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Mann–Whitney U test

The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values X and Y from two populations have the same distribution.

Version
v1 · 2026-09-28 · History
Domain-specific #
10548
Domain group
Formal Sciences
Origin domain
Experimental Design & Statistics
Subdomain
Nonparametric Statistics → Experimental Design & Statistics

Core Idea

Mann–Whitney U test is treated here as the recurring nonparametric statistics identity summarized by this source-grounded definition: The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values X and Y from two populations have the same distribution. The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected.

Scope of Application

  • The sample sizes. In practice some of this information may already have been supplied and common sense should be used in deciding whether to repeat it.

  • Calculations. The smaller value of U 1 and U 2 is the one used when consulting significance tables.

  • ExamplesIllustration of calculation methods. Using the direct method, we take each tortoise in turn, and count the number of hares it beats, getting 6, 1, 1, 1, 1, 1, which means that.

  • A more computationally-efficient form with factored out. Note that since , the mean used in the normal approximation is the mean of the two values of U.

  • A more computationally-efficient form with factored out. Therefore, the absolute value of the z-statistic calculated will be same whichever value of U is used.

Clarity

A clear use of Mann–Whitney U test names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values X and Y from two populations.

Manages Complexity

Mann–Whitney U test compresses multiple nonparametric statistics details into a stable diagnostic relation. The source shows both the central mechanism—this probability can be simply calculated by dividing U by its maximum value, which is the product of the two sample sizes.—and the practical consequence—if the number of ties is small (and especially if there are no large tie bands) ties can be ignored when doing calculations.

Abstract Reasoning

  1. Type the carrier. Identify the nonparametric statistics entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values X and Y from two populations have the same distribution.
  3. Check operation and conditions.

Knowledge Transfer

Within the home domain. Knowledge about Mann–Whitney U test transfers literally when a new case preserves the same carrier type, relation, and recognition test. In practice some of this information may already have been supplied and common sense should be used in deciding whether to repeat it. The smaller value of U 1 and U 2 is the one used when consulting significance tables. Beyond the home domain. No canonical parent is asserted for Mann–Whitney U test.

Neighborhood in Abstraction Space

Mann–Whitney U test sits in a sparse region of the domain-specific corpus (62nd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Statistical Tests & Choice Measurement (7 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08