How to detect variables discriminating a sample from the rest of the samples? I have a traditionally structured data set where rows are observations and columns are variables. There are only a few observations but comparatively more variables. The observations are regions of a country and the variables are characteristics (i.e., population size, mean income, number of males, number of females, etc.). I need to find out which characteristics can distinguish one region from the rest. For example, I need to find out if population size distinguishes region 1 most from regions 2, 3, 4, etc.
Which statistical methods are available to perform this type of analysis? Your help is appreciated.
Just in case it is not clear, my data looks something like the following.

     A, B, C, D
R1   8, 9, 5, 4
R2   5, 8, 4, 5
R3   7, 9, 7, 4

Where R1 = region 1, R2 = region 2, R3 = region 3, A = population, B = average income, C = number of males, D = number of females. My queries are something like this: 


*

*how is R1 different from the set {R2, R3}? 

*how is R2 different from the set {R1, R3}? 

*how is R3 different from {R1, R2}? 


The expected answers look something like this:


*

*A make R1 different from {R2, R3}? 

*{A, D} make R2 different from {R1, R3}?

 A: I had similar problem and was advised to use Decision Tree Algorithm. In your case classes would be R1, R2, etc. It has R implementation in library(rpart) - function rpart.
A: This is not a complete answer, but whenever I am exploring my data for the first time I like to use the describe() function from the Hmisc library in the free statistical program R. The library is available for download from within R or from its website.
Sample code for exploring your data might look like this:
## Generate example data
Data <- as.data.frame(matrix(data = c(10,11,10,27,5,3,4,15,55,10,10,9,1,2,1,9,12,12,12,17,50,40,50,100,1,2,4,3,9,7,8,10), nrow = 4, ncol = 8, byrow = FALSE))

## Load Hmisc library
library(Hmisc)

## Generate descriptive statistics
describe(Data)

The describe() command will provide you with the number of total, unique, and missing observations of each variable along with means and frequencies. You might also consider further exploring your data with the hist(), density(), and summary() functions. Type help(function_name) at the R command line for details.
