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?
shapiro.test(residuals(aligned_data))
anova(aligned_data)
Thanks in advance and any help is appreciated.