Let's see if I understand this correctly. The normality assumption means that for each group I am testing the response within each group is normally distributed. So in order to check all the groups together would I calculate the residuals and then try to fit the combination of all residuals to a normal distribution?
Edit: If normality in this case means tha: The responses in group A should be normally distributed with respect to group A. The responses in group B should be normally distributed with respect to group B. etc. Is the way of checking this to individually check each group? Or is it valid to calculate the residual of each group, for each group the mean value will be different. And then check whether the residuals are normally distributed in one go?
I'm concerned than doing it in one go could lead to the results showing normally distributed when within the group they're not normally distributed.