CONTENTS

Cover

Wiley Series in Statistics in Practice

Title Page

Copyright

Dedication

Preface

Acknowledgments

Chapter 1: Introduction

1.1 Introduction and Overview

1.2 The Aim of the Book: Get Involved!

1.3 The Approach and Style: Clarity, Clarity, Clarity

Part I: Basic Statistical Measures and Concepts

Chapter 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 Kendall–Thiel Robust Line

2.6 Minitab®

2.7 Microsoft Excel

Chapter 3: Laboratory Detection Limits, Nondetects, and Data Analysis

3.1 Introduction and Overview

3.2 Types of Laboratory Data Detection Limits

3.3 Problems with Nondetects in Statistical Data Samples

3.4 Options for Addressing Nondetects in Data Analysis

Chapter 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

Chapter 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

Chapter 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

6.7 Data Transformations

Exercises

Part II: Statistical Procedures for Mostly Univariate Data

Chapter 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

Chapter 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 Interrelationships

8.4 The Problem with Multiple Tests or Comparisons: Site-Wide False Positive Error Rates

8.5 Tests for Equality of Variance

Exercises

Chapter 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 Nonparametric Kruskal–Wallis Tests

Exercises

Chapter 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: Statistical Procedures for Mostly Multivariate Data

Chapter 11: Correlation, Covariance, Geostatistics

11.1 Introduction and Overview

11.2 Correlation and Covariance

11.3 Introduction to Geostatistics

Exercises

Chapter 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

Chapter 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

Chapter 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: Bounded Influence Methods

14.6 Robust Regression Methods for Multiple-Variable Data

Exercises

Chapter 15: Multiple Linear Regression

15.1 Introduction and Overview

15.2 The Need for Multiple Regression

15.3 The Multiple Linear Regression (MLR) 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

Chapter 16: Categorical Data Analysis

16.1 Introduction and Overview

16.2 Types of Variables and Associated Data

16.3 One-Way Analysis of Variance Regression Model

16.4 Two-Way Analysis of Variance Regression Model With no Interactions

16.5 Two-Way Analysis of Variance Regression Model With Interactions

16.6 Analysis of Covariance Regression Model

Exercises

Chapter 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

Chapter 18: Nonlinear Regression

18.1 Introduction and Overview

18.2 The Nonlinear Regression Model

18.3 Assumptions of Nonlinear Least Squares Regression

Discussion of Results

Exercises

Part IV: Statistics in Environmental Sampling Design and Risk Assessment

Chapter 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

Chapter 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

Chapter 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

Answers for Exercises

Index

End User License Agreement

List of Tables

Table 3.1

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 5.1

Table 5.2

Table 5.3

Table 5.4

Table 5.5

Table 5.6

Table 5.7

Table 5.8

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 7.1

Table 7.2

Table 7.3

Table 7.4

Table 7.5

Table 7.6

Table 7.7

Table 7.8

Table 7.9

Table 7.10

Table 8.1

Table 8.2

Table 9.1

Table 9.2

Table 9.3

Table 9.4

Table 9.5

Table 9.6

Table 9.7

Table 9.8

Table 9.9

Table 9.10

Table 9.11

Table 9.12

Table 9.13

Table 9.14

Table 9.15

Table 9.16

Table 9.17

Table 10.1

Table 10.2

Table 10.3

Table 10.4

Table 10.5

Table 10.6

Table 10.7

Table 10.8

Table 11.1

Table 11.2

Table 11.3

Table 11.4

Table 11.5

Table 12.1

Table 12.2

Table 12.3

Table 13.1

Table 13.2

Table 13.3

Table 13.4

Table 13.5

Table 13.6

Table 14.1

Table 14.2

Table 15.1

Table 15.2

Table 15.3A

Table 15.3B

Table 15.4

Table 16.1

Table 16.2

Table 16.3

Table 19.1

Table 20.1

Table 20.2

Table 20.3

Table 20.4

Table 20.5

Table 21.1

Table 21.2

Table 21.3

List of Illustrations

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Figure 5.24

Figure 5.25

Figure 5.26

Figure 5.27

Figure 5.28

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 8.1

Figure 9.1

Figure 9.2

Figure 10.1

Figure 10.2

Figure 10.3

Figure 10.4

Figure 10.5

Figure 10.6

Figure 10.7

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 12.1

Figure 12.2

Figure 12.3

Figure 12.4

Figure 12.5

Figure 12.6

Figure 12.7

Figure 12.8

Figure 12.9

Figure 12.10

Figure 12.11

Figure 12.12

Figure 12.13

Figure 12.14

Figure 12.15

Figure 12.16

Figure 13.1

Figure 13.2

Figure 13.3

Figure 13.4

Figure 13.5

Figure 13.7

Figure 13.8

Figure 13.6

Figure 13.9

Figure 13.10

Figure 13.11

Figure 13.12

Figure 13.13

Figure 13.14

Figure 14.1

Figure 14.2

Figure 14.3

Figure 14.4

Figure 14.5

Figure 14.6

Figure 14.7

Figure 14.8

Figure 14.9

Figure 14.10

Figure 15.1

Figure 15.2

Figure 15.3

Figure 15.4

Figure 15.5

Figure 15.6

Figure 15.7

Figure 15.8

Figure 15.9

Figure 15.10

Figure 15.11

Figure 15.12

Figure 15.13

Figure 15.14

Figure 16.1

Figure 16.2

Figure 16.3

Figure 16.4

Figure 17.1

Figure 17.2

Figure 17.3

Figure 18.1

Figure 18.2

Figure 18.3

Figure 18.4a

Figure 18.4b

Figure 18.5

Figure 18.6

Figure 18.7

Figure 19.1

Figure 19.2

Figure 19.3

Figure 19.4

Figure 20.1

Figure 20.2

Figure 20.3

Figure 21.1

Figure 21.2

Figure 21.3

Figure 21.4

Guide

Cover

Table of Contents

Preface

Part 1

Chapter 1

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Statistical Applications for Environmental Analysis and Risk Assessment

Joseph Ofungwu

Hackettstown, NJ

Copyright © 2014 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Ofungwu, Joseph.

Statistical applications for environmental analysis and risk assessment /Joseph Ofungwu. – First edition.

pages cm – (Statistics in practice)

Includes bibliographical references and index.

ISBN 978-1-118-63453-0 (hardback)

1. Environmental risk assessment–Statistical methods. I. Title.

GE145.O38 2014

363.7′02–dc23

2013047836

Dedication

To Divine Providence

Preface

Although the subject of environmental statistics has been around for decades, the average environmental professional is far from comfortable with statistics, in my experience. This should be concerning because the protection of public health and ecological well-being falls largely on these professionals, and statistics should be a prominent part of their arsenal. It is fair to say that the environmental profession revolves around data. The environmental engineer, geologist, or scientist routinely collects data from soil, sediment, water, ambient air or other environmental media, for analysis and interpretation to determine the potential presence and concentrations of environmental contaminants. Based on the results of the data analysis and professional judgment, the practitioner makes a recommendation to the appropriate environmental protection authority that remedial action is necessary to reduce contaminant concentrations and minimize exposure risks, or that the exposure risks are minimal, warranting no further action. More often than not, the environmental regulatory authority concurs.

As it turns out, environmental data samples are rarely well-behaved, with nondetects, outliers, skewness, sustained and/or cyclical trend as habitual offenders in many data samples. Without functional familiarity with at least the basic statistical analysis principles and practices, how can we make sense of data such as these? Even more worrying, risk management decisions are often legalistic, based on numbers produced by statistical and associated analyses, where even a single mishandled outlier could possibly result in serious consequences for public and environmental health.

One reason for the lukewarm attitude toward statistics is the lack of regular access to competent software, as manual computation of most statistical procedures is now considered “ancient.” An insufficient statistics or math background is another reason. Not surprisingly, cost is mainly to blame for the lack of software access. The freely available, high-quality software system, R, along with others such as ProUCL and VSP used in this book, has come to the rescue in this regard. Although these systems have been in existence for over a decade, many in the environmental profession have still not heard the “good news.” The allure of a zero-cost, high-powered software package should be irresistible. No excuse to wait any longer!

Given the above context, this book describes fundamental statistical concepts and their applications in unambiguous language without assuming prior knowledge of statistics; draws attention to the important but often overlooked role of statistics in environmental contaminant sampling and exposure risk assessment; and provides packaged software scripts and macros using freely available software, to get the aspiring as well as practicing environmental professional off to a running start. Performing routine tests such as probability plots and box plots, t tests and Wilcoxon tests, regression analysis and trend tests on your environmental data samples should now be almost effortless. Furthermore, with increasing familiarity and comfort level, the cost–benefit analysis for the free software packages versus the more user-friendly commercial systems can be more knowledgeably evaluated, in terms of potential productivity gains.

R has brought excitement to statistics. I hope you become addicted for a worthy cause.

Joseph Ofungwu
February 2014

PS: Supplementary material for this book may be found by entering the following ISBN at booksupport.wiley.com: 9781118634530.

Acknowledgments

I owe a debt of gratitude to Steve Quigley, the Associate Publisher at Wiley, for his enthusiastic support and encouragement through the numerous twists and turns that finally brought this book to closure. Many thanks to Sari Friedman at Wiley, unfailingly courteous and professional. The book production was superbly orchestrated, thanks to Danielle LaCourciere and Faraz Sharique Ali for their expertise. I also wish to express my sincere appreciation to the many reviewers of the book proposal whose comments and criticisms alike helped shape the final product.

Chapter 1
Introduction

1.1 Introduction and Overview

Statistics is viewed by many as a branch of mathematics and since math is widely regarded as a difficult subject, people often assume automatically that statistics must be just as difficult. In truth, there is much not to “fear” in statistics, which in some cases involves nothing more complex than elementary arithmetic operations. As proof that statistics is not as “unappetizing” as it might seem, it is one of the few disciplines that find useful applications across a wide variety of professions, including the medical and biomedical, social sciences and psychology, economics, environmental and engineering professions, and so on. The environmental profession is almost completely driven by data, but surprisingly does not seem to have embraced statistics as much as some of the other professions just mentioned. Environmental engineers, geologists, scientists, or other professionals engaged in miscellaneous practice, research, or related activities have to work routinely with data from soil and sediment, surface and groundwater, ambient air, and other environmental media, for a variety of reasons or purposes. Data are collected to investigate or monitor an environmental concern, analyzed, and interpreted to gain insights into the situation, and the findings used to support decisions on response actions or predict future outcomes.

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