DoE – Categorical Variables

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    Hi all,

    I used mintab to create a screening DoE. I have 2 categorical variable, but there are not only A&B option, but also another two. It is a needle position within dispensing process and I need to check more locations then 2. Is it possible to include them all in one DoE or I have to split it?

    Thank you in advance for any advice



    Robert Butler

    Sure – it’s called dummy variables and it is my understanding that there are commands in Minitab which will allow you to do this without having to write separate code.

    Before going there however, you say you have “a needle position” – is there any way to characterize the position in terms of location such as height relative to a baseline or some such thing? If there is then you can treat the variable as continuous.

    Dummy variables – in your case you have 4 settings therefore you re-code the settings as follows:
    Setting 1: D1 = 0, D2 = 0, D3 = 0
    Setting 2: D1 = 1, D2 = 0, D3 = 0
    Setting 3: D1 = 0, D2 = 1, D3 = 0
    Setting 4: D1 = 0, D2 = 0, D3 = 1

    and you run your regression on whatever variables you have in your list and instead of the variable setting you use D1,D2, and D3. The coefficients for these three variables will be whatever they are and the way you determine the effect of any of the settings is to plug in the combination of D1,D2, and D3 values associated with a given setting.

    If you want more details the book Regression Analysis by Example by Chatterjee and Price has a good discussion of the method.


    Chuck White

    Dummy variables work fine for regression analysis, but are trickier for factorial DOEs. The proposed scheme wouldn’t work here since not all combinations are possible (for example, what needle position would correspond to D1=1, D2=1, D3=1 ?).

    I can think of 3 options for handling this situation:

    1. You can use a two dummy variable scheme where:
    D1=0, D2=0 is needle position 1
    D1=0, D2=1 is needle position 2
    D1=1, D2=0 is needle position 3
    D1=1, D2=1 is needle position 4
    The downside is that you’ll have an additional variable which could double the number of runs, and properly analyzing the results can be tricky.

    2. You can choose two representative needle positions (probably the extremes), and only use those for your screening DOE. For both options 1 and 2, you would need to use a Fractional Factorial or Plackett-Burman design. Definitive Screening designs require three levels for each factor.

    3. Use a General Full Factorial design with four levels for the needle position factor. The downside to this is that you won’t have an option for a fractional design, and if you have more than two or three factors, you can end up with a huge number of experimental runs.

    If you are truly looking for a screening DOE, then the last option is probably not the best. I would likely lean toward option 2, and plan on a follow-up study after determining the most important factors. If needle position is one of them, then you can choose a design to include all four levels for the follow-up.


    Robert Butler

    You don’t use the dummy variable designations in the DOE. What you use are the categorical identifiers 1,2,3,4 and, as noted, you cannot fractionate these. What you can do is run a saturated design for each of the categorical levels or, again as noted, if there is some way to rank the categorical identifiers then you would use just the two extreme levels and treat the variable as you would any other two level factor.


    Chris Seider

    Leo, if the DOE is expensive–ONE option is to use the most 2 extreme positions and just do a 2k factorial design and see if the position even has an impact to POTENTIALLY look at other positions,.


    Chuck White

    @rbutler — Sorry, I misinterpreted your suggestion as a novel approach to transform a factor with 4 levels into multiple factors with 2 levels since Leo said he wants a screening design. You may not be familiar with Mintab software, but there is no need for the user to specify dummy (indicator) variables as you described. Minitab handles that in the background, so the user just needs to specify that the factor is categorical, and the number of levels.

    Leo — another question occurred to me. Is the needle position a setting choice, or are all four positions always used in the process (like a 4 cavity tool)? If the latter is true, you should not use the needle position as a factor at all. Instead you should include it as a blocking variable, and it will be no problem to include 4 blocks in whatever screening design you choose. If needle position is a choice, then it sounds like we all agree that the best option would be to choose the 2 extreme positions (if they can be ranked) for a 2-level design.

    Good luck.

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