Emphasize differences between distributions? I am dealing with a distribution pair which looks like:

I am looking for a transformation, which would emphasize the differences between 0 and 1 even more. I've tried with log transforms and it helps, yet I am sure there must be something more involved.
Thanks!
 A: I think your best bet is to: 


*

*Not transform the distributions for groups 0 and 1; 

*Use the shift function to compare the entire distributions for groups 0 and 1.


The use of the shift function involves computing the differences between the deciles of the two distributions and plotting those differences against the deciles of the distribution for group 0. The plot will be augmented with confidence intervals of the decile differences derived via bootstrap. Examining the resulting plot will reveal how the distributions differ (if at all).  
The shift function will be defined differently if the two groups are independent versus if they are dependent.
This blog post on the shift function: a powerful tool to compare two entire distributions provides several examples on how to interpret the shift function: https://garstats.wordpress.com/2016/07/12/shift-function/. The R code used in the post is available here: https://github.com/GRousselet/blog/tree/master/shift_function.
See also the article Beyond differences in means: robust graphical methods to compare two groups in neuroscience by Rousselet et al also provides many examples of working with the shift function. The article was published in the European Journal of Neuroscience doi: 10.1111/ejn.13610 and its preprint can be found here: https://www.biorxiv.org/content/10.1101/121079v2. 
