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