DOE – Balanced? or Unbalanced Designs?

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    B W Jones

    DOE – Balanced? or Unbalanced Designs?   this is a concern, question and / or issue that’s arisen from our software evaluations.  Good? Bad? or just right?
    Also, should the software alert the user an unbalanced design is being created? used? and define the dangers of such?
    Feedback from this knowledgable community would be most helpful!
    Thanks – Wendell Jones


    Robert Butler

      There are two advantages to balanced designs.
      1. If the sample sizes are equal the test statistic is relatively insensitive to small deviations from the assumption of equal variances for the treatments.
      2. The power of the test is maximized ifthe samples are of equal size.
      While balanced designs are certainly desireable the fact is that you will find numerous situations where it will not be possible to use a balanced design. Indeed, if you do enough design work, the simple circumstance of the complete failure of one of the design points in an otherwise balanced design (with no chance for the repetition of the experiment) will force you to deal with an unbalanced situation. 
      From the standpoint of software selection I would want to make sure that the software could build and analyze unbalanced designs.  I would also want to make sure that the package could analyze my data if I had a failure of one or more of my design points. Rather than depending on machine generated warnings I would make sure that anyone attempting to use a computer to generate a design either have the training necessary to understand the issues surrounding design choice or have immediate access to someone who does. 


    John Noguera

    I concur with Robert, but would add that VIF score should be included (with a clear explanation linking score to degree of multicollinearity).
    Any relation to Brad Jones?

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