# Statistics for Environmental Engineers

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The idea of using charts to assist operation is valid in all processes. Plotting the data in different forms — as time series, Cusums, moving averages — has great value and will reveal most of the important information to the thoughtful operator. Charts are not inferior or second-class statistical methods. They reflect the best of control chart philosophy without the statistical complications. They are statistically valid, easy to use, and not likely to lead to any serious misinterpretations.

Control charts, with formal action limits, are only dressed-up graphs. The control limits add a measure of objectivity, provided they are established without violating the underlying statistical conditions (independence, constant variance, and normally distributed variations). If you are not sure how to derive correct control limits, then use the charts without control limits, or construct an external reference distribution (Chapter 6) to develop approximate control limits. Take advantage of the human ability to recognize patterns and deviations from trends, and to reason sensibly.

Some special characteristics of environmental data include serial correlation, seasonality, nonnormal distributions, and changing variance. Nonnormal distribution and nonconstant variance can usually be handled with a transformation. Serial correlation and seasonality are problems because control charts are sensitive to these properties. One way to deal with this is the Six Sigma approach of arbitrarily widening the control limits to provide a margin for drift.

The next chapter deals with special control charts. Cumulative score charts are an extension of Cusum charts that can detect cyclic patterns and shifts in the parameters of models. Exponentially weighted moving average charts can deal with serial correlation and process drift.

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