How to determine the effects of three level categorical factor in design of experiments I'm designing a set of experiments with three factors, two of them are quantitative variables with two levels (Temperature and Pressure, Lo and Hi) which I have designated -1 and +1 in my table. I have a third variable (C) that is the material being tested, this is a categorical variable and I have three to test.
Would designating C to have levels -1,1,2 (these levels being material a, material b and material c) be appropriate, and then how would the effect of C be calculated? As for a two-level I would do the mean(hi)-mean(lo) but C has three levels and being categorical is not linked in this manner (i.e. the materials are independent and not related to each other). I have been looking through Montgomerys Design and Analysis of Experiments but not been able to find something I fully understand.



Would designating C to have levels -1,1,2 (these levels being material a, material b and material c) be appropriate

and

(i.e. the materials are independent and not related to each other)

so NO, you should not code that way. Represent the materials variable with two dummy variables. There are many questions on site about this, so search.

and then how would the effect of C be calculated?

There is not one "the effect of C". Since there are three materials, describing differences between them requires at least two parameters, maybe more. If, say, the effect of temperature is different for different materials, that is an interaction, which also needs representation in the model and wil lead to more parameters.
