# Statistics for Environmental Engineers

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In the case study, all interactions and three main effects were insignificant. This means that the experiment can be interpreted by collapsing the design onto the two significant factors. Figure 29.3 shows permeability in terms of factors 1 and 2, which now appear to have been replicated four times. You can confirm that the main effects calculated from this view of the experiment are exactly as obtained from the previous analysis.

This gain in apparent replication is common in screening experiments. It is one reason they are so efficient, despite the confounding that the inexperienced designer fears will weaken the experiment. To appreciate this, suppose that three factors had been significant in the case study. Now the collapsed design is equivalent to a 2 design that is replicated twice at each condition. Or suppose that we had been even

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more ambitious with the fractional design and had investigated the five factors in just eight runs with a 2

2

design. If only two factors proved to be significant, the collapsed design would be equivalent to a 2 experiment replicated twice at each condition.

Finding an insignificant factor in a fractional factorial experiment always has the effect of creating apparent replication. Screening experiments are designed with the expectation that some factors will be inactive. Therefore, confounding usually produces a bonus instead of a penalty. This is not the case in an experiment where all factors are known to be important, that is, in an experiment where the objective is to model the effect of changing prescreened variables.

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