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Dec 13, 2021 at 3:07 vote accept Sean Raleigh
Dec 11, 2021 at 20:21 comment added Eoin Yes, I was a bit sloppy in my wording - if you want actual orthogonality, not just independence, code the values as -1 and +1. If this answers your question, please remember to upvote and mark the question as answered.
Dec 10, 2021 at 18:31 comment added Sean Raleigh This is getting much closer to the answer I was looking for. I will note that the vectors that represent the two balanced factors in the design matrix are not orthogonal. (Their inner product will be 20--the number of cases where both take value 1.) But the fact that they are uncorrelated means some transformation of those vectors will be orthogonal. So I think this is pretty close.
Dec 6, 2021 at 15:50 history edited Eoin CC BY-SA 4.0
added 26 characters in body
Dec 6, 2021 at 15:43 history answered Eoin CC BY-SA 4.0