Similarly, Eqs. 3.6-3.8 can be readily obtained from the information in columns 5 through 8 of Table 3.4.

Randomization and Blocking. Randomization of experiments is desired to reduce the inferential validity of data collected in spite of unspecified disturbances. For example, the run numbers in Table 3.2 are written on pieces of paper and a drawing is made to pick the sequence of experiments to be conducted. Blocking is used to eliminate unwanted variability. The variability may be introduced by changes in raw materials. For example, the substrate may be prepared in batches that may be enough for 4 batch runs, necessitating the use of two batches of raw materials to run the eight experiments of the 23 factorial design of the fermentation example. The experimental design can be arranged in two blocks of four runs to minimize the effect of variations due to two different batches of substrate. If runs 1, 4, 6, 7 use one substrate batch, and runs 2, 3, 5, 8 use the second substrate batch, two data points from each substrate batch are used in the computation of the main effects. This eliminates the additive effect associated with substrate batches from each main effect. There is a tradeoff in this experimental design. The RTS interaction and the experiments using a specific substrate batch are confounded (Table 3.4). All experiments with one of the substrate batches correspond to experiments where RTS is —, and all experiments with the other substrate batch correspond to RTS being +. Therefore, one cannot estimate the effect of the three-factor interaction separately from the effect of substrate batch change. Fortunately, the three-factor interaction is usually less important than the main effect and the two-factor interactions which are measured more precisely bv this design.

The concept of confounding is discussed further in the section on fractional factorial design. More detailed treatment of blocking and confounding is available [78].

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