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Level I

## Factorial design with categorical factors set to different ranges

I have three continuous conditions I am testing:

Factor A : 1-10

Factor B: 1-5

Factor C: 2-6

The issue I am having is that Factor B and C are also categorical . Meaning, I want to test Factor A and B or A and C but I cannot have any runs that test B and C together. Is there a way to specify this in JMP?

1 ACCEPTED SOLUTION

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Staff

## Re: Factorial design with categorical factors set to different ranges

I recommend using the Custom Designer, which allows you to set constraints on factor ranges. You would specify Factor A as a continuous factor with range 1-10. You'd then specify a continuous "Factor B/C" with a range of 1-6, and then a categorical factor "B or C" that takes two levels: B and C. The setup would look something like this:

In the resulting design, "B or C" will tell you which of Factor B or C to include in the run, and "Factor B/C" gives you the value for that factor.

You can then use the Disallowed Combinations filter to ensure Factor B's range is limited to 1-5 and Factor C's range is limited to 2-6. That would look something like this:

Note that you'll want to deselect the Include Minimum/Maximum Value options under the red triangles as appropriate to ensure that a value of 5 is allowed for Factor B and a value of 2 is allowed for Factor C.

This setup makes interpretation of main effects and interactions a little different than a more "standard" design in which Factors A, B, and C are entered directly into the design, so you'll use a slightly different model than you would otherwise. Because the main effects of "Factor B/C" and "B or C" are essentially meaningless, you'd capture the main effects of Factor B and Factor C through the "Factor B/C"-by-"B or C" interaction. To capture the two-way interactions (i.e., Factor A-by-Factor B and Factor A-by-Factor C), you'll want to include the three-way interaction in the model. The model looks like this:

If you want to include quadratic terms for curvature, just be sure to cross "B or C" with the quadratic term for "Factor B/C" so that Factors B and C ultimately can have quadratic terms in the model.

I hope this helps! Please post any follow-up questions.

2 REPLIES 2
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Level VII

## Re: Factorial design with categorical factors set to different ranges

It would be helpful if you explained the factors.  My first thought is what you want is to nest B & C in A.  This would not be a factorial as you do not want all (or even a fraction of all) of the treatment combinations. It depends on what B & C are.

Highlighted
Staff

## Re: Factorial design with categorical factors set to different ranges

I recommend using the Custom Designer, which allows you to set constraints on factor ranges. You would specify Factor A as a continuous factor with range 1-10. You'd then specify a continuous "Factor B/C" with a range of 1-6, and then a categorical factor "B or C" that takes two levels: B and C. The setup would look something like this:

In the resulting design, "B or C" will tell you which of Factor B or C to include in the run, and "Factor B/C" gives you the value for that factor.

You can then use the Disallowed Combinations filter to ensure Factor B's range is limited to 1-5 and Factor C's range is limited to 2-6. That would look something like this:

Note that you'll want to deselect the Include Minimum/Maximum Value options under the red triangles as appropriate to ensure that a value of 5 is allowed for Factor B and a value of 2 is allowed for Factor C.

This setup makes interpretation of main effects and interactions a little different than a more "standard" design in which Factors A, B, and C are entered directly into the design, so you'll use a slightly different model than you would otherwise. Because the main effects of "Factor B/C" and "B or C" are essentially meaningless, you'd capture the main effects of Factor B and Factor C through the "Factor B/C"-by-"B or C" interaction. To capture the two-way interactions (i.e., Factor A-by-Factor B and Factor A-by-Factor C), you'll want to include the three-way interaction in the model. The model looks like this:

If you want to include quadratic terms for curvature, just be sure to cross "B or C" with the quadratic term for "Factor B/C" so that Factors B and C ultimately can have quadratic terms in the model.

I hope this helps! Please post any follow-up questions.

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