Initially, I wanted to do a two-factorial (4x3) repeated measures ANOVA in order to analyse my data. To be more precise, I do have two factors with factor1 having 4 levels (A, B, C, D), factor2 having 3 levels (t1, t2, t3). In addition, it is a repeated measures design as all 28 subjects (s) are confronted with all the 4 levels (A, B, C, D) within the 3 timepoints (t1, t2, t3). However, it turned out, that according to Shapiro Wilk test my data are not normally distributed. That is why now I wanted to use the aligned rank transform ANOVA as a non-parametric alternative for a two-factorial rmANOVA. Within this method, data are aligned before doing the ANOVA.
The question is: After alignment, do the aligned data need to be normally distributed before performing the ANOVA for a valid outcome? I am not sure about this, as the ART seems to be a non-parametric method, but still includes an ANOVA (with normally distributed data as a premise).
I am using the R-library "ARTool" and have come up with the following code:
library(ARTool) aligned_data <- art(dependentVariable ~ factor1 * factor2 + Error(s), data=data)
Now does the following Shapiro Test need to tell me, that my data is normally distributed in order to continue and trust the results?
Thanks in advance and any help is appreciated.