The mathematical procedure of the permutation test for statistical inference is presented by means of the 2-sample problem in its theoretical and practical mode of operation. The bootstrap method, the jackknife method and especially the permutation or randomization method are discussed in more detail. The different variants of the permutation method are discussed. The implementation of permutation methods and their superiority to asymptotic approximation is presented using fictitious numerical examples and an empirical study. The mechanism of random selection, which is of essential importance for the permutation method, is described by a 'cuboid parable'. The principles and similarities of the treated procedures are clearly explained with the help of this parable. The problem of performing an invariance permutation test for interaction in independent factorial designs is discussed. A possible solution to the 2 x 2 interaction is suggested. 3 simulation studies comparing the method of asymptotic approximation with the permutation method were carried out.