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We're piloting a multiple variable testing program at my company. For starters, we're looking at a test with 3 factors (a, b, c), 2 levels (-1,+1) each. Based on research from several standard texts, we picked the test cells as

  1. (1)
  2. bc
  3. ac
  4. ab

The generator is c=ab and defining relation is I=abc

My questions:

  1. How the balanced fractional design above different from just having a control (-1), and 3 test cells a, b, c? If in the design above all 2nd and 3rd order interactions are confounded with main effects, then what do we gain from it information-wise vs. the simpler design that just tests the main effects individually?

  2. What are some techniques to analyze the results? The answer that we ultimately want to get to is- what is the optimal combination of factors a, b and to maximize the response variable y?

Thanks

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