We consider the problem of testing whether two samples of contaminated data,
possibly paired, are from the same distribution. Is is assumed that the
contaminations are additive noises with known moments of all orders. The test
statistic is based on the polynomials moments of the difference between
observations and noises. . A data driven selection is proposed to choose
automatically the number of involved polynomials. We present a simulation study
in order to investigate the power of the proposed test within discrete and
continuous cases. A real-data example is presented to demonstrate the method