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3k FULL FACTORIAL DESIGN quadratic interactions

Discussion in 'DOE - Design of Experiments' started by maxim, Apr 20, 2023.

  1. maxim

    maxim New Member

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    If i make a 3k FULL FACTORIAL DESIGN, i get quadratic interactions. What is it suppost to be? (One effect cant interact with himself). And Why do i need this. It is just somethink you have to do, to get your matrix and equation?

    Here some example:
    upload_2023-4-20_15-49-57.png
     
    maxim, Apr 20, 2023
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  2. Miner

    Miner Moderator Staff Member

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    I think these are simple quadratic terms, not quadratic interactions. Either way, you cannot add them to this experiment as a 3^k factorial design.
    Consider this: You have 9 runs, which give you 9-1=8 degrees of freedom. You have two factors with 3 levels each. Each factor has 3-1=2 degrees of freedom, so the factors consume 4 degrees of freedom. You have a 2-way interaction, which consumes the remaining degrees of freedom (2x2=4). You started with 8 df - 4 df (factors) - 4 df (interaction) = 0 df remaining. This is a fully saturated design, which means that you cannot even analyze this without adding replicates or removing the 2-way interaction from the model. There is no way to add quadratic terms without adding replicates.

    If this were a poorly constructed face-centered response surface design (RSM), you could add quadratic terms to it, but it would probably be underpowered.
     
    Miner, Apr 20, 2023
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    maxim likes this.