Statistics for Environmental Engineers

464 Pages·2002·7.547 MB·English

by  Linfield C. Brown, Paul Mac Berthouex

Statistics for
Environmental
Engineers
Second Edition
Paul Mac Berthouex
Linfield C. Brown
LEWIS PUBLISHERS
A CRC Press Company
Boca Raton London New York Washington, D.C.
© 2002 By CRC Press LLC
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Preface to 1st Edition
When one is confronted with a new problem that involves the collection and analysis of data, two crucial
questions are: How will using statistics help solve this problem? And, Which techniques should be used?
This book is intended to help environmental engineers answer these questions in order to better under-
stand and design systems for environmental protection.
The book is not about the environmental systems, except incidentally. It is about how to extract
information from data and how informative data are generated in the first place. A selection of practical
statistical methods is applied to the kinds of problems that we encountered in our work. We have not
tried to discuss every statistical method that is useful for studying environmental data. To do so would
mean including virtually all statistical methods, an obvious impossibility. Likewise, it is impossible to
mention every environmental problem that can or should be investigated by statistical methods. Each
reader, therefore, will find gaps in our coverage; when this happens, we hope that other authors have
filled the gap. Indeed, some topics have been omitted precisely because we know they are discussed in
other well-known books.
It is important to encourage engineers to see statistics as a professional tool used in familiar examples
that are similar to those faced in one’s own work. For most of the examples in this book, the environmental
engineer will have a good idea how the test specimens were collected and how the measurements were
made. The data thus have a special relevance and reality that should make it easier to understand special
features of the data and the potential problems associated with the data analysis.
The book is organized into short chapters. The goal was for each chapter to stand alone so one need
not study the book from front to back, or in any other particular order. Total independence of one chapter
from another is not always possible, but the reader is encouraged to “dip in” where the subject of the
case study or the statistical method stimulates interest. For example, an engineer whose current interest
is fitting a kinetic model to some data can get some useful ideas from Chapter 25 without first reading
the preceding 24 chapters. To most readers, Chapter 25 is not conceptually more difficult than Chapter 12.
Chapter 40 can be understood without knowing anything about t-tests, confidence intervals, regression,
or analysis of variance.
There are so many excellent books on statistics that one reasonably might ask, Why write another
book that targets environmental engineers? A statistician may look at this book and correctly say,
“Nothing new here.” We have seen book reviews that were highly critical because “this book is much
like book X with the examples changed from biology to chemistry.” Does “changing the examples” have
some benefit? We feel it does (although we hope the book does something more than just change the
examples).
A number of people helped with this book. Our good friend, the late William G. Hunter, suggested
the format for the book. He and George Box were our teachers and the book reflects their influence on
our approach to engineering and statistics. Lars Pallesen, engineer and statistician, worked on an early
version of the book and is in spirit a co-author. A. (Sam) James provided early encouragement and
advice during some delightful and productive weeks in northern England. J. Stuart Hunter reviewed the
manuscript at an early stage and helped to “clear up some muddy waters.” We thank them all.
P. Mac Berthouex
Madison, Wisconsin
Linfield C. Brown
Medford, Massachusetts
© 2002 By CRC Press LLC
Preface to 2nd Edition
This second edition, like the first, is about how to generate informative data and how to extract information
from data. The short-chapter format of the first edition has been retained. The goal is for the reader to
be able to “dip in” where the case study or the statistical method stimulates interest without having to
study the book from front to back, or in any particular order.
Thirteen new chapters deal with experimental design, selecting the sample size for an experiment,
time series modeling and forecasting, transfer function models, weighted least squares, laboratory quality
assurance, standard and specialty control charts, and tolerance and prediction intervals. The chapters on
regression, parameter estimation, and model building have been revised. The chapters on transformations,
simulation, and error propagation have been expanded.
It is important to encourage engineers to see statistics as a professional tool. One way to do this is to
show them examples similar to those faced in one’s own work. For most of the examples in this book,
the environmental engineer will have a good idea how the test specimens were collected and how the
measurements were made. This creates a relevance and reality that makes it easier to understand special
features of the data and the potential problems associated with the data analysis.
Exercises for self-study and classroom use have been added to all chapters. A solutions manual is
available to course instructors. It will not be possible to cover all 54 chapters in a one-semester course,
but the instructor can select chapters that match the knowledge level and interest of a particular class.
Statistics and environmental engineering share the burden of having a special vocabulary, and students
have some early frustration in both subjects until they become familiar with the special language.
Learning both languages at the same time is perhaps expecting too much. Readers who have prerequisite
knowledge of both environmental engineering and statistics will find the book easily understandable.
Those who have had an introductory environmental engineering course but who are new to statistics, or
vice versa, can use the book effectively if they are patient about vocabulary.
We have not tried to discuss every statistical method that is used to interpret environmental data. To
do so would be impossible. Likewise, we cannot mention every environmental problem that involves
statistics. The statistical methods selected for discussion are those that have been useful in our work,
which is environmental engineering in the areas of water and wastewater treatment, industrial pollution
control, and environmental modeling. If your special interest is air pollution control, hydrology, or geosta-
tistics, your work may require statistical methods that we have not discussed. Some topics have been
omitted precisely because you can find an excellent discussion in other books. We hope that whatever
kind of environmental engineering work you do, this book will provide clear and useful guidance on
data collection and analysis.
P. Mac Berthouex
Madison, Wisconsin
Linfield C. Brown
Medford, Massachusetts
© 2002 By CRC Press LLC
The Authors
Paul Mac Berthouex is Emeritus Professor of civil and environmental engineering at the University of
Wisconsin-Madison, where he has been on the faculty since 1971. He received his M.S. in sanitary
engineering from the University of Iowa in 1964 and his Ph.D. in civil engineering from the University
of Wisconsin-Madison in 1970. Professor Berthouex has taught a wide range of environmental engi-
neering courses, and in 1975 and 1992 was the recipient of the Rudolph Hering Medal, American Society
of Civil Engineers, for most valuable contribution to the environmental branch of the engineering
profession. Most recently, he served on the Government of India’s Central Pollution Control Board.
In addition to Statistics for Environmental Engineers, 1st Edition (1994, Lewis Publishers), Professor
Berthouex has written books on air pollution and pollution control. He has been the author or co-author
of approximately 85 articles in refereed journals.
Linfield C. Brown is Professor of civil and environmental engineering at Tufts University, where he
has been on the faculty since 1970. He received his M.S. in environmental health engineering from Tufts
University in 1966 and his Ph.D. in sanitary engineering from the University of Wisconsin-Madison in
1970. Professor Brown teaches courses on water quality monitoring, water and wastewater chemistry,
industrial waste treatment, and pollution prevention, and serves on the U.S. Environmental Protection
Agency’s Environmental Models Subcommittee of the Science Advisory Board. He is a Task Group
Member of the American Society of Civil Engineers’ National Subcommittee on Oxygen Transfer
Standards, and has served on the Editorial Board of the Journal of Hazardous Wastes and Hazardous
Materials.
In addition to Statistics for Environmental Engineers, 1st Edition (1994, Lewis Publishers), Professor
Brown has been the author or co-author of numerous publications on environmental engineering, water
quality monitoring, and hazardous materials.
© 2002 By CRC Press LLC
Table of Contents
1 Environmental Problems and Statistics
2 A Brief Review of Statistics
3 Plotting Data
4 Smoothing Data
5 Seeing the Shape of a Distribution
6 External Reference Distributions
7 Using Transformations
8 Estimating Percentiles
9 Accuracy, Bias, and Precision of Measurements
10 Precision of Calculated Values
11 Laboratory Quality Assurance
12 Fundamentals of Process Control Charts
13 Specialized Control Charts
14 Limit of Detection
15 Analyzing Censored Data
16 Comparing a Mean with a Standard
17 Paired t-Test for Assessing the Average of Differences
18 Independent t-Test for Assessing the Difference of Two Averages
19 Assessing the Difference of Proportions
20 Multiple Paired Comparisons of k Averages
© 2002 By CRC Press LLC
21 Tolerance Intervals and Prediction Intervals
22 Experimental Design
23 Sizing the Experiment
24 Analysis of Variance to Compare k Averages
25 Components of Variance
26 Multiple Factor Analysis of Variance
27 Factorial Experimental Designs
28 Fractional Factorial Experimental Designs
29 Screening of Important Variables
30 Analyzing Factorial Experiments by Regression
31 Correlation
32 Serial Correlation
33 The Method of Least Squares
34 Precision of Parameter Estimates in Linear Models
35 Precision of Parameter Estimates in Nonlinear Models
36 Calibration
37 Weighted Least Squares
38 Empirical Model Building by Linear Regression
39 The Coefficient of Determination, R2
40 Regression Analysis with Categorical Variables
41 The Effect of Autocorrelation on Regression
42 The Iterative Approach to Experimentation
43 Seeking Optimum Conditions by Response Surface Methodology
© 2002 By CRC Press LLC
44 Designing Experiments for Nonlinear Parameter Estimation
45 Why Linearization Can Bias Parameter Estimates
46 Fitting Models to Multiresponse Data
47 A Problem in Model Discrimination
48 Data Adjustment for Process Rationalization
49 How Measurement Errors Are Transmitted into Calculated Values
50 Using Simulation to Study Statistical Problems
51 Introduction to Time Series Modeling
52 Transfer Function Models
53 Forecasting Time Series
54 Intervention Analysis
Appendix — Statistical Tables
© 2002 By CRC Press LLC
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1
Environmental Problems and Statistics
There are many aspects of environmental problems: economic, political, psychological, medical, scientific,
and technological. Understanding and solving such problems often involves certain quantitative aspects,
in particular the acquisition and analysis of data. Treating these quantitative problems effectively involves
the use of statistics. Statistics can be viewed as the prescription for making the quantitative learning process
effective.
When one is confronted with a new problem, a two-part question of crucial importance is, “How will
using statistics help solve this problem and which techniques should be used?” Many different substantive
problems arise and many different statistical techniques exist, ranging from making simple plots of data
to iterative model building and parameter estimation.
Some problems can be solved by subjecting the available data to a particular analytical method. More
often the analysis must be stepwise. As Sir Ronald Fisher said, “…a statistician ought to strive above all
to acquire versatility and resourcefulness, based on a repertoire of tried procedures, always aware that
the next case he wants to deal with may not fit any particular recipe.”
Doing statistics on environmental problems can be like coaxing a stubborn animal. Sometimes small
steps, often separated by intervals of frustration, are the only way to progress at all. Even when the data
contains bountiful information, it may be discovered in bits and at intervals.
The goal of statistics is to make that discovery process efficient. Analyzing data is part science, part
craft, and part art. Skills and talent help, experience counts, and tools are necessary. This book illustrates
some of the statistical tools that we have found useful; they will vary from problem to problem. We
hope this book provides some useful tools and encourages environmental engineers to develop the
necessary craft and art.
Statistics and Environmental Law
Environmental laws and regulations are about toxic chemicals, water quality criteria, air quality criteria,
and so on, but they are also about statistics because they are laced with statistical terminology and
concepts. For example, the limit of detection is a statistical concept used by chemists. In environmental
biology, acute and chronic toxicity criteria are developed from complex data collection and statistical
estimation procedures, safe and adverse conditions are differentiated through statistical comparison of
control and exposed populations, and cancer potency factors are estimated by extrapolating models that
have been fitted to dose-response data.
As an example, the Wisconsin laws on toxic chemicals in the aquatic environment specifically mention
the following statistical terms: geometric mean, ranks, cumulative probability, sums of squares, least
squares regression, data transformations, normalization of geometric means, coefficient of determination,
standard F-test at a 0.05 level, representative background concentration, representative data, arithmetic
average, upper 99th percentile, probability distribution, log-normal distribution, serial correlation, mean,
variance, standard deviation, standard normal distribution, and Z value. The U.S. EPA guidance doc-
uments on statistical analysis of bioassay test data mentions arc-sine transformation, probit analysis,
non-normal distribution, Shapiro-Wilks test, Bartlett’s test, homogeneous variance, heterogeneous vari-
ance, replicates, t-test with Bonferroni adjustment, Dunnett’s test, Steel’s rank test, and Wilcoxon rank
sum test. Terms mentioned in EPA guidance documents on groundwater monitoring at RCRA sites
© 2002 By CRC Press LLC