The Kruskal-Wallis test is a non-parametric statistical method used to compare three or more independent groups. It is commonly referred to as the non-parametric analog of the one-way ANOVA. Use this test when:

• Normality is Violated: Your sample data is skewed, highly non-normal, or sample sizes are too small to robustly assume normality.
• Ordinal or Continuous Scale: The dependent variable is measured on an ordinal scale (e.g. Likert scale) or a continuous interval scale.
• Independent Groups: The observations in one sample group must be independent of observations in the other groups.
• Similar Distributions: The groups should have roughly similar shape/dispersion; in this case, the test compares group medians. If shapes differ, the test compares group mean ranks.

The test evaluates the following statistical hypotheses:

• Null Hypothesis ($H_0$): The medians of all sample populations are equal (there is no difference between groups).
• Alternative Hypothesis ($H_1$): At least one group median is statistically different from the others.
• P-value Interpretation: If the calculated $p$-value is less than or equal to the significance level $alpha$ (commonly $0.05$), we reject $H_0$.
• Post-Hoc Testing: Rejecting $H_0$ indicates that a significant difference exists, but does not specify which groups differ. To identify specific pairwise differences, you should perform non-parametric post-hoc pairwise comparison tests, such as Dunn's Test.