# What statistical tests should be applied to the attached distributions?

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.

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Can you explain where these distributions came from? For example, what sort of data is it and what were the sample sizes? –  mark999 Apr 26 '12 at 10:11
Edit added above –  Ben J Apr 26 '12 at 10:18
My approach would be not to do any tests, and instead to just describe what I see. Others may disagree. I would consider the question "how much of a difference is there (if any)?" rather than "is there a difference?". –  mark999 Apr 26 '12 at 10:51
I agree with @mark999. It's clear that there is a difference - you don't need a statistical test to see that. What are your scientific goals? To see if there is a difference, to describe the difference or something else? –  MånsT Apr 26 '12 at 11:16
Speaking generally (not specifically about your data), if the sample size is very large, tiny differences (which are not of any practical significance) can be highly statistically significant. –  mark999 Apr 26 '12 at 11:57
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