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The Kruskal–Wallis test by ranks, Kruskal–Wallis test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric statistical test for testing whether samples originate from the same distribution. [1] [2] [3] It is used for comparing two or more independent samples of equal or different sample sizes.
[2] [3] His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of origami during the early era of television. [2] He was the oldest of five children, three of whom, including himself, became researchers in mathematics and physics; see Joseph Kruskal and Martin Kruskal .
However, with the Kruskal–Wallis test there is no a priori ordering of the populations from which the samples are drawn. When there is an a priori ordering, the Jonckheere test has more statistical power than the Kruskal–Wallis test.
Wilson Allen Wallis (November 5, 1912 – October 12, 1998) was an American economist and statistician who served as president of the University of Rochester. [3] He is best known for the Kruskal–Wallis one-way analysis of variance, which is named after him and William Kruskal.
The Kruskal-Wallis test is based on the ranks of the data. The advantage of the Van Der Waerden test is that it provides the high efficiency of the standard ANOVA analysis when the normality assumptions are in fact satisfied, but it also provides the robustness of the Kruskal-Wallis test when the normality assumptions are not satisfied.
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The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
Kruskal was born to a Jewish family [2] in New York City to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of origami during the early era of television.