Statistics for Environmental Engineers

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Censored data. Great effort and expense are invested in measurements of toxic and hazardous substances that should be absent or else be present in only trace amounts. The analyst handles many specimens for which the concentration is reported as “not detected” or “below the analytical method detection limit.” This method of reporting censors the data at the limit of detection and condemns all lower values to be qualitative. This manipulation of the data creates severe problems for the data analyst and the person who needs to use the data to make decisions.


Large amounts of data (which are often observational data rather than data from designed experiments). Every treatment plant, river basin authority, and environmental control agency has accumulated a mass of multivariate data in filing cabinets or computer databases. Most of this is happenstance data. It was collected for one purpose; later it is considered for another purpose. Happenstance data are often ill suited for model building. They may be ill suited for detecting trends over time or for testing any hypothesis about system behavior because (1) the record is not consistent and comparable from period to period, (2) all variables that affect the system have not been observed, and (3) the range of variables has been restricted by the system’s operation. In short, happenstance data often contain surprisingly little information. No amount of analysis can extract information that does not exist.


Large measurement errors. Many biological and chemical measurements have large measurement errors, despite the usual care that is taken with instrument calibration, reagent preparation, and personnel training. There are efficient statistical methods to deal with random errors. Replicate measurements can be used to estimate the random variation, averaging can reduce its effect, and other methods can compare the random variation with possible real changes in a system. Systematic errors (bias) cannot be removed or reduced by averaging.

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