In many sciences researchers often meet the problem of establishing if the distribution of a categorical variable is more concentrated, or less heterogeneous, in population P1 than in population P2. An approximate nonparametric solution to this problem is discussed within the permutation context. Such a solution has similarities to that of testing for stochastic dominance, that is, of testing under order restrictions, for ordered categorical variables. Main properties of given solution and a Monte Carlo simulation in order to evaluate its degree of approximation and its power behaviour are examined. Two application examples are also discussed.