I am trying conduct stochastic dominance analysis (First Order and Second Order Stochastic Dominance) to compare the cumulative distributions between two groups. My data consists of various observations which have a group identifier variable (say 1 or 2) and the variable of interest (for which I'd like to compare CDFs) is an integer value from 0 to 5. What is the best way to conduct analysis to compare these distributions?
I have looked into Wilcoxon signed rank test, Mann-Whitney U test, and Kruskal-Wallis / Dunn's Test. However, as far as I am aware, none of these are tests of stochastic dominance so much as they are simple tests with the null hypothesis of equality of distribution. So, rejecting the null here simply tells me that the distributions are different, but not the additional aspect I am looking for (i.e., that one distribution dominates the other).
I have looked into Wilcoxon signed rank test, Mann-Whitney U test, and Kruskal-Wallis / Dunn's Test. However, as far as I am aware, none of these are tests of stochastic dominance so much as they are simple tests with the null hypothesis of equality of distribution. So, rejecting the null here simply tells me that the distributions are different, but not the additional aspect I am looking for (i.e., that one distribution dominates the other).
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