In testing for the normality assumption for 2 way ANOVA, the question whether normality within cells implies normality of residuals has been asked before and I have found so far different answers from different forums and still it's not clear to me.
I have the data of 6 patients that have been treated twice with 2 different drugs and each with 3 different levels of dose. So there are 2 drugs with 3 levels and I end up with six cells.
Doing 2 way anova I get a significant interaction and also the data passes the homoscedasticity test (Levene test). The normality assumption is true when is tested within each cell (6 cells were tested separately). However, when I do the test over the residuals of the anova model the result is the opposite (p<0.01).
Can someone please explain which of these two normality tests should I rely on (over residuals or within each cell) and if the normality of residuals matters.
How can I confirm that I am allowed to run 2 way ANOVA? Does this difference stem from the low sample size of my population?