In the attached images (bottom of this post), I wish to compare the plotted distributions as follows. Each plot shows two distributions labelled 'Forwards' and 'Backwards'. For each attached example, I wish to compare each of 'Forwards' and 'Backwards' of sub-figure a with 'Forwards' and 'Backwards' of sub-figure c (and same for sub-figures b and d)
Now considering a and c from the distros A example, the distributions are approximately bimodal. I was thinking of taking the absolute values of these distributions so that they are no longer bimodal and then comparing them. (Probably I'm barking up the wrong tree with this?)
However, I am uncertain as to what test I should use to test for differences. I was initially inclining towards a ranksum test since the distributions are clearly non-uniform. But, I was also maybe considering a Kolmogorov-Smirnov Test.
EDIT: Note about distributions: Each 'Forwards' and 'Backwards' data distribution consists of ~7000 and ~5000 data points respectively. Each data point within a given data set indicates the difference in value of a property specific to an artificial neural network. Hence all data points represent such measurements over collections (~7000 and ~5000) of neural networks.