[R] Comparing two pairs of non-normal datasets in R?

[Peter Sebastian Masny]

Hi all,

I'm using R to analyze some research and I'm not sure which test would be 
appropriate for my data.  I was hoping someone here might be able to help.

Short version:
Evaluate null hypothesis that change A1->A2 is similar to change C1->C2, for 
continuous, non-normal datasets.


Long version:

I have two populations A and C.  I take a measurement on samples of these 
populations before and after a process.  So basically I have:
A1 - sample of A before process
A2 -  sample of A after process
C1 - sample of C (control) before process
C2 - sample of C (control) after process

The data is continuous and I have about 100 measurements in each dataset.  
Also, the data is not normally distributed (more like a Poisson).

By Wilcoxon Rank Sum, A1 is significantly different than A2 and C1 is 
different than C2.

Here is the problem:
C1 is only slightly different than C2 (Wilcoxon, p<.02), while A1 is more 
noticeably different than A2 (p<1E-22).  What I would like to do is assume 
that the changes seen in C are typical, and evaluate the changes in A 
relative to the changes in C (i.e. are the changes greater?).

Any thoughts?



Thanks,
Peter Masny