Statistics for Environmental Engineers

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Specimens 1 through 6 were taken in November 1977, specimens 7 through 12 in February 1978, and specimens 13 through 17 in August 1978. A large seasonal variation is apparent. If we were to compute the variances of the inlet and outlet counts, it would be huge and it would consist largely of variation due to seasonal differences. Because we are not trying to evaluate seasonal differences, this would be a poor way to analyze the data. The paired comparison operates on the differences of the daily inlet and outlet counts, and these differences do not reflect the seasonal variation (except, as we shall see in a moment, to the extent that the differences are proportional to the population density).


FIGURE 17.2 Copepod population density (organisms/m3).

5000 0

0    20000    40000    60000    80000

Inlet Copepod Density

-5000 -10000 -15000

8    9    10    11    12

In (Inlet Copepod Density)

FIGURE 17.3 The difference in copepod inlet and outlet population density is larger when the population is large, indicating nonconstant variance at different population levels.








0.0 -0.1 -0.2 -0.3

It is tempting to tell ourselves that “I would not be foolish enough not to do a paired comparison on data such as these.” Of course we would not when the variation due to the nuisance factor (season) is both huge and obvious. But almost every experiment is at risk of being influenced by one or more nuisance factors, which may be known or unknown to the experimenter. Even the most careful experimental technique cannot guarantee that these will not alter the outcome. The paired experimental design will prevent this and it is recommended whenever the experiment can be so arranged.

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