Pre-post distribution comparisons I have a study looking at classroom socialization.  Students named the top other students they wanted to read a book with before and after treatment.  There was also a control group that received no treatment.  Before the treatment you have a few really popular kids getting all the votes and a lot dorkier kids getting few to no votes.  So you have a heavy negative skewed distribution that looks like this:
Figure 1

It is hypothesized that the treatment will cause the dorkier kids to get picked more and the popular kids to get picked less.  In other words the distribution will become normal (see Fig 2).  And for the control group the negative skew will remain the same or become worse (see Fig 3).
Figure 2

Figure 3

Is there a hypothesis test to show this change in the treatment group?  Almost like a repeated measures var test or repeated measures distribution test.
Note this is a cross post from talkstats.com.  They are aware I am posting here and am connecting this post to that one.
 A: One option you might consider is the Kolgomorov-Smirnov two-sample test. I'd do two comparisons: 1) the pre-distribution to the intervention distribution and 2) the pre-distribution to the control distribution. Note that instead of using kernal density estimates as it looks like you have above, you'll just use the empirical distribution functions of the samples. The procedure will look for the maximum vertical deviation between your distributions and reject at a specified $\alpha$ level based on whether this difference is extreme enough. The graphs in your question appear to have been created in R, and there is an R implementation of this test in the stats package, described here. 
A: There are several methods in Biostatistics that used to test pre-post treatment effects, i.e., change scores, percentage change scores, analysis of covariance (ANCOVA) or random effects models. If your underlying interest is mean performance change in pre-post treatment as well as treatment vs. control group, random-effects model (random intercept model) might be helpful, as change score or ANCOVA take the difference between pre-post performances or take pre-performance as a covariate to test the treatment effect.  It is equivalent to the repeated measure analysis of variance if you data is balanced. 
Also due to the skewness of the distribution in the different groups, bootstrapping may be helpful, depending on whether you wanna test the hypothesis or you wanna a reliable "effect size" and confidence interval. 
