Preface to the Second Edition

The main changes for the second edition of the book have been the correction of a few errors that have either been pointed out by readers of the first edition or noticed by me in the updating of references and the text, particularly in terms of the software needed for calculations and changes to the web sites, and the addition of some exercises at the end of chapters. I would particularly like to thank students attending my workshops and courses at statistics.com for helping me to clarify parts of the text that were not altogether clear in the first edition.

The aims of the book are still the same as for the first edition; namely, to introduce environmental scientists and managers to the statistical methods that will be useful for them in their work, and also as a text suitable for a course in statistics for graduate students in the environmental science area.

Bryan Manly

March 2008

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Preface to the First Edition

This book is intended to introduce environmental scientists and managers to the statistical methods that will be useful for them in their work. A secondary aim was to produce a text suitable for a course in statistics for graduate students in the environmental science area. I wrote the book because it seemed to me that these groups should really learn about statistical methods in a special way. It is true that their needs are similar in many respects to those working in other areas. However, there are some special topics that are relevant to environmental science to the extent that they should be covered in an introductory text, although they would probably not be mentioned at all in such a text for a more general audience. I refer to environmental monitoring, impact assessment, which all have their own chapters here.

The book is not intended to be a complete introduction to statistics. Rather, it is assumed that readers have already taken a course or read a book on basic methods, covering the ideas of random variation, statistical distributions, tests of significance, and confidence intervals. For those who have done this some time ago, Appendix A is meant to provide a quick refresher course.

A number of people have contributed directly or indirectly to this book. I must first mention Lyman McDonald of West, Inc., Cheyenne, WY, who first stimulated my interest in environmental statistics, as distinct from ecological statistics. Much of the contents of the book are influenced by the discussions that we have had on matters statistical. Jennifer Brown from the University of Canterbury in New Zealand has influenced the contents because we have shared the teaching of several short courses on statistics for environmental scientists and managers. Likewise, sharing a course on statistics for MSc students of environmental science with Caryn Thompson and David Fletcher has also had an effect on the book. Other people are too numerous to name, so I would just like to thank generally those who have contributed data sets, helped me check references and equations, etc.

Most of this book was written in the Department of Mathematics and Statistics at the University of Otago. As usual, the university was generous with the resources that are needed for the major effort of writing a book, including periods of sabbatical leave that enabled me to write large parts of the text without interruptions, and an excellent library.

However, the manuscript would definitely have taken longer to finish if I had not been invited to spend part of the year 2000 as a visiting researcher at the Max Planck Institute for Limnology at Plön in Germany. This enabled me to write the final chapters and put the whole book together. I am very grateful to Winfried Lampert, the Director of the Institute, for his kind invitation to come to Plön, and for allowing me to use the excellent facilities at the Institute while I was there.

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1

The Role of Statistics in

Environmental Science

1.1  Introduction

In this chapter the role of statistics in environmental science is considered by examining some specific examples. First, however, an important point needs to be made. The need for statistics is obvious in this area because much of what is learned about the environment is based on numerical data. Therefore, the appropriate handling of data is crucial. Indeed, the use of incorrect statistical methods may make individuals and organizations vulnerable to being sued for large amounts of money. In the United States, it certainly appears that increasing attention to the use of statistical methods is driven by the fear of litigation.

In this context, it is important to note that there is usually no single correct way to gather and analyze data. At best, there may be several alternative approaches that are all about equally good. At worst, the alternatives may involve different assumptions and lead to different conclusions. This will become apparent from some of the examples in this and the following chapters.

1.2  Some Examples

The following examples demonstrate the nontrivial statistical problems that can arise in practice, and are intended to show the importance of the proper use of statistical theory. Some of these examples are revisited again in later chapters.

For environmental scientists and resource managers there are three broad types of situations that are often of interest:

1.Baseline studies intended to document the present state of the environment in order to establish future changes resulting, for example, from unforeseen events such as oil spills

1

human activity. The net result was that the sampling probabilities used in the study design were not quite what they were supposed to be. The investigators considered that the effect of this was minor. However, the authors of the National Oceanic and Atmospheric Administrations guidance document for assessing the damage from oil spills argue that this could be used in an attempt to discredit the entire study (Bergman et al. 1995, Section F). It is, therefore, an example of how a minor deviation from the requirements of a standard study design may lead to potentially very serious consequences.

The Oil Spill Trustees’ Coastal Habitat Injury Assessment

The Exxon Valdez Oil Spill Trustee Council was set up to oversee the allocation of funds from Exxon for the restoration of Prince William Sound and Alaskan waters. Like the Exxon Shoreline Ecology Program, the 1989 Coastal Habitat Injury Assessment study that was set up by the council was based on a stratified random sampling design of a type that will be discussed in Chapter 2. There were 15 strata used, with these defined by five habitat types, each with three levels of oiling. Sample units were shoreline segments with varying lengths, and these were selected using a GIS system, with probabilities proportional to their lengths.

Unfortunately, so many sites were misclassified by the GIS system that the 1989 study design had to be abandoned in 1990. Instead, each of the moderately and heavily oiled sites that were sampled in 1989 was matched up with a comparable unoiled control site based on physical characteristics, to give a paired-comparison design. The investigators then considered whether the paired sites were significantly different with regard to species abundance.

There are two aspects of the analysis of the data from this study that are unusual. First, the results of comparing site pairs (oiled and unoiled) were summarized as p-values (probabilities of observing differences as large as those seen on the hypothesis that oiling had no effect). These p-values were then combined using a meta-analysis, which is a method that is discussed in Chapter 4. This approach for assessing the evidence was used because each site pair was thought of as an independent study of the effects of oiling.

The second unusual aspect of the analysis was the weighting of results that was used for one of the two methods of meta-analysis that was employed. By weighting the results for each site pair by the reciprocal of the probability of the pair being included in the study, it was possible to make inferences with respect to the entire set of possible pairs in the study region. This was not a particularly simple procedure to carry out, because inclusion probabilities had to be estimated by simulation. It did, however, overcome the problems introduced by the initial misclassification of sites.

The Biological Monitoring Survey

The Biological Monitoring Survey was instigated by the National Oceanic and Atmospheric Administration to study differences in impact between oiling alone and oiling combined with high-pressure hot-water washing at sheltered rocky sites. Thus there were three categories of sites

used. Category 1 sites were unoiled. Category 2 sites were oiled but not washed. Category 3 sites were oiled and washed. Sites were subjectively selected, with unoiled ones being chosen to match those in the other two categories. Oiling levels were also classified as being light or moderate/ heavy, depending on their state when they were laid out in 1989. Species counts and percentage cover were measured at sampled sites.

Randomization tests were used to assess the significance of the differences between the sites in different categories because of the extreme nature of the distributions found for the recorded data. These types of test are discussed in Chapter 4. Here it is just noted that the hypothesis tested is that an observation was equally likely to have occurred for a site in any one of the three categories. This can certainly provide valid evidence of differences between the categories. However, the subjective methods used to select sites allows the argument to be made that any significant differences were due to the selection procedure rather than the oiling or the hot-water treatment.

Another potential problem with the analysis of the study is that it may have involved pseudo-replication (treating correlated data as independent data), which is also defined and discussed in Chapter 4. This is because sampling stations along a transect on a beach were treated as if they provided completely independent data, although in fact some of these stations were in close proximity. In reality, observations taken close together in space can be expected to be more similar than observations taken far apart. Ignoring this fact may have led to a general tendency to conclude that sites in the different categories differed, when this was not really the case.

General Comments on the Three Studies

The three studies on the Exxon Valdez oil spill took different approaches and led to answers to different questions. The Exxon Shoreline Ecology Program was intended to assess the impact of oiling over the entire spill zone by using a stratified random sampling design. A minor problem is that the standard requirements of the sampling design were not quite followed because of site misclassification and some restrictions on sites that could be sampled. The Oil Trustees’ Coastal Habitat Study was badly upset by site misclassification in 1989, and was therefore converted to a paired-comparison design in 1990 to compare moderately or heavily oiled sites with subjectively chosen unoiled sites. This allowed evidence for the effect of oiling to be assessed, but only at the expense of a complicated analysis involving the use of simulation to estimate the probability of a site being used in the study, and a special method to combine the results for different pairs of sites. The Biological Monitoring Survey focused on assessing the effects of hot-water washing, and the design gives no way for making inferences to the entire area affected by the oil spill.

All three studies are open to criticism in terms of the extent to which they can be used to draw conclusions about the overall impact of the oil spill in the entire area of interest. For the Exxon Coastal Ecology Program and the Trustees’ Coastal Habitat Injury Assessment, this was the result of using stratified random sampling designs for which the randomization