  For testing the statistical significance of a treatment effect, we usually
compare between two parts of a population, one is exposed to the treatment, and
the other is not exposed to it. Standard parametric and nonparametric
two-sample tests are often used for this comparison. But direct applications of
these tests can yield misleading results, especially when the population has
some hidden sub-populations, and the impact of this sub-population difference
on the study variables dominates the treatment effect. This problem becomes
more evident if these subpopulations have widely different proportions of
representatives in the samples taken from these two parts, which are often
referred to as the treatment group and the control group. In this article, we
make an attempt to overcome this problem. Our propose methods use suitable
clustering algorithms to find the hidden sub-populations and then eliminate the
sub-population effect by using suitable transformations. Standard two-sample
tests, when they are applied on the transformed data, yield better results.
Some simulated and real data sets are analyzed to show the utility of the
proposed methods.
