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Math Help - A fractional factorial design

  1. #1
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    A fractional factorial design

    Hi,

    I recently attempted an experimental set-up according to a fractional factorial design. At first, the idea was that I'd investigate 5 factors on two levels and I designed the experiment in accordance with a 2^5-2 design to keep the experiments limited.

    However, along the way I excluded one factor but forgot to change my plan, I should have used a 2^4-1 plan but instead hang on to the old 2^5-2 plan - changing only 4 factors.

    * Now, realizing that my data is not orthogonal when analyzed as a 2^4-1, should I analyse it as was it a 2^5-2 instead?
    * What happens if my design isn't orthogonal?

    (Factors A, B and C were according to yates normal order while the fourth factor is confounded with AB instead of ABC.)

    Happy for some input on this, I seldom perform these kinds of tests...
    Cheers!
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  2. #2
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    Oct 2009
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    Quote Originally Posted by Harald View Post
    Hi,

    I recently attempted an experimental set-up according to a fractional factorial design. At first, the idea was that I'd investigate 5 factors on two levels and I designed the experiment in accordance with a 2^5-2 design to keep the experiments limited.

    However, along the way I excluded one factor but forgot to change my plan, I should have used a 2^4-1 plan but instead hang on to the old 2^5-2 plan - changing only 4 factors.

    * Now, realizing that my data is not orthogonal when analyzed as a 2^4-1, should I analyse it as was it a 2^5-2 instead?
    * What happens if my design isn't orthogonal?

    (Factors A, B and C were according to yates normal order while the fourth factor is confounded with AB instead of ABC.)

    Happy for some input on this, I seldom perform these kinds of tests...
    Cheers!
    Interesting question. I would be highly surprised if the effects aren't orthogonal; that isn't the problem. The problem is that fractional factorial designs confound effects, and that a 2^5-2 and a 2^4-1 have (presumably) different confounding structures.

    My intuition is that, if you look at the confounding relationship of the 2^5-2 and cross out all the terms involving the factor that you dropped then you should have the new confounding relationships. It may or may not be the confounding structure of some 2^4-1. I don't know off the top of my head, but it wouldn't surprise me either way. You may have inadvertently ended up confounding terms that you didn't need to. There's also a chance that you can now estimate some things you couldn't in the 2^5-2.

    If this is a serious experiment, I would consult a statistician. I'm far from an expert on fractional factorial designs.
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