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Abstract. 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.

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A partial ordering ofω-words can be introduced with regard to whether anω-word can be transformed into another by a Mealy machine. It is known that the poset ofω-words that is introduced by this ordering is a join-semilattice. The width of this join-semilattice has the power of continuum while the depth is at leastℵ0. We have created a technique for proving that power-characteristicω-words are incomparable. We use this technique to show that this join-semilattice is not modular.