I am having two group of people, one group doing well, the other doesn't. We want to decrease the disparities of performance of these two groups after a treatment. How am i able to see if the treatment has been effective or not?
So it seems you have no randomization and two groups that are by selection different from each other on a variable or variables of interest. You can not really compare them directly to each other (well you could, but the inference is weak for many reasons). However, if the group doing well is an example of "doing well" on some set of indices, you could see if they change without treatment relative to changes in the group that gets the treatment. Again, these groups did not start the same and you did not randomize, so your inferences are limited.
By the way, researchers do the opposite all the time and pretend the group doing well is a control group.................ugh.
Mann-Whitney test or the Kolmogorov-Smirnov test. The Kolmogorov-Smirnov test compares the cumulative distribution of the two data sets ( two group of people), and computes a P value that depends on the largest discrepancy between distributions.
The KS test is sensitive to any differences in the two distributions. Substantial differences in shape, spread or median will result in a small P value. In contrast, the MW test is mostly sensitive to changes in the median.
http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture14.pdf
You are actually not interested in comparing the poor to the rich. What you want is to compare the poor without subsidy offer to the poor with subsidy offer.
Then you should not ask "if the treatment has been effective or not?" but rather "What is the effect of the treatment?" / "How effective was the treatment?".
The concrete way to analyze your data depends on the kind of data (what, precisely, is your data? On what scale it is measured? What is its [assumed] distribution?...). From this follows what kind of effect measure one would reasonable investigate (a mean difference, a ratio, an odds ratio, ...), and also the kind of analysis. A further important point might be if there are (known) covariables that you like to consider (diseases, addictions, family status, employment status, ...) - given you have a large enough sample.
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