A non-parametric test for nomimal data made up from two independent variables

#1
I have been looking for a statistical test to run for some experimental data I have acquired.

I have two groups (IV); Stress and Control mice.

I have been looking at cell morphology.

I performed a sholl analysis (which places concentric circles from the soma of the cell every 5 microns to the end) to compare morphology (e.g. length or volume) between conditions.

E.g.

Stress cell length 5um v control cell length 5um
Stress cell length 10um v control cell length 10um
Stress cell length 15um v control cell length 15um etc. etc.

I have been looking online for so long but I'm just not sure what to do.
I was thinking about performing a series of t tests to compare the means of each of those variables, but was wondering if I should just be running a repeated measure ANOVA instead (despite only having two IVs) to reduce the amount of statistical tests I am running.

Also, I had a look at the Shapiro Wilk statistics to see if the data is normally distributed and some of these variables (e.g. length at 5ums or 20ums) have a significant result. As such I figured I should be using a non-parametric test to avoid having to transform the data.
I was considering Kruskal wallis but my data is nominal.

Sorry for the long post, just thought I would be thorough.

:confused: :confused: