Separation of specific effects

Let us start with a simple case. We shall use the design above as an example. It was suspected that the alias + bj was important. It is not possible to know if either or both of the terms are important. Everywhere in the design above, the variation of 13 is always the same as the variation of 24. To be able to separate the confounded effects, we must therefore run experiments in which the variation of 13 is different from the variation of 24. This can be achieved in two experimental runs for which the following relation applies 

There are many possible settings for which the above relation applies. One example of such variable settings would be as shown on the next page. 

The experiment with all variables at the (+l)-level has already been run, Exp. no 8. It will be necessary to run one complementary experiment. These two experiments define the smallest possible fractional factorial design, 2 . It is seen that the following confounding pattern is obtained 

From this small design the following estimates can be obtained 

As estimates of b, b.. -, and b are already known from the previous design, the two interaction effects can now be estimated. 

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