R help - Jun 2004 - Comparing two pairs of non-normal datasets in R?

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

Have you considered "qqplot(A1, A2)" and "qqplot(C1, C2)"? 
If A2,
A2, C1, C2 are "more like Poisson", I might try "qqplot(sqrt(A1),
sqrt(A2))", etc.:  Without the "sqrt", the image might be
excessively
distorted by largest values, at least in my experience. 

      hope this helps.  spencer graves

Peter Sebastian Masny wrote:
>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
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>  
>

On Tuesday 08 June 2004 10:43 am, you wrote:
> If I understand you correctly, you have two set of ***paired***
> data, one set from the A population, and one from the C population.
>
> Form the pairwise differences:
>
> 	A.diff <- A1 - A2
> 	C.diff <- C1 - C2
Alas, they are not paired.  A1 and A2 are samples from the same population, 
but of different members.  Also, the number of measurements is different for 
each dataset.
> Boxplots and histograms of A.diff and C.diff will tell you
> (much more than a test ever would) what's ***really*** going on.
The boxplots I have clearly show the difference, but I need a p value to go 
with it.

Here are the boxplots if that helps:
http://www.ps.masny.dk/guests/misc/A1.png
http://www.ps.masny.dk/guests/misc/A2.png
http://www.ps.masny.dk/guests/misc/C1.png
http://www.ps.masny.dk/guests/misc/C2.png
> P.S. BTW --- you say that your data are continuous, but that their
> distributions are ``more like a Poisson''.  The Poisson
distribution
> is DISCRETE!!!
Hence the "like".  The data is indeed continuous, but a distribution
graph
increases towards one extreme...

Visually, the results are convincing, but I really need a test of 
significance.



Thank you very much for the help,

Peter

> Here are the boxplots if that helps:
> http://www.ps.masny.dk/guests/misc/A1.png
> http://www.ps.masny.dk/guests/misc/A2.png
> http://www.ps.masny.dk/guests/misc/C1.png
> http://www.ps.masny.dk/guests/misc/C2.png
Here is how I would do it:
It looks like your distributions can be characterized by
just a single parameter.

Then your question is:
   Is the change in the parameter value from A1 to A2
   larger than that from C1 to C2?
(Larger meaning what?: Difference? Ratio?)

So I suggest
- you estimate your four parameters
- compute your two differences or ratios
- compute the difference of those
- and repeat all this for many resamples (bootstrapping)

Then you get a bootstrap distribution of the 
value that you hope is significantly non-zero.
>From that distribution you can read your p-value.
(Preferably based on a BCa confidence interval)

library(boot)

Does that make sense?

  Lutz