I was reading a research paper where they had a 2x3 repeated measures factorial design with a single DV. A suitable approach to this analysis would be a univariate repeated measures ANOVA. However, its possible that sphericity is violated (and a GG/HF adjustment required). They chose to use a MANOVA instead.
I'm writing a term paper on how F test results/interpretations could differ between a sphericity violated case (both with and without adjustment) and a non-violated case, between the univariate and multivariate approaches.
I want to base my paper on the paper that I read (same design), but I dont have access to the original dataset (lets assume for this question that I'm unable to get it from the authors). How do I generate a dataset, of the same design as outlined above, where I can guarantee that sphericity will be violated? And likewise, a dataset where sphericity is guaranteed to not be violated?
I'd be happy to generate this using R, MATLAB, or Python
I'd like a way to control the means of these sub groups so I can manually make sure that factorx_1 and factorx_2 are significantly different for example