and Inter-relationships

8.4 The Problem with Multiple Tests or Comparisons: Site-wide False Positive Error Rates (SWFPR)

8.5 Tests for Equality of Variance

EXERCISES

9. Applications of Hypothesis Tests: Comparing Populations, Analysis of Variance

9.1 Introduction and Overview

9.2 Single Sample Tests

9.3 Two-Sample Tests

9.4 Comparing Three or More Populations: Parametric ANOVA and Non-Parametric Kruskal-Wallis Tests

EXERCISES

10. Trends, Autocorrelation and Temporal Dependence

10.1 Introduction and Overview

10.2 Tests for Autocorrelation and Temporal Effects

10.3 Tests for Trend

10.4 Correcting Seasonality and Temporal Effects in the Data

10.5 Effects of Exogenous Variables on Trend Tests

EXERCISES

PART III BIVARIATE AND MULTIVARIATE DATA ANALYSES

11. Correlation, Covariance, Geostatistics

11.1 Introduction and Overview

11.2 Correlation and Covariance

11.3 Introduction to Geostatistics

EXERCISES

12. Simple Linear Regression

12.1 Introduction and Overview

12.2 The Simple Linear Regression Model

12.3 Basic Applications of Simple Linear Regression

12.4 Verify Compliance with the Assumptions of Conventional Linear Regression

12.5 Check the Regression Diagnostics for the Presence of Influential Data Points

12. 6 Confidence Intervals for the Predicted Y Values

12.7 Regression for Left-Censored Data (Non Detects)

EXERCISES

13. Data Transformation versus Generalized Linear Model

13.1 Introduction and Overview

13.2 Data Transformation

13.3 The Generalized Linear Model (GLM) and Applications for Regression

13.4 Extension of Data Transformation and Generalized Linear Model to Multiple Regression

EXERCISES

14. Robust Regression

14.1 Introduction and Overview

14.2 Kendall-Theil Robust Line

14.3 Weighted Least Squares Regression

14.4 Iteratively Reweighted Least Squares Regression

14.5 Other Robust Regression Alternatives

14.6 Robust Regression Methods for Multiple-Variable Data

EXERCISES

15. Multiple Linear Regression

15.1 Introduction and Overview

15.2 The Need for Multiple Regression

15.3 The Multiple Linear Regression Model

15.4 The Estimated Multivariable X-Y Relationship based on a Data Sample

15.5 Assumptions of Multiple Linear Regression

15.6 Hypothesis Tests for Reliability of the MLR Model

15.7 Confidence Intervals for the Regression Coefficients and Predicted Y Values

15.8 Coefficient of Multiple Correlation (R), Multiple Determination (R²), Adjusted R², and Partial Correlation Coefficients

15.9 Regression Diagnostics

15.10 Model Interactions and Multiplicative Effects

EXERCISES

16. Categorical Data Analysis

16.1 Introduction and Overview

16.2 Types of Variables and associated Data

16.3 One-Way Analysis of Variance (ANOVA) Model

16.4 Two-Way Analysis of Variance (ANOVA) Regression Model with no Interactions

16.5 Two-Way Analysis of Variance (ANOVA) Model with Interactions

16.6 Analysis of Covariance (ANCOVA) Regression Model

EXERCISES

17. Model Building: Stepwise Regression and Best Subsets Regression

17.1 Introduction and Overview

17.2 Consequences of Inappropriate Variable Selection

17.3 Stepwise Regression Procedures

17.4 Subsets Regression

EXERCISES

18. Nonlinear Regression

18.1 Introduction and Overview

18.2 The Nonlinear Regression Model

18.3 Assumptions of Nonlinear Least Squares Regression

EXERCISES

PART IV STATISTICS IN ENVIRONMENTAL SAMPLING DESIGN AND RISK ASSESSMENT

19. Data Quality Objectives and Environmental Sampling Design

19.1 Introduction and Overview

19.2 Sampling Design

19.3 Sampling Plans

19.4 Sample Size Determination

EXERCISES

20. Determination of Background and Applications in Risk Assessment

20.1 Introduction and Overview

20.2 When Background Sampling is required and when it is not

20.3 Background Sampling Plans

20.4 Graphical and Quantitative Data Analysis for Site versus Background Data Comparisons

20.5 Determination of Exposure Point Concentration and Contaminants of Potential Concern

EXERCISES

21. Statistics in Conventional and Probabilistic Risk Assessment

21.1 Introduction and Overview

21.2 Conventional or Point Risk Estimation

21.3 Probabilistic Risk Assessment using Monte Carlo Simulation

EXERCISES

Appendix A: Software Scripts

Appendix B: Datasets

References

Index