Statistics for Environmental Engineers

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The experimenter who does not think of pairing (blocking) the experiment works at a tremendous handicap and will make many wrong decisions. Imagine that the collecting for A was done on M, W, F, of one week and collection for B was done in another week. Now the paired analysis cannot be done and the difference will not be detected. This is why we speak of a paired design as well as of a paired t-test analysis. The crucial step is making the correct design. Pairing is always recommended.

Case Study to Emphasize the Benefits of a Paired Design

A once-through cooling system at a power plant is suspected of reducing the population of certain aquatic organisms. The copepod population density (organisms per cubic meter) were measured at the inlet and outlet of the cooling system on 17 different days (Simpson and Dudaitis, 1981). On each sampling day, water specimens were collected within a short time interval, first at the inlet and then at the outlet. The sampling plan represents a thoughtful effort to block out the effect of day-to-day and month-to-month variations in population counts. It pairs the inlet and outlet measurements. Of course, it is impossible to sample the same parcel of water at the inlet and outlet (i.e., the pairing is not exact), but any variation caused by this will be reflected as a component of the random measurement error.

The data are plotted in Figure 17.2. The plot gives the impression that the cooling system may not affect the copepods. The outlet counts are higher than inlets counts on 10 of the 17 days. There are some big differences, but these are on days when the count was very high and we expect that the measurement error in counting will be proportional to the population. (If you count 10 pennies you will get the right answer, but if you count 1000, you are certain to have some error; the more pennies the more counting error.) Before doing the calculations, consider once more why the paired comparison should be done.

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