A new nonparametric test for two sample problem based on order statistics is suggested. This test can be successful in the case of small samples. The probabilities of the statistic are given. Comparisons with KolmogorovSmirnov, Mann Whitney-Wilcoxon, and Wilks’ empty block test for small sample sizes are made by the simulation.

Using a combinatorial approach, we introduce the translated Whitney numbers. This seems to be more natural than to write a product of anarithmetical progression in terms of a power variable and conversely. We also extend our ideas to translated r-Whitney numbers of both kinds and to translated Whitney-Lah numbers.