On permutation tests with several test statistics to compare two populations

One of the practical problems during estimation real processes with regression models seems to be inevitable obsolescence such models as a result of changes of these processes. Updating the model, however make sense when such changes would be statistically significant. Indication of it can be carried out with comparing the populations - today and when the model was created. Usually parametric tests are carried out but it needs to require the set of assumptions related to the knowledge of distribution. Permutation tests let to pass over typical limitation and don't require knowledge of the distribution of examined populations. In the classic form - proposed by R. A. Fisher, single test statistics must be used. This paper proposes the extension, using at the same time two test statistics to verify the hypothesis of equality of two multi-dimensional populations. The critical region is determined used original division based on cells. Theoretical considerations were supplemented with the results of simulations carried out with R 2.15.0.