Embedded full factorials

The appearance of embedded full factorials as a result of the inertness of one or more of the variables studied may occur in any factorial design. Fig. 4.3 illustrates the reason, using as an example the 2fb fractional factorial design with signs defined by the relation 3 = 12. If we eliminate... 

The first-order design embedded in Table 1, 2, is an example of a full factorial design— it employs all combinations of the two level variations of each independent variable, three in this example. The number of experiments of the full factorial designs increases exponentially with the number of independent variables, namely 2. For instance, the first-order full factorial design with 10 variables would require 10 computer runs and the second-order design would require even more. 

Table 2 is a half-fraction of a full 2 design. Looking carefully at these experiments one can see that the combination of each set of three variables, for example B, C, and D. constitutes a full 2 design. One says then that the full factorial for By C, and D is embedded in the half-fraction factorial design. This also means that, if D is found to be unimportant, one can interpret the experiment as a full factorial design for factors A, B, and C without any confounding between interactions of the remaining factors. 

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