  Parametric hypothesis testing associated with two independent samples arises
frequently in several applications in biology, medical sciences, epidemiology,
reliability and many more. In this paper, we propose robust Wald-type tests for
testing such two sample problems using the minimum density power divergence
estimators of the underlying parameters. In particular, we consider the simple
two-sample hypothesis concerning the full parametric homogeneity of the samples
as well as the general two-sample (composite) hypotheses involving nuisance
parameters also. The asymptotic and theoretical robustness properties of the
proposed Wald-type tests have been developed for both the simple and general
composite hypotheses. Some particular cases of testing against one-sided
alternatives are discussed with specific attention to testing the effectiveness
of a treatment in clinical trials. Performances of the proposed tests have also
been illustrated numerically through appropriate real data examples.
