# Statistics for Environmental Engineers

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We strongly prefer working with experimental conditions that are statistically designed. It is comparatively easy to arrange designed experiments in the laboratory. Unfortunately, in studies of natural systems and treatment facilities it may be impossible to manipulate the independent variables to create conditions of special interest. A range of conditions can be observed only by spacing observations or field studies over a long period of time, perhaps several years. We may need to use historical data to assess changes that have occurred over time and often the available data were not collected with a view toward assessing these changes. A related problem is not being able to replicate experimental conditions. These are huge stumbling blocks and it is important for us to recognize how they block our path toward discovery of the truth. Hopes for successfully extracting information from such historical data are not often fulfilled.

### Special Problems

Introductory statistics courses commonly deal with linear models and assume that available data are normally distributed and independent. There are some problems in environmental engineering where these fundamental assumptions are satisfied. Often the data are not normally distributed, they are serially or spatially correlated, or nonlinear models are needed (Berthouex et al., 1981; Hunter, 1977, 1980, 1982). Some specific problems encountered in data acquisition and analysis are:

Aberrant values. Values that stand out from the general trend are fairly common. They may occur because of gross errors in sampling or measurement. They may be mistakes in data recording. If we think only in these terms, it becomes too tempting to discount or throw out such values. However, rejecting any value out of hand may lead to serious errors. Some early observers of stratospheric ozone concentrations failed to detect the hole in the ozone layer because their computer had been programmed to screen incoming data for “outliers.” The values that defined the hole in the ozone layer were disregarded. This is a reminder that rogue values may be real. Indeed, they may contain the most important information.

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