The Kruskal-Wallis test is a non-parametric statistical hypothesis test serving as the distribution-free counterpart to one-way Analysis of Variance (ANOVA). Unlike ANOVA, which tests for differences in population means based on normality assumptions, this theorem evaluates whether independent samples originate from identical populations by comparing the equality of their rank sums rather than raw data values. The methodology relies on assigning ordinal ranks to observations across all groups and determining if at least one group exhibits a different central tendency, thereby allowing inference without requiring the underlying data to satisfy specific distributional forms such as normality.
Prerequisite chain context: requires Ranks and Rank Sums in Nonparametric Statistics.