Statistics for Environmental Engineers

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Neither of these approaches is as attractive as using categorical variables to create a collective data set that can be fitted to a single model while retaining the distinction between the individual data sets. This technique allows the model structure and the model parameters to be evaluated using statistical methods like those discussed in the previous chapter.

Case Study: Acidification of a Stream During Storms

Cosby Creek, in the southern Appalachian Mountains, was monitored during three storms to study how pH and other measures of acidification were affected by the rainfall in that region. Samples were taken every 30 min and 19 characteristics of the stream water chemistry were measured (Meinert et al., 1982). Weak acidity (WA) and pH will be examined in this case study.

Figure 40.1 shows 17 observations for storm 1, 14 for storm 2, and 13 for storm 3, giving a total of 44 observations. If the data are analyzed without distinguishing between storms one might consider models of the form pH = во + ftWA + P2WA2 or pH = в3 + (в1 03)exp(-02WA). Each storm might be described by pH = во + PWA, but storm 3 does not have the same slope and intercept as storms 1 and 2, and storms 1 and 2 might be different as well. This can be checked by using categorical variables to estimate a different slope and intercept for each storm.

Method: Regression with Categorical Variables

Suppose that a model needs to include an effect due to the category (storm event, farm plot, treatment, truckload, operator, laboratory, etc.) from which the data came. This effect is included in the model in the form of categorical variables (also called dummy or indicator variables). In general m — 1 categorical variables are needed to specify m categories.

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