GLM vs ANOVA: Mauchly's test needed? Suppose I have an experimental design with a continuous DV, and three IV (within-subject factors). I could analyse them using an ANOVA, or using a GLM with a Gaussian link function. The DV shows a normal distribution. For ANOVA analysis, Mauchly's test is typically used to check sphericity. Is this required when using the GLM, or is it sufficient to prove normality of the DV?
 A: Sphericity is another way of saying that the errors are equally distributed.  This is an assumption of regression/anova/glm(gaussian).  These are fundamentally the same model.  
Testing these assumptions using significance tests is not helpful, but you should assess the veracity of the assumption of equally distributed errors in some way.  
Normality of the dependent variable is not an assumption of any of these models.
A: A GLM with a Gaussian response distribution and an identity link function is the same as an OLS regression model.  An ANOVA is also a special case of a standard regression model / a GLM.  However, your design has repeated measures.  That requires you to take the non-independence of the data into account.  A repeated measures ANOVA does so, but by convention when people just say "ANOVA" (i.e., not 'rmANOVA') they don't mean the repeated measures version.  Likewise, when people just say "GLM", they aren't typically referring to that.  You could be, but it's ambiguous.  If you are, then note that these are just different names for the same thing, and as the same thing, they have the same assumptions.  If you are thinking of these as different models, then at least one of them is wrong.  
At any rate, to use rmANOVA on data like you describe, the assumption of sphericity should hold, in addition to the residuals being normally distributed.  
