I'm considering performing a MANCOVA for a project, and during my research I came across a statement that gave me pause, quoted in the question title. You can find the statement in the middle of the first paragraph of this article: https://web.pdx.edu/~newsomj/mvclass/ho_manova.pdf
I understand this to mean, in other words, suppose you have four response variables and two of them are percent accuracy, and the other two are number of a certain kind of omission or something. In this case, higher percent accuracy is "better" while lower omission count is "better," so the pattern of expected group differences is not all the same direction. While it is not hard to simply create a kind of inverted omission variable that is some sort of complement to the omission responses, I'm still curious. I've never heard or read anywhere else that the directionality of the group differences must be the same, but I can't find anything else to corroborate or refute this. In all the examples I see of a MANCOVA or MANOVA, indeed all the responses are usually some performance metric on a test or something where it is true that the expected pattern of group differences is in the same direction, but it's not clear that this is mandatory. Can someone add some insight to this?
