Two-sample problems in statistical data modelling

A common problem in mathematical statistics is to check whether two samples differ from each other. From modelling point of view it is possible to make a statistical test for the equality of two means or alternatively two distribution functions. The second approach allows to represent the two-sample test graphically. This can be done by adding simultaneous confidence bands to the probability-probability (P-P) or quantile-quantile (Q-Q) plots. In this paper we compare empirically the accuracy of the classical two-sample t-test, empirical likelihood method and several bootstrap methods. For a real data example both Q-Q and P-P plots with simultaneous confidence bands have been plotted using the smoothed empirical likelihood and smoothed bootstrap methods.