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DOE: Reducing the Model

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  • #38052

    Rainman
    Participant

    When we reduce the model in a DOE, we cannot take out an insignificant main effect if that main effect is part of a significant interaction that we are leaving in.
    If we have a significant three way interaction that we are leaving in the model, say A*B*C, do we have to also leave in all the contained two way interations (A*B, A*C, B*C) even if they are not significant?  Obviously all three of the main effects would have to be left in.

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    #113376

    Robert Butler
    Participant

    While there is a school of thought that insists you must keep an insignificant main effect in a model when an interaction involving that effect is significant there is also a school of thought that disagrees with this practice. 
      With the exception of the issues of full and reduced models in mixture designs, I prefer the second method so my answer to your question is keep only those terms that are significant and disregard the rest.

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    #113717

    melvin
    Participant

    Coming from the opposite school of thought – I can’t see ignoring the hierarchy of variables, i.e., leave the A, B, C, AB, BC, and AC in.
    If you make necessary interaction plots, they clearly indicate importance of the variables.
    Bob
     

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    #113729

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                     
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113730

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                      
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113731

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                       
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113732

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                        
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113733

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                         
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113734

    Paddy
    Participant

    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B                          
     
    .   If A*B*C turns out to be statistically significant, then all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, if A*B was insignificant is should be removed.   A*B is not a sub-set of A*B*C.
    Once the model has been reduced

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    #113735

    Paddy
    Participant

    Sorry about all the posts – had some problems when I was writing it!
    The answer is simply no – you do not have to keep insignificant interactions in the model.
    Let’s say you are using Minitab to analyse a 3-factor (A, B & C) design with teh following results:
    Factor       p-value
    A              0.98
    B               0.54
    C              0.03
    A*B          0.99
    A*C          0.33
    B*C          0.76
    A*B*C     0.00               
    A*B*C turns out to be statistically significant, so all factors A, B and C have to be retained in the model even if they are not signficant.   This is because Minitab needs them to be included if it is to calculate the 3-way interaction.   However, all the 2-way interactions are insignificant and can be removed.   The 2-ways are not sub-sets of A*B*C.
    Once the model has been reduced we’d end up with the following in Minitab:
    A              0.98
    B               0.54
    C              0.03
    A*B*C     0.00 
    A and B are not significant but are kept in to allow A*B*C to be determined.
    Now, when you build the Y=f(x) model from the coefficients, you only use the significant terms:
    Y = Constant + Ccoefficicnet*C + ABCcoefficient*A*B*C
    What the practical significance of each of the terms is, is another question.
    I hope this helps and again, sorry for all the incomplete posts I logged.
    Paddy

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    #113748

    Mikel
    Member

    Your answer makes absolutely no sense. Try explaining why.

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    #113751

    Mikel
    Member

    Go try that in Minitab 14 – it does not work.
    And again why, except to get minitab to do the analysis, do you want to include insignificant mains of 2-ways? It is not possible for a coefficient to be equal to 0?

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    #113756

    Paddy
    Participant

    Stan,
    I don’t
    62713

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    #113757

    Paddy
    Participant

    Stan,
    I don’t follow you.   Please note that you responded to an incomplete message from me.   If you want to add your insight, then please respond to message 62713 which was my complete one.
    Thanks

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    #113761

    Mikel
    Member

    Read the message – no inisght.
    Minitab 14 does not work the way you say – cannot remove 2-ways and leave 3-ways.
    Modeling does not require leaving mains or 2-ways.

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    #113766

    Paddy
    Participant

    Just did it in Minitab 14.1 and it worked fine!

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    #113771

    Mikel
    Member

    In minitab 14.1, I have a 3 factor experiement, where I have a statistically significant 3-way interaction and some insignificant 2-way interaction. If I try to take 1,2 , or all 3 of the 2-ways out, I get a message that says
    —————————MINITAB—————————General factorial model is non-hierarchical.—————————OK   —————————

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    #113773

    Paddy
    Participant

    Strange.   I just repeated the test on a 3 factor DOE (full factorial) with only the 3-way interaction significant.   I can take out any or all the 2-ways without any complaint from MTB.   I’ve never seen the message you mention.

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    #113780

    BeenThereDoneThat
    Participant

    Include the main effects – don’t be a cowboy statistician.This debate, loosely called ‘school of thought’ is the battle of the statisticians vs. the cowboys. Six Sigma is about removing the ‘seat of the pants’ philosophy and replacing it with solid, data based methodology.’A lady declares that by tasting a cup of tea made with milk she can discriminate whether the milk or the tea infusion was first added to the cup. We will consider the problem of designing an experiment by means of which this assertion can be tested.’And so begins R.A. Fisher’s 1935 book, ‘The Design of Experiments’Whan analyzing the results from a DOE, the essential methodology is the ANOVA table. Fisher, Pearson and Gossett enjoyed endless debates in the literature about the ‘degrees of freedom’ – an essential concept in assessing the expected size of a purported effect for purely random data. The F-test of the ANOVA table and others like it always consider the size of a posited effect against what would be expected for random data. As with any model, the validity of the necessary assumptions of ANOVA using residual plots is required.The original general methodology of DOE has been extended to included extremely complex designs. There may be imposed restrictions for totals of components to be 100%. The response may be non-linear. There may be uncontrolled, but measurable ‘noise’ factors.When starting to using the simpler DOE designs, the experimenter can take shortcuts when constructing the model that end up making little, if any, practical difference to the numerical results. Neglecting main effects where an interaction term is found to be significant is an example of such a short cut. This should not be done as a rule. Most statistical software will either diallow the model or give the user a warning.When an interaction term is included in the model, and the corresponding main effects are not, the number of degrees of freedom in the ANOVA table is altered. This will usually make little practical difference in the numerical results, but is contributing to miscalculations of the mean-square error(adjusted). The software will blindly calculate a p-value that can be misleading.On the practical side, what you would be proposing is that two supposedly independent, random factors are somehow locked together to produce a significant effect. Most process owners would question the assumption and look for a lurking variable.Since the mean-square error(adjusted) of the error term is altered, this effects the p-values of every other term in your model. If the design is a fractional factorial, I would suspect that the graphical output of your statistical software has labeled an interaction with only one of the possible two-way interactions. Examining the main effects will tell you which one is the most likely interaction that is causing the effect. MINITAB will print the full interaction table if you choose the option. This topic is covered in well in the article by Shree Pandis https://www.isixsigma.com/library/content/c020429a.asp.This entire topic is termed the ‘hierarchical model’ in the DOE discipline. Accepting a non-hierarchical model can be done and will probably not mislead you, but it is best to use the tools in the correct, mathematical manner. One day you will be faced with a very complex model. This is not the time to learn how to use the tool correctly.Stan:
    If you have a main effect for A of zero with a significant AB effect, there is most likely a lurking variable that was missed. The conclusion from the DOE will be that you can explain the data, but not the experimental reality. Social scientists deal with this kind of situation constantly when they gather data that is observable and make conclusions based on unobservable, lurking factors such as ’empathy’ or ‘compassion’ by conducting factor analysis. Paddy:
    Correct – when you have ABC, include A, B, and C. You usually don’t need AB, BC, and AC. Some partial factorial design might give you results that don’t make practical sense, but it is unlikely and depends on the design used.

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    #113784

    Mikel
    Member

    Nonsense, and don’t call me a cowboy again. Those are the Arizona non-Metrosexual guys.
    There is a difference between analysis and modeling. Minitab even tells you so and uses multiple regression for the modeling. And this nonsense about a lurking variable – where do you come up with this stuff? By definition, a non significant variable has a coefficient of 0 (or at least you can’t prove it does not). Use step wise regression when deciding on your final model, your adjusted r squared being the determining factor.

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    #113787

    BeenThereDoneThat
    Participant

    Nonsense? I’m not sure what you mean.I agree about the difference between analysis and modeling. I see analysis as the part from the mathematicians talking about tasting tea. The modeling part is more the practical side – what makes sense in the light of the experimental setup and the real situation.MINITAB is great software and defaults are well designed to make the software a good practical tool, but you can still run a t-test that violates the essential assumptions of the test.This is not about the size of the coefficient – hence my point that this will make little practical difference to the model.Errors in the the number of degrees of freedom for alternate models will alter the mean-square-error, the p-values and r-factors, making Hamilton r-factor ratio tests a bit dicy. Stepwise regression is a bit of an art – not for people who are just learning DOE.When you leave the main effects in the model, you can’t go wrong. If you neglect them automatically you could miss something important. If you propose a model with a 3-way interaction without acknowledging the independence of the 3 variables, then you are proposing a situation where they are not independent – they are likely linked to a variable not included in the experiment or the model.I don’t like hand waving when it come to the maths.
    The cowboy metaphor was for fun and not directed at any active member of the forum, I’m glad someone picked up the reference to that well known…. what was his name?

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    #113791

    Ken Feldman
    Participant

    BTDT, does this mean you will be debating Stan on the issue of factors left in a DOE?  I believe Phil will be able to put together a fabulous event.  Vinny, with his rigorous PhD could be a judge along with Mr. Butler and the very wordy but kindly mjones.  Of course, you would have to submit a green paper first so the judges could evaluate your respective positions.  The winner would get one of the Stans’ Ford Motor products. Do you think Stan will accept your challenge?

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    #113798

    MudaSensei
    Participant

    What’s the dress code for this fabulous event?……..a 10 gallon J R Ewing hat with a COWBOY outfit?
    Oh, for refreshments……… I like my tea with the milk added at the end of infusion !!
    Is there a Bookie for this event…….Darth, are you taking any bets?

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    #113799

    BeenThereDoneThat
    Participant

    “I am disinclined to acquiesce to your request”Mathematics is not democratic. “…It means no.”P.S. Tea will be served where half the cups have milk first and the other half have tea first.

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    #113813

    Mikel
    Member

    I agree.

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    #113819

    Dayton
    Member

    Excellent.  With Phil planning, it will be a grand event.   I envision utilizing the card pack of famous dead mathematicians as models for wall and ceiling hangings reminiscent of the great dining hall at Hogwarts School of Wizardry and Witchcraft ala Harry Potter.  
     
    But, as a volunteer judge along with the erstwhile Mr. Butler and wordy but kind mjones, we will insist upon not merely dwelling upon a rather pedantic discussion of the significance and inclusion of various factorial components but an in depth series of Arrhenius equations using Boltzmann’s constant determining the life expectancy of the new Matrix Semiconductor write-once flash memory chip, Matrix 3-D Memory (3DM), when used in Mike Carnell’s PDA for the purposes of supporting patented algorithms applied in performing Six Sigma Black Belt 360 degree evaluations of South African diamond mining process design modalities based on a 1.5 Sigma shift in either drill bit alignments or employee body cavity searches.   Calculation and reference materials must be limited to: 1.) a wide-lined elementary school writing/printing pad (white with light blue lines) 2.) 3 each number 2 pencils  3.) reams of printed isixsigma.com discussion of the appropriateness of the 1.5 sigma shift (not to exceed 27 pounds and or two cubic feet)  and 4.) Mike Carnell’s White Paper on Utilizing Patented Algorithms to Support and Drive Effective 360 Degree Evaluations of Academically Trained Six Sigma Black Belts.
     
    Yours in the continued support of effective Six Sigma rhetoric and debate,
     Vinny

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    #113820

    Mikel
    Member

    Perfect as long as it is somewhere warm that also has warm, clear, salty water (sorry Mike, that leaves Galveston out).
    Could we invite Reigle as the guest buffoon?

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    #113822

    Ken Feldman
    Participant

    Vinny, excellent contribution and recommendations.  To assure that Stan doesn’t back out again, if the Judges approve, if BTDT is Ok, I would be pleased to offer the VaderYacht as the site of the debate.  We can anchor off of the Fl Keys or any nearby Bahama Island.  Guest Buffoons are invited and each side can pick one.  We could even have a Consultant Showcase whereby famous SS consultants can hawk their wares.  This might help defray the expenses.  Or possibly we can get BOA to fund it.  BTW, who will be attending the SS conference next week in Miami?  Welch is supposed to be speaking as well as Jones from BOA.  Keep a close eye on Jones’ nose as he gives his speech but don’t stand too close or in front of him unless you want to get skewered. 
    Frankly, I am not optimistic.  BTDT seems to be a big talker but without a stick.  Stan has a propensity for talk but no action.  Possibly the combined Karma of the Forum can convince them to make this a reality. 

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    #113823

    Dayton
    Member

    Hmmm….. it’s a thought, but, no, I’m afraid that I must insist upon being the only buffoon.  
     
    Reigle may certainly attend and play the lute off to the side singing sweetly the praises of Dr. Harry as we meander in and out of the 1.5 Sigma shift elements of the debate. 
     
    Warm, clear salty water – good, good, but how to get Mike there, … again hmmmm…  Well.., I once took a sabbatical in Florida and floated the state from pool bar to pool bar swimming in Margaritas, so maybe there’s opportunity for Phil to kill many bird’s with one well planned debate stone.
     Vinny  

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    #113824

    Ken Feldman
    Participant

    Here is a final incentive for you Vinny.  Miami is the headquarters for Burger King and since I have a connection there, we can have a planned Stealing Spree where attendees can go around, with BK’s approval, and swipe Sponge Bob balloons from the top of local restaurants.  Phil has contacted me and indicated that he has made arrangements with Home Depot to provide spray paint so we can repaint the VaderYacht.  Unfortunately, Dr. Barry of the Bench is currently traveling in Africa and will be unavailable to dispense the mood enhancers which will be necessary to make the Debate comprehensible.  As a last gesture, Mrs. Darth has offered to let Attendees tour her jail and meet her customers.  Lunch is planned there after the tour.  A Taser demo is planned for those wanting to try it out on Stans.

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    #113827

    Dayton
    Member

    I’m in and looking forward to a weekend of flamboyant Six Sigma dogma forming intellectual debauchery.Vinny

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    #113832

    Mikel
    Member

    Thanks for the offer of the tasers, and while it does sound stimulating, I am an old school guy who prefers stimulates of the liquid, pill, or mushroom form (legality of course is a matter of opinion and is optional especially if this is to take place in South Florida).

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    #113876

    DrSeuss
    Participant

    Rainman,
    The beauty of the DOE is that if you started your analysis with an orthogonal array, namely, an arrangement of factor combinations that was established using typical software, such as, Minitab; then the independence of your factors and interactions is guaranteed.  Basically, each main effect and interaction effect is independent of each other (one does not depend on the others being significant or not).  Keep the main effects and 3-way interaction and kill the insignificant 2-ways.

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