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Blocking in 2-level factorial

Discussion in 'DOE - Design of Experiments' started by Sumpan W., Jul 12, 2017.

  1. Sumpan W.

    Sumpan W. New Member

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    I want to know what if the block effect is significant in 2-level factorial experiment. I just know that the block will be excluded from the model if its effect is insignificant resulting in a reduced model to be obtained. On the other hand, I haven't known what to do if the block is significant. Is the model including block and factors be valid for use? Can anybody kindly share your knowledge/idea/comment for the issue?
     
  2. Bev D

    Bev D Moderator Staff Member

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    The best way is to plot your results (individual data points not just the averages) in main effect plots. Depending on which software you are using this may be an option or you may have to do it 'manually'. JMP has a multi-variate plot function.
    Also most DoE software have a summary statistics output that will display the p-values of reach factor including the blocking factor(s).

    I strongly recommend that you learn how to plot your results and interpret them before 'trusting' any statistical software modeling...a great book to get started with this is: Quality improvement through planned experimentation by Moen, Nolan and Roland.
     
  3. Sumpan W.

    Sumpan W. New Member

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    Thank you, Bev, for your reply. I use Minitab, usually. Plotting according to you is not difficult but I don't get how it helps. My question is, assuming significant block effect, should the model with block and other significant terms be valid for use? Technically, blocking factor is not a focus for an experiment, just a factor whose effect need to be blocked for the precision of the experiment result. So, in my opinion, the block should not be included in the final model although it's proved significant.
    Using Minitab 16, coefficients for not only focal effect terms but also block are shown in analysis result for the model. I have never seen any example of 2-level factorial with significant block in text books or on websites to show what the conclusion is eventually. Therefore, I'm not sure what I should conclude and do for the next in such case.
    Anyway, with Minitab 17, I found that the final model without block (in spite of significance) is given as well with a note "Equation averaged over blocks." I also copy my example result obtained from Minitab 17 to show you for reference below, please take a look and kindly get back to me with your comment. Hopefully, I do not trouble you too much.

    Results for: 2k fact with blk.mtw

    Factorial Regression: Response versus Blocks, A, B, C, D

    Analysis of Variance

    Source DF Adj SS Adj MS F-Value P-Value
    Model 7 4726.25 675.18 63.17 0.000

    Blocks 1 72.25 72.25 6.76 0.032
    Linear 4 3769.50 942.38 88.18 0.000
    A 1 342.25 342.25 32.02 0.000
    B 1 4.00 4.00 0.37 0.558
    C 1 1.00 1.00 0.09 0.767
    D 1 3422.25 3422.25 320.21 0.000
    2-Way Interactions 2 884.50 442.25 41.38 0.000
    A*D 1 812.25 812.25 76.00 0.000
    B*C 1 72.25 72.25 6.76 0.032
    Error 8 85.50 10.69
    Total 15 4811.75


    Model Summary

    S R-sq R-sq(adj) R-sq(pred)
    3.26917 98.22% 96.67% 92.89%


    Coded Coefficients

    Term Effect Coef SE Coef T-Value P-Value VIF
    Constant 26.625 0.817 32.58 0.000
    Blocks

    1 2.125 0.817 2.60 0.032 1.00
    A -9.250 -4.625 0.817 -5.66 0.000 1.00
    B 1.000 0.500 0.817 0.61 0.558 1.00
    C 0.500 0.250 0.817 0.31 0.767 1.00
    D 29.250 14.625 0.817 17.89 0.000 1.00
    A*D -14.250 -7.125 0.817 -8.72 0.000 1.00
    B*C -4.250 -2.125 0.817 -2.60 0.032 1.00


    Regression Equation in Uncoded Units

    Response = 26.625 - 4.625 A + 0.500 B + 0.250 C + 14.625 D - 7.125 A*D - 2.125 B*C

    Equation averaged over blocks.
     
  4. Bev D

    Bev D Moderator Staff Member

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    If a blocked factor is significant it may have practical importance in the model. It really depends on what the blocked factor is. The key to successful experimentation does not lie in our ability to crunch numbers through statistical software - it lies in our ability to understand what is actually happening. The plot is ten thousand times more insightful than the statististical output. The design of the study and our scientific knowledge of the system is one hundred thousand times more important than the statistical output. While I realize that many people are seduced by the seeming simplicity of the pure statistical calculations, the calculation of mathematical formulas is no substitute for thinking. I cannot provide any advice on how to develop a proper model unless I understand what the process is, what the factors are and how the process behaves naturally and the study design. I also need to see the plots of the data.

    I'm sure others can dissect the statistical table (I can too but I refuse to as it is not the important part of your study) but it will only provide academic interpretation of mathematical numbers not insight to what you need to do with your process.

    I have several articles that address this topic in the resources tab of this forum. I recommend that you particularly read "profound statistical concepts" as it does include a case study where data was blocked as well as examples of the considerations I mention in this post. You will find examples of blocking in the book I mentioned. I also recommend that you read Deming's article "On Probablity as a Basis for Action". It is free and can be easily found with a simple Internet search for the title...
     
    Miner and Atul Khandekar like this.
  5. Miner

    Miner Moderator Staff Member

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    Can you provide more information regarding context? On what specifically did you block? In some cases the blocking variable may be fixed and you can use it in your model. For example, you blocked on a parallel process stream. While you could investigate why the streams are different, you might also accept that they are different and adjust accordingly.

    In other cases the blocking variable might be random (e.g., day of week), and you cannot use that in your model, but must now determine which lurking variable made day of week significant. Once you identify that factor, include it in your model in place of the block.
     

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