If there were no difference in the population medians for the Kruskal- Wallis test, we would expect the average ranks of all of the samples to be fairly close to one another.

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The Kruskal-Wallis test is a non-parametric method used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable. If the population medians are the same (indicating no difference between the groups), the ranks of the data points, when combined and ranked across all groups, should be randomly distributed among the groups. This would result in the average ranks of the samples being similar to each other, as the test essentially compares these ranks to assess differences.

If There Were No Difference in the Population Medians for the Kruskal-