The Kruskal-Wallis ANOVA and Mood's Median Test are two useful and general nonparametric tests for comparing two or more independent samples. They can be used to test whether such samples come from the same distribution. They are powerful alternatives to the one-way analysis of variance.
The Kruskal-Wallis ANOVA uses the sum of difference between mean ranks of these samples as the statistic. The statistic of Mood's median test only relates to the number of larger or smaller than the median value but not their actual distance from the median, so it is not as effective as Kruskal-Wallis ANOVA.
As an example, researchers want to know whether the enhanced eyesight of young patients, who use three different therapies to enhance their eyesight, comes from the same distribution. Thirty students' enhanced eyesight, after adopting these three therapies, was recorded.
At first, we use Kruskal-Wallis ANOVA.
Also, we use Mood's Median Test.