Analysis for a CFE 2 Plan

When we use a CFE 2 plan to determine the interaction effects, we introduce associated variances that can be easily used to produce answers to the aspects concerning the interaction between the factors of the process [5.33, 5.34]. 

In order to obtain the effect on the response values of factor A when it varies from level Aj to A2, we must extract the results obtained with Aj from the results obtained with A2. According to Table 5.50, we can write the following relations  

It is easy to observe that we subtract all results from the sum of responses that contain symbol a . By the same procedure, we can write the effect of factors B and C. It results in  

The interaction effect AB is obtained by subtracting the effect of A at the level Bj from the effect of factor A at level B2. This is written mathematically as follows  

The remaining interaction effects AC and BC are written using the same definition. Then, we obtain the following relations  

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