Choosing the most efficient statistical test of several ones that are at the disposal of the statistician is regarded as one of the basic problems of statistics. According to the classical Neyman–Pearson theory the uniformly most powerful tests are considered the best. However, it is well known that they exist merely for a narrow class of statistical models which do not fully cover the diversity of problems arising in theory and practice. One can still say that within the framework of parametric statistics this problem is not at all crucial. The point is that quite formal methods of constructing tests have been developed, for example, Bayes or likelihood ratio tests. They possess a number of remarkable properties and usually turn out to be asymptotically optimal in the sense of one or another definition of this concept.

The situation is quite different under the nonparametric approach. There exist numerous statistical tests proposed as a rule for heuristic reasons. The Kolmogorov–Smirnov and omega-square tests can serve as classical examples for goodness-of-fit testing. In other cases nonparametric procedures arise as simple substitutes of computationally complicated parametric procedures. The Wilcoxon rank test has been proposed in exactly this way. One more reason for using nonparametric tests is concerned with unreliable information on the distribution of observations in cases when it is reasonable to use, instead of the highly suitable parametric test, a nonparametric one, which is possibly less efficient but more robust with respect to changes of this distribution.