Abstract The Kruskal-Wallis is a non-parametric method for testing whether samples originate from the same distribution. When the null hypothesis is rejected, at least one sample stochastically dominates at least one other sample. The test does not identify where this stochastic dominance occurs. Consequently, a decision limit for Kruskal-Wallis test is derived based on the gamma distribution and Bonferonni approximation that shows graphically where this stochastic dominance occurs. Simulation studies confirm the validity and robustness of the decision limit in small and large samples. An application is given to illustrate the method.