Attention DOE Experts!!!!

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

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.
airacad.com
Good Luck
Anne

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

Sounds like somebody’s had a tough day…

Are you using loglinear modeling?   

  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. 

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?

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

Darth,
The

Darth,
The basic approach use

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

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.

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

  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.

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

You don’t know what you are talking about.

  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.

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.”

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!
Wow, my head is swimming.
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.

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

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).

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.

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!

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

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.