Page 10 - Statistics for Environmental Engineers

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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