I have two groups of animals and 60 to 100 variables per animal (describing their behavior during 24h). I want to know whether the two groups of animals behave differently (I have 11 data points per group), and I do not care much about knowing what is different.
I started by doing a SVM followed by a permutation to assess the accuracy of the SVM statistically. Got a good accuracy (5/6 correct prediction) but it is far from getting to the significant threshold (p>0,2), due to the over-dispertion of the distribution of accuracy scores, probably linked to the the low sample size.
Now I am wondering about a most simpler approach: making a PCA and do a basic wilcox test on the first component (keeping p<0.05 as the threshold, since I am doing only one test). I think it is allowed: since the PCA does not use the grouping variable, it will treat inter- and between- groups variance similarly. The fact that the p-value with 11 animals per group is super super low make me wonder if I do not make any wrong assumption here.