What Kruskal-Wallis and Mann-Whitney actually run on

From Raw Values to Ranks

Fifteen toy fragment lengths (mm) from three schools. Neither test ever looks at these raw numbers — both convert them to ranks first. Watch what that conversion does.

Raw values

Plotted at their true position on the number line

Bethel Glenns/Dragon Woodville

Rank sums, and the H statistic

Once every point has a rank, Kruskal-Wallis only needs each group's rank total

SchoolnRank sum RR² / n