My current understanding is that sphericity violations inflate the F-value and therefore type I error. I'd like to know how exactly this manifests itself mathematically.
To follow-up, why does sphericity only concern itself with repeated measures within a given factor? In other words, how is it that differences in the variance of the differences among all possible groups in, say, a 2x2 design not impact the F-value estimates? Intuitively, one might think that it would affect the F-value of the interaction in a 2x2 design.
I am looking for simple mathematical illustration of the way in which sphericity violations affect RM-ANOVA results.