Complexity and consistency of statistical criteria

We investigate relations between consistency of statistical criteria sequences in finite probability spaces and asymptotic complexity of test calculations. It is proved that for every consistent test sequence it is possible to construct another consistent sequence for which complexity of calculations of membership functions of new criteria critical sets can be made asymptotically small in comparison with similar complexity for initial criteria. However such simplification appears to be fictitious as a matter of fact. To prevent fictitious simplification of calculations of membership functions of critical sets in a sequence of criteria it is necessary to set additional restrictions on classes of considered criteria. It is shown, that in case of such natural restrictions any simplification of calculations can lead to a failure of a consistency of criteria sequence. Estimations of efficiency of two-level criteria are resulted, when simple but not consistent in the given class of alternatives criteria work at first, and only in case of nonacceptance of a hypothesis hard computable but consistent criteria are applied.