Excel fractional factorial designs

The fractional design has an important characteristic. Its contrasts do not miK main effects with interaction effects involving two factors, but with interaction effects involving three factors, which in principle should be less significant. If these interaction effects are really negligible, the contrasts wiU furnish excellent approximations to the main effects calculated from the frill factorial. We should have, for example, I2 =l = 2. In general, we expect that Ij = IJ = J, where J stands for any main effect. 

Four of the runs in Table 4.9 are identical to runs in Table 4.6. The responses for these runs are the same in both tables and represent real values. The other four runs have level combinations for which the experiments had not been performed. Their response values are simulations obtained from the experimental data in Table 4.6. The calculated contrasts are also shown in Table 4.9, where we can observe that their values are in excellent agreement with the estimates of the average and the main effects determined from the 2y design (Table 4.7). Analyzing the results of the 2 quarter-fraction, which would be obtained in the initial stage of the investigation, the research workers could decide if they should perform more runs to arrive at a half-fraction or even the 2 complete factorial, if they should introduce new factors in place of the 1 and 5 variables (which appear to have little influence on the response), or even if they woifld rather change the levels of the variables. ... 

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