# Attention DOE Experts!!!!

Six Sigma – iSixSigma Forums Old Forums General Attention DOE Experts!!!!

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• #38077

Darth
Participant

If I want to reduce my prediction equation what do I do?  Here is the situation for a 2 level 3 factor experiment:
1.  I have some significant and some nonsignificant Main effects
2.  I have some significant and some nonsignificant two way interactions
3.  I have a significant 3 way interaction
I know that if I have a significant 2 way interaction, I have to keep the relevant nonsignificant main effects in the formula.  But, if I have a significant 3 way interaction, what do I have to keep in the formula?  All relevant nonsignificant main effects?  All nonsignificant two way interactions?  What?

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#113501

Dayton
Member

Is this homework?   Are you getting certified or something?   The forums not here to do your class work for you.  Youll never learn anything like this.  Sorry to get tough with you but youll thank me later when you can do this on your own.   Theres something about teaching a man to cut bait and hes learned a trade for life, or something like thatVinny

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#113502

Juggler
Participant

Usually I find that three factor interactions are not real.  Try reanalyzing your data using only main effects and two factor interactions.

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#113505

Anne
Participant

I do agree with Vinny.
You need to take a DOE Course, you may want to look into Air Academy Associates, they have an excellent DOE seminar and software DOE Pro.
Good Luck
Anne

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#113507

Thaly
Member

I agree with juggler. I’d recheck my numbers if I had a situation like that. The most likely situation is that the noise was very high during the experiment. Try doing more replicates or seprating the factor levels further.
But to answer your question, you’d have to include all the non-significant main effects that contribute to the interaction efect (A,B,C = ABC)

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#113508

Mike Carnell
Participant

Darth,
Have you cheched the size of the effect?
Regards,
Mike

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#113515

Darth
Participant

So far, some pretty lousy answers coupled with a few insults.  It is a hypothetical teaching question.  Somebody asked what if they have a real 3 way interaction, how do they handle the model reduction.  It’s an easy answer for significant 2 way interactions….you include the significant and insignificant main effects that are relevant.  What do you do if you have a 3 way interaction?  It is obvious you will include the significant and insignificant main effects but do you also include the two way interactions that contain the factors?  Don’t tell me to take a class or look at my data!!  Does anybody have the expertise to provide an answer?   Thanks.

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#113517

Dayton
Member

Sounds like somebodys had a tough day

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#113518

Solo
Member

Dr.,
Too bad this is just a hypothetical, more details on the context of these interactions might be helpfull…
However, if the factor interactions have been determined to be insignificant on the output, what would possibly make them significant enough to include them upon model reduction?  I would have to guess nothing would, as long as all factors and interactions that have been determined significant are included, and there is high confidence in those determinations.  Would you agree with this logic?
-Solo

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#113519

Dayton
Member

Are you using loglinear modeling?

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#113520

Darth
Participant

Vinny, the day wasn’t too bad.  The frustration is that I have tried to contribute to others on this Forum but when I need a little help, I am told to go take a class and read a book.  I was hoping I deserved a little bit more help.
Here is the question rephrased again:
I have factors A, B and C.  After the experiment I find A and B are significant, C is not significant but AxC is significant.  My model would include A, B, C and AxC, correct?  I include the nonsignificant C in the model because the 2 way is significant and I need the C to remain.  Correct so far????  It’s a rule as far as I am concerned.
Now to extend this further, in another experiment, I find A and B are significant, C is not significant, AxC is significant but BxC and AxB are not but AxBxC is significant.  What do I include in the model?  Obviously A, B and C since the 3 way is significant.  Of course AxC since it is significant.  But what about BxC and AxB since they contain terms in the 3 way.  That is the question.  I am looking for a definitive rule if one exists not guesses and supposition.  I have to believe there is some guideline that someone on this Forum knows about.

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#113521

Robert Butler
Participant

Earlier this week Rainman asked the same question under the thread “Reducing the Model.  The answer depends on which school of thought is appropriate for the circumstances of your model reduction efforts
The hierarchical school of thought insists if you have an interaction you must include all of the main effects involved in the interaction.  In this case, for a significant 3 way interaction you would include the three mains and for a 2 way you would include the two mains.  To the best of my knowledge the hierarchical approach stops at the inclusion of insignificant main effects. Darth on Friday’s question is reasonable and if the hierarchical view was consistent it should demand the inclusion of all insignificant mains and all insignificant 2 ways buried in a significant 3 way interaction.
The other school of though is to include only those terms that test out as significant after the model is reduced using the methods of stepwise regression (backward elimination and forward selection with replacement).  Thus if a main effect is not significant and a 2 or 3 way interaction involving that term is then only the interaction is included in the final model.
Both schools have their defenders and detractors. As with so many things in the world of statistical analysis the choice of which school to follow is driven by the object and the needs of your efforts.  Outside of the world of mixture designs, including an insignificant main effect in conjunction with a significant interaction involving that term makes sense if the magnitude of the change induced in the process by the statistically insignificant main effect is physically important.  Otherwise you are wasting your time.  In the world of mixture designs the issues are a little more complex.
When the final model contains a 3 or 4 way interaction and when that model proves to be very good at predicting process behavior and useful for process control I’ve found the biggest problem has been one of interpretation in order to give the term physical meaning.  Sometimes my investigators have been able to give it meaning, sometimes further work has revealed the higher order interaction to be a mask for a lurking variable, and sometimes we have just accepted the resultant equation and moved on.  In those few instances where the last case has occurred the teams I’ve worked with went to great lengths to make sure anyone using the final model was aware of its shortcoming – namely our inability to give it physical meaning.

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#113522

Anonymous
Guest

Darth,
What resolution design did you use?
Andy

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#113523

Mikel
Member

Anne,
I agree with you that this Darth fellow needs to learn on his own – he is just leaving an environment where he never had to use sophisticated tools – but to suggest DOE lite from Air Academy? Why don’t you suggest something real like Dr. Box or Dr. Montgomery?
The methods taught by Air Academy are incorrect for things like analyzing standard deviation. Their treatment of sample size is offensive as well – they assume that the student is an idiot and their advice also leads to extremely large sample sizes compared to what is needed.
Mr. Darth, you might start by looking in your Minitab help menu for advice on hierarchical errors – or are just trying to get advice on your homework?

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#113524

Mikel
Member

My advice to you is to go to one of the real gurus in Six Sigma – someone like Stewart or Harry or George. ;-)
My vote is to leave all affected main and two way interactions in the model – that is the technically correct answer. However, when you look at the size of the coefficients for the mains and two ways (if they are insignificant) you will find they they have very little effect on the prediction.
By the way, the student that asks such a question should be told to focus on learning what is useful. The odds of ever encountering such a situation are not quite six sigma, but still very small.

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#113525

Mikel
Member

The same logic holds for three ways as it does for two ways.

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#113527

Darth
Participant

And by the way, any word from the missing Don Julio?

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#113528

Darth
Participant

Now that’s the type of answer I was looking for, thanks.  To tell the truth, Rainman was complaining to me that he felt he didn’t get adequate response to his post so I did him a favor and posted under my name.  I knew I would at least get a response from Stan :-).  Given your previous posts I have confidence in your response and appreciate it.

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#113529

Mikel
Member

We are striving for consistency aren’t we?Going to Mexico City in a few weeks. Any suggestions? Or better yet, join me and we can sample everything.

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#113532

Darth
Participant

Very tempting!!!!  But alas, I have a job now and must keep the nose to the grindstone.  Maybe I should have taken the other job offer :-).
How about trying to find PENCA AZUL ANEJO 750  if it isn’t too expensive.
Regards to Mrs. Stan, the little Stan/Stanette and Dog Stan….and don’t forget Babe of a Sister.

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#113533

Mikel
Member

Finish your homework yet? Anne will be checking up on you.
Remember your Air Academy matra – the sample size for everything is 17 – double that if you are interested in variation reduction.

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#113535

Sorour
Participant

Darth,
The

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#113536

Sorour
Participant

Darth,
The basic approach

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#113537

Sorour
Participant

Darth,
The basic approach use

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#113538

Sorour
Participant

Darth,
The easiest way to think about this is to ask yourself how are you going to control an ABC interaction, by using the A knob, B knob and C knob. Therefore they have have to be in the model so that you can use them. That’s the only reason why they have to stay in the model, its a practical one. leaving the 2 ways in has no practical use, although it might please the mathematicians amongst us.  Hope this helps.
Paul

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#113540

Dayton
Member

Darth,

Sorry about the smart-alecky beginning to this.  Had I believed that you really needed or were asking for help Id either have tried to come up with a logical response on the order of Robert Butlers or would have pretended not to have seen it if the answer eluded me.  I’ll try to be more in tune with your cries for help in the future. :-)

As Roberts response was logical and direct, are you saying his conclusion was not the first and only approach that you come up with on your own or one that you would have immediately offered to your class upon their posing the question?  (I’m still looking for the rule also.)
Vinny

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#113541

Rainman
Participant

Darth,
Thanks for stirring the pot on this and taking some abuse.  But then everyone needs abuse sometimes.
Thanks to the rest of the crew for a more complete discussion.  I had heard it both ways, I had seen it both ways, but now I feel I understand it better.
Rainman

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#113545

Darth
Participant

Vinny, I know I appear at times to be omnipotent but believe it or not, I don’t know everything.  Once in a while I do post a question for genuine help.  I will make it obvious in the post that I really need it so hopefully people will respond.

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#113546

DoubleJ
Participant

Where were you taught to keep main effects in any sort of model (prediction equation) if they are not significant but show up in higher order terms?  There is nothing wrong by leaving all the terms in the model but it is unnecessary to have any terms in a model other than ones that have a significant effect.  By definition they are insignificant and will not changes the prediction of the model.  If you have some practical experience running DOEs it is easy to leave all the terms in the model and compare it to the model that only has significant values, very little (significant) difference.   DoubleJ

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#113548

Mikel
Member

Paul,
I think your first three responses were better than this one. This is about as confusing an answer as I have seen and has no basis in logic or statistics.

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#113550

Darth
Participant

Since most of the responses indicated that is what is done, I wonder where we all learned it but you didn’t.

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#113552

Dayton
Member

Not omnipotent?  Next youll be saying that youre not omniscient, and I dont know how well handle that revelation.  Much worse than the quadrilateral Stans.
Vinny

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#113553

DoubleJ
Participant

Dearth:
So, you are satisfied with the correct answer via majority vote?  Im sure most people on this board also think nothing can travel at a speed greater than light in a vacuum but that doesnt make them right.  Anyway, the answer to your question appears to be inconsequential.  It doesnt sound like you actually plan on doing any sort of real analysis.  I only feel sorry for those you teach.

DoubleJ

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#113554

Robert Butler
Participant

This issue about the rule is interesting.  Way back when I was taking classes I had one professor who offered the thoughts of school #1 and one who offered the thoughts of school #2.  Until this exchange I really hadn’t paid any more attention to the differences.  After responding to Rainman I took some time during the following evenings to do some rummaging in the hopes of finding something more than a T.L.A.R. algorithm (That Looks About Right) with respect to the two choices. If they offered anything at all, the best the more modern texts (as in 1980’s-present modern) gave was a single sentence advocating one school or the other without providing proof.  Given the antiquity of the two approaches I hoped a check of my early texts (as in 1950’s – 1960’s early) would reveal something. They too, if they had anything to say, offered only single sentences espousing one school or the other.  Perhaps I’m not looking under the right heading or topic but I was unable to find any critical analysis of either point of view.
The best indirect discussion I was able to find was in Davies – The Design and Analysis of Industrial Experiments 2nd Edition pp.255 and 256.
pp. 255 “When an interaction is large the corresponding main effects cease to have much meaning. (In reference to a prior example involving a significant interaction and insignificant main effects) The existence of a large interaction means that the effect of one factor is markedly dependent on the level ofthe other, and when quoting the effect of one factor it is necessary to specify the level of the other. ….
When the interaction can be assumed negligible it may be inferred that the factors operate independently, and conclusions based on the significance or non-significance of the main effects may legitimately be drawn.”
pp. 256 “It is clear from the expectations that all main effects and interactions should be tested against the residual by the F-test; if F exceeds the tabulated value at the level of significance chosen, we conclude that the factor affects the response.  Note, however, that if AB is significant and A is not significant we cannot conclude that A has no effect. The existence of AB means that both A and B affect the response, but not independently. The non-existence of A simply means that A affects the respopnse in different ways at the various levels of B and that when its effect is averaged over the values of B used in the experiment the average effect is small. In quoting the effect of A it is thus necessary to state also the level of B, and vice versa.”
If indirect statements such as those above are all there is then it is certainly easy to see how the two different approaches to model building could arise.  If there is nothing more concrete than this the choice of which school of thought to follow would appear to be driven by nothing more than who-taught-you-what-when.
As I mentioned in a prior post, my personal preference is to only go with the significant effects and include non-significant ones only if by including them we are accounting for physically meaningful differences.

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#113555

Darth
Participant

As usual a meaningful and thought out response.  Thanks for taking the time to make it a little clearer or not depending on one’s point of view.

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#113557

Darth
Participant

Mr. Butler attempted to provide some support for his response.  Could you do likewise other than provide a stupid analogy, an inconsequential judgement and meaningless sympathy for my students?
Gracefully, Dearth

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#113558

Mikel
Member

The truth is that the hierarchical rule has to do with the analysis, not the prediction equation. When using a software like Minitab, if you disregard the main effects and two ways and just use the coefficients for the constant and the three way as is suggested, you get a different model than if you used mulitple regression and developed the prediction equation. The multiple regression equation, of course, is the better predictor.

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#113560

Mikel
Member

Please tell us how to develop the model that only has the significant factors included.

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#113561

Itu
Participant

Non-sense. The regression results assume independent factors and are unable to predict the interaction effects that exist in this example. The DOE model is superior in this case.

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#113562

Mikel
Member

You don’t know what you are talking about.

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#113563

BeenThereDoneThat
Participant

Statistical tests are all about calculating a signal/noise ratio. This test statistic is compared against a theoretical value based on the distribution of the sampling error. The test statistic could be an F value, a T value or otherwise. This methodology requires an accurate estimate of the pure, random error (noise).In a DOE, You must include all main effects for two-way and three-way interactions, even if they are not significant, because you need the correct number of degrees of freedom of the independent factors to calculate the number of degrees of freedom ‘left over’ to calculate the mean error – the ‘noise’ in the DOE. If you neglect the main effects when including a corresponding interaction term, the mean error will increase such that your p-values (the signal/noise ratio) on all the terms in the model will increase.If you do not include the main effects in the mathematical world, you may not be able to find some terms which are significant. In the physical world, you are proposing a situation where it it not possible to vary the two (or more) factors independently. Whether this makes sense will depend on the physical situation. If you were trying to convince me that this is the case, then I would like an experiment that proves the independence of the factors.When you are conducting partial factorial experiments, there is always a possibility that what appears to be a main effect is really a confounded higher order interaction, but it is rare. Consider the physical situation in light of the maths.I have often seen 3-way interactions, but including them in the mathematical model made little mathematical or practical difference in the resultant decisions. We has a case where the value of an option on a software package depended on the computer’s CPU speed, memory and number of simultaneous users.The central issue here is assessing the number of degrees of freedom for the error term in the ANOVA table. The question on degrees of freedom has been actively debated in the past by Sir R.A. Fisher and others in the Proc. Royal Soc. The debate is based on the number of choices in the physical world dictating what is done mathematically.The reason we use the statistical tests is to be able to defend decisions from the ‘seat of the pants’ stakeholders. I hope the reason the DOE was done in the first place was to accurately determine the interaction terms that have confused and clouded the simpler tests done in the past.If this problem was easy to solve, it would have been solved by now.

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#113564

Robert Butler
Participant

I think we are talking about two different parts of the same problem.  “The Rule” I was referring to (and the rule I thought Rainman and Darth were discussing) is as follows:
1. We have a full factorial design – for sake of arguement we will assume we can test for factors A and B and AB.
2. We set up the regression analysis with all possible terms included.
3. We run stepwise regression using backward elimination and forward selection with replacement allowing all terms in the model. If the design is complete, none of the horses have died, and a reasonable degree of orthogonality has been maintained, then both of these approaches should reduce to the same “final” model.
4. The “final” model says the significant factors are A,and AB.
5.  “The Rule”:  One school of thought insists the final model should be A and AB.  The other insists the final model should be A,B, and AB even though, when analyzed using the accepted methods of stepwise regression, B does not test out as significant.
My impression is that Stan and Beentheredonethat are talking about rules surrounding steps #2 and #3 and not “The Rule” of step #5.  If this is the case, I certainly agree – you have to have all of the terms present when you start your analysis – you will go wrong with great assurance if you don’t.

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#113579

Mikel
Member

I agree. My point was that there is a difference between the analysis and the prediction model. If we settle for the model that Minitab forces us into in Darth’s scenario, we need to know that there is a better model using stepwise regression.
It is easy to prove, so all that want to come back with the dogma you were taught, also come back with an example. Otherwise, I’m out of this one.
Darth – you did a nice job with your homework problem, but you have once again shown that the knowledge base is pretty shallow.

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#113610

Mark J. Anderson
Participant

Sorry, but with a three-factor interaction (3fi), to maintain model hierarchy, which we highly recommend, you must keep all three main effects and all the two-factor interactions (2fi). I’d be very interested to see that actual response data for this case because I’ll bet the 3fi is really an indication of other problems, for example, a need for transformation, outlier(s) or even that there really are no significant effects.Also, I advise you keep both ‘parents’ of 2fi’s even thought they appear insignificant. “Model hierarchy maintains the relationships between main effects, two-factor interactions, three-factor interactions, etc. For example, if an interaction, such as BD, is a significant term, then the model should also include the main effects B and D, even if the main effects do not appear to be statistically significant on their own. Consider the coefficient for the interaction term to be a correction to the coefficients to the parent terms. A well-formulated model should include all main effects present in the interactions. A model that does not contain the main effects may not remain stable if the method of coding is changed. Also, the actual models will be incorrect if they have been derived from non-hierarchical coded models and are not reported….For additional details on model hierarchy see:1.”A Property of Well-Formulated Polynomial Regression Models”, Julio Piexoto, The American Statistician, Feb 1990, Vol.44, No.1.2.”The Selection of Terms in Response Surface Models – How Strong is the Weak Heredity Principle”, John A. Nelder, The American Statistician, Nov 1998, V52, No.4.”

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#113618

Robert Butler
Participant

Thanks for the citations.  I pulled the relevant issues now all I have to do is sit down and read them.

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#113621

Mikel
Member

Mark,
Who is this “we” you refer to?
Thank you for the help. I always find enlightenment in being recited to from a textbook while getting your company’s advertisement at the same time! All this without actually saying anything!
You are basically saying that nothing exists in nature without a main effect component, but truth is that models exist where the coefficient for the main effect is 0. The classic definition of a catylyst is that it has no effect by itself (main effect coefficient of 0).
The modeling is from multiple regression and there are no hierarchical constraints.
But thanks for the advert, I know where to go now for a recitation from a textbook.

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#113626

Mark J. Anderson
Participant

Stan,
Ouch — you sure know how to hurt a guy. :(
I was trying to be helpful, but you are right on in skewering me for promoting my company.  Sorry about that.  Normally I am more circumspect.
Mark

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#113627

Darth
Participant

Promises, promises, you can never stay away from a good debate.

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#113648

Mikel
Member

Somebody has to pick up the slack since you got that stupid job and don’t spend all of your time posting. ;-)
How about getting a job where you can come out and play more?

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#113651

Darth
Participant

Gotta get me job like you where I can post all the time, afford a mansion on the river and drive 5 Fords….  Wait, I need a job that lets me drive Vettes so your job is out.

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#113656

BeenThereDoneThat
Participant

Darth:
I will send you a simple example you can run in Minitab where the 2-way interaction is significant while the individual factors are not.The numbers are simple enough that a hand calculation shows the effect on mean-error and degrees of freedom.Interested?Post a temporary email address – the forum is regularly ‘spidered’ by spammers for addresses.

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#113657

Darth really Stan
Participant

[email protected]
I promise to share with Darth since he can’t even do his own homework these days.

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#113658

Darth
Participant

I can be reached at:
[email protected]

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#113660

Mikel
Member

Hey – make up your mind whether you are going to work or not.
I was going to try to sound as sauve and sophisticated as you when I answered (I was even going to use spell checker).

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#113672

Anonymous
Guest

Robert,
Thanks for clarifying the resolution of the design. ( I thought the original question might be directed to aliasing of a three-way interaction.)
Of course, it is not possible to have a ‘significant’ AB interaction without either an A main effect or a B main effect – assuming homoscedasticity at each level. (One of the assumptions of Anova.)
This can be confirmed by drawing all possible interaction, and the only one that comes close to having a significant interaction without an A main effect or a B main effect is the anti-synergistic interaction.
Cheers,
Andy

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#113712

mjones
Participant

Not to put in a vote for “majority rule” but I do think the majority got it right.
In Minitab, you MUST include the main effects to calculate interactions. However, you do not have to include 2-ways to calculate 3-ways. I have presumed that gives the better answer as it reduces the model a bit but was required for Mtb to simply make the calculation.
A couple of  ‘rules of thumb’ (learned in the school of reality, non-academic classroom) – I find it is rare that neither main effect is significant when a 2-way is significant. I’ve never seen a significant 3-way (that makes sense) without a significant main effect.
When these rules of thumb are broken there is, as someone suggested, usually a lurking variable. Most of the time I’ve found it to be (or my BBs have found it when pushed to go look deeper) a measurement problem. So, if you get a 3-way or 4-way that does not make sense, go back and revalidate your MSA. If it is OK, re-look at your variables and your experiment.
Bottom line: regardless of the academic view, you must be able to explain, make sense of, and use the results of your analysis — or the work was a waste of time. If you can understand what is happening with a 3-way and use the results, great! If you cannot, you have a basic practical problem — regardless of the theory of the best estimate of your equation with variables in or out.
Also, keep in mind the effects that are not significant usually have such small coefficients that they contribute little to the equation anyway.

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#113742

Mikel
Member

You are incorrect when you say you do not have to include 2-ways to get 3-ways. Try it in Minitab 14 – it will not let you do it. Now try it in step wise regression – no restrictions!
So I again conclude the hierarchical restriction is for analysis purposes, not modeling. The majority is just repeating what they were taught and assuming that because the analysis and modeling CAN be done under the same drop down menu that it is the only way. Six Sigma teaches you to think if done right – not to be a lemming.
Since you have never seen a 3-way without a main – how do you know that the rules of thumb, lurking variables, measurement systems, etc. are a fact? Done much with chemistry in your industrial career?
Lurking variables and measurement system show up in the error term, not in a three way interaction.

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#113778

mjones
Participant

Stan-
Not sure what’s happening with your Mtb, but I get Mtb 13 & 14 to run main effects and 3-ways without 2-ways. I’m using Stat> DOE> Factorial> Analyze. It works fine.
Agree: We must think and not be lemmings. This is all about understanding what is happening so we can control our processes.
I said, I’ve never seen a valid, significant 3-way without a valid, significant main effect. Not saying it can’t happen; I’ve just not seen it. I’ve done some chemistry stuff, yes, and I know there are cases where catalyst interactions can make that happen. Can it happen? Certainly! But I think it is relatively rare. And, even more rare is the BB that can clearly and simply explain 3-ways and 4-ways when they do happen. Much more common are problems with measurement systems and other variables that give the appearance of significant high-level interactions.
An example: Had a MBB with a ‘really cool’ DOE example of higher level interactions. This was from jam-rates on a copier and, no doubt, there are multiple interactions. However, first problem: the Y is discrete (number of jams/time), but it could work OK if the numbers are high. Second problem: measuring the number of jams and time accurately. Third problem: initially were looking at the whole copier as a system instead of looking at the components/steps in a process (copiers are actually little factories with multiple steps in picking up paper, moving it, printing it, sorting it, etc.). Once we dug into the pieces of the process, most of the 3-ways went away; and we got to a robust process controlling the little x’s that made the most difference.
I’ve got half-dozen stories about silkscreening and non-wovens in different industries that go about the same way. Again, the root cause was usually an ineffective MSA (e.g., not all the promised MSA fixes were done, or were not effective, all kinds of excuses, didn’t think that would matter, etc., etc.) and this kills the DOE. Some cases, they simply missed a key x, like measuring variation across the web of the print.
Bad measurement system and missing x’s can make things look like 3-ways, 4-ways, and all kinds of weird things. They don’t always show up in the error term — especially with fractionals — or the answer would be “nothing is significant”. And that is another issue, not related to Darth’s initial question.
Not like lemmings, we need to understand what the data is telling us and be able to act on it.
Cheers!

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#113782

BeenThereDoneThat
Participant

Mark:
This looks like the references from page 2.16 of ARD-version 3.Is that so?;)

0
#113788

BeenThereDoneThat
Participant

Figured it out for myself. There is no direct relationship between the references. They both come from a third, common source.Lurking variables!

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#113851

Mark J. Anderson
Participant

What is “ARD”?
Mark

0
#113860

Brookiep
Participant

Darth
The real issue is not just looking at the statistical significance it’s to look at the practical significance as well. You do this by looking at the sum of the squares for the factor vs the sum of the squares for the total. Firstly you need to know how much unexplanied error there is in your model
SSError/SSTotal
Should be less than 10%. If that is OK than the experiment is valid, the next step is to look at the contribution form the interation of interest i.e your third order interation. AxBxC
SSInteration/SSTotal
If the effect is <1% or is very small then remove the interation from the model as it's impact on the experiment is very small. Just because a factor or interation is statisticly significant does not mean that it has any real effect.
To move on maybe read something on practical vs statistical significance.

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