Coding Multilevel Designs
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 This topic has 13 replies, 5 voices, and was last updated 14 years, 9 months ago by Bob Rome.

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July 18, 2007 at 2:36 pm #47602
Hi,
I’m trying to determine a prediction equation for a multilevel design. It’s a 4 factor design where we’ve set 3 levels for 3 of the factors and 2 for the remainder. I’ve always been taught to code your design however I’ve never used coding with a multlevel design.
Can anyone advise if this can be done and if so how to do this?0July 18, 2007 at 2:47 pm #158803
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.The codes for the variables with 3 levels would be 1, 0, 1 (given that the middle level is truly midway between the low and the high) and for the 2 level it would be 1,1.
If the middle level isn’t the actual mid point then to determine the code for the midpoint you would need to do the following:
v1 = (maximum + minimum)/2
v2 = (maximumminimum)/2
coded value = (actual value – v1)/v20July 18, 2007 at 2:58 pm #158804Thankyou,
In this model how would this affect how calculate the Y average High & Low i.e. how do I treat the 0’s? Do I bother about them?
Also is it truely always advisable to use coding in DOE’s?0July 18, 2007 at 4:53 pm #158813
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.I’m not sure I understand the first part of your question – for the 3 level variable you can compute the average response for the high, medium, and low settings and for the 2 levels you can compute the averages for the high and the low settings if you want to. Usually, one does a regression analysis and uses the resultant model to predict Y for a given setting of X’s. In the case where X and X^2 are both significant the predicted Y response will be a function of both the linear and the curvilinear behavior of the X in question.
As for the second part – see the post cited below and the discussion of which it is a part.
https://www.isixsigma.com/forum/showmessage.asp?messageID=733480July 19, 2007 at 1:58 pm #158831Thanks Rob
In BB class we were taught to use excel to code the table and then calculate the Average high and low, effect and coefficient to get the prediction equation.
Is this not the same thing as just setting up your design in Minitab using coded values. If so, if I have 4 factors with different levels, i.e. Temp & Time with two levels (1,+1) and Depth & Speed with three levels (1,0,+1) and enter these as coded levels in Minitab will it recognise the 0 and interprete it properly?0July 19, 2007 at 4:47 pm #158844
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.I don’t have Minitab but based on what I know about the package I would expect Minitab would not have a problem with the three level coding and that what you did with the Excel sheet and what Minitab does with the codes are one and the same. You might want to contact Minitab directly with your question. I understand their help desk is very good.
0July 19, 2007 at 5:40 pm #158849
abhishek simhadriParticipant@abhisheksimhadri Include @abhisheksimhadri in your post and this person will
be notified via email.Hi BB,
I think Rob is right …. there is a way in Minitab to use three levels in a factor…. using center points. You should select center points as 1 in a three level factor or 2 in case of 4 levels 3 in of 5 etc …. However a lot of care needs to be exercised since a DOE assumes a straight line relationship between any two end points….. else a response surface / taguchi design needs to be used ….
Hope that helps.
regards
Abhishek0July 19, 2007 at 6:30 pm #158853
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.A DOE won’t assume anything.
If the DOE is set up for 3 levels then the resultant matrix will allow you as the investigator to examine both linear and curvilinear effects for those variables.
If the DOE is set up for only 2 levels of a variable then the resultant matrix will allow only an investigation of linear effects.
If the DOE is set up so that some variables have 2 levels and others have 3 then for those variables with only 2 levels the design will permit an investigation of only linear effect and for those variables with 3 levels the design will permit an investigation of both linear and curvilinear effects.
The only care that needs to be taken is in the analysis phase of the design. If you, as the investigator, fail to include curvilinear terms for those factors with 3 levels then the machine, being a TOM*, will not test for curvilinear behavior. This is true regardless of type of DOE employed.
*Totally Obedient Moron0July 19, 2007 at 7:59 pm #158858
abhishek simhadriParticipant@abhisheksimhadri Include @abhisheksimhadri in your post and this person will
be notified via email.Hi Rob,
I was takling about the assumptions for performing a DOE in Minitab… Minitab assumes a straight line relationship between 2 levels or between one end point and the center point … always. If there a curve relationship a taguchi design / response surface is to be used ( In Minitab ).0July 19, 2007 at 8:08 pm #158859
Robert ButlerParticipant@rbutler Include @rbutler in your post and this person will
be notified via email.Abhishek,
That is a very interesting observation and it may explain an issue I’ve had to face repeatedly over the years. On more occasions that I care to think about I’ve had to correct investigators who insisted DOE was of little value because all it permitted was an analysis of linear effects.
The next time I run into this problem I’m going to ask the individual how they know this. If they cite the Minitab (or perhaps even some other program) menu choices I will have a much easier time disabusing them of their belief. Thanks.0July 30, 2007 at 3:55 pm #159298My experience w/ Minitab is it will not design a 3 level DOE, nor a mix of 23 level. It will do centerpoints as a 3rd level but only as centerpoints – meaning all factors set to center for the treatment. What it will do is let you define and existing 3 level matrix but you have to make sure it picks up the center factor settings. You’ll know if it doesn’t when they don’t show up on the plots. It was some months back when I did an experiment like this using Minitab but I don’t recall at the moment what I had to do to get it to pick up the center settings – something in the options (v14). Anyone else worked through this?
0July 30, 2007 at 4:27 pm #159299I just checked it out – I had to use General Full Factorial to set up and GLM to analyze. Otherwise it would not recognize 3 levels.
0July 30, 2007 at 9:57 pm #159307Just tried it with Ver15 with 3, 4, 5, and 6 level factors. No problem setting up or analyzing, although you do have to reduce the order of the terms unless you have replicates.
0July 31, 2007 at 2:38 pm #159322Yeah, the GLM won’t give you P values unless you free up some degress of freedom either through reducing terms or more rep’s. Don’t get the Pareto & normal plots too. I don’t know why that is…
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