Statistics for Environmental Engineers

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First Iteration


Design — Because each run takes several days to complete, the experiment was performed in small sequential stages. The first was a two-level, two-factor experiment — a 22 factorial design. The two experimental factors are dilution rate (D) and residual phenol concentration (C). The response is phenol oxidation rate (R). Each factor was investigated at two levels and the observed phenol removal rates are given in Table 43.1.


Analysis — The data can be analyzed by calculating the effects, as done in Chapter 27, or by linear regression (Chapter 30); we will use regression. There are four observations so the fitted model cannot have more than four parameters. Because we expect the surface to be relatively smooth, a reasonable model is R = b0 + bjC + b2D + b12CD. This describes a hyperplane. The terms bjC and b2D represent the main effects of concentration and dilution rate; b12CD is the interaction between the two factors.


The fitted model is R = —0.022 — 0.018C + 0.2D + 0.3CD. The response as a function of the two experimental factors is depicted by the contour map in Figure 43.2. The contours are values of R, in units of g/h. The approximation is good only in the neighborhood of the 22 experiment, which is indicated by the four dots at the corner of the rectangle. The direction toward higher removal rates is clear. The direction of steepest ascent, indicated by an arrow, is perpendicular to the contour line at the point of interest. Of course, the experimenter is not compelled to move along the line of steepest ascent.

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