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ANOVA caluculation in DOE

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  • #37472

    ROSS
    Member

    Hi All: Pls see the DOE design as belowing(Random data): Full Factorial DesignFactors: 4 Base Design: 4, 16 Runs: 34 Replicates: 2 Blocks: none Center pts (total): 2 And the ANOVA is as belowing: Analysis of Variance for y (coded units)Source DF Seq SS Adj SS Adj MS F PMain Effects 4 5.242 5.242 1.3105 2.20 0.1022-Way Interactions 6 5.003 5.003 0.8338 1.40 0.259Curvature 1 3.447 3.447 3.4470 5.78 0.025Residual Error 22 13.110 13.110 0.5959 Lack of Fit 5 3.214 3.214 0.6429 1.10 0.394 Pure Error 17 9.896 9.896 0.5821Total 33 26.802 Can experts on it tell me the detail clculation method about the ANOVA in DOE? Thanks very much! It is urgent to me, thanks again. If you have some samples for it, pls send to [email protected]

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    #110469

    ROSS
    Member

    Hi:
       Can some experts who has experiments on it help me?
      Tks!

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    #110470

    Robert Butler
    Participant

         The interpretation of your ANOVA is as follows:
      Everything in the printout you provided is being compared to the pure error.  The F values are computed by taking the ratio of the pure error adjusted mean square to that of the adujsted mean squares of the other terms.  Based on what you provided your initial analysis is saying nothing is significant except the curvature.  From what you have provided you cannot tell which variable(s) exhibited curvature-only that one or more of them did. 
     

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    #110475

    ROSS
    Member

    Robert :
       Thanks for your feedback!
      But I need is not for the interpretation  but the detail clculation method about the ANOVA in DOE. Can you help me? My emaill address [email protected] .
    Tks!

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    #110493

    Robert Butler
    Participant

    The details of the calculations go on for pages and I don’t know of any way to summarize them in a form short enough for a posting.  Chapter 9 in Applied Regression Analysis, 2nd Edition, Draper and Smith is titled “Multiple Regression Applied to Analysis of Variance Problems” (pp.423-453) is an excellent discussion of the issue.
    For one-way ANOVA Chapter 10 of Statistical Theory and Methodology in Science and Engineering by Brownlee (pp.309-330) is very good and while it will not give you the equations for a multiple way ANOVA it does give you an excellent understanding of the concepts involved.
      As an aside, the printout of your problem concerns me.  While I obviously don’t know the particulars of your problem and the thought you put into it I would offer the following:
      1. The only reason you do not have lack-of-fit is because you included a generic term for curvature.
      2. Curvature is the only significant effect.
      3. The fact that you included center points suggests you suspected their might be curvature.
      4. You should not have had to wait for the completion of 34 experiments before you discovered this.
      At the very latest, you should have run an analysis of your data after you had completed the first replicate and the two center points.  This analysis would have given you all of the information you now posess but with a lot fewer experiments.  A better approach would have been to have run an analysis for the mains after you had completed a half replicate and the two center points.  If you had discoverd the importance of the curvature you could have stopped, revisited your issues, and changed the design to focus on the curvilinear behavior of the various X’s.

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    #110524

    ROSS
    Member

    Robert:
      Thanks for your help very much!
      And can you paste your email address or send email to me(tonysun[email protected]), I have some sample about ANOVA calculation and want to discuss with you.
      Tks!

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    #111148

    Jeggy
    Participant

    Hi
    by the equation SS=(contrast)^2/8*n
    n is replicate number
    you should be able to find SS
    but as you aware that minitab mix all the main effects into one factor.
    And all 2-way interaction into one factor.
    Any experts know how to seperate them?
    like ANOVA below
    Source   DF  SS  MS  F
    A      1   …
    B      1
    C     1
    AB    1
    AC     1
    BC    1
    ABC     1
     

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