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The Mann–Whitney 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, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.
The test is named after Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples. [3] The test was popularized by Sidney Siegel (1956) in his influential textbook on non-parametric statistics. [4]
To test the difference between groups for significance a Wilcoxon rank sum test is used, which also justifies the notation W A and W B in calculating the rank sums. From the rank sums the U statistics are calculated by subtracting off the minimum possible score, n(n + 1)/2 for each group: [1] U A = 54 − 7(8)/2 = 26 U B = 37 − 6(7)/2 = 16
Over his career Wilcoxon published over 70 papers. [3] His most well-known paper [4] contained the two new statistical tests that still bear his name, the Wilcoxon rank-sum test and the Wilcoxon signed-rank test. These are non-parametric alternatives to the unpaired and paired Student's t-tests respectively. He died on November 18, 1965.
It may result in a known statistic (e.g., in the two independent samples layout ranking results in the Wilcoxon rank-sum / Mann–Whitney U test), and provides the desired robustness and increased statistical power that is sought.
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In statistics, a ranklet is an orientation-selective non-parametric feature which is based on the computation of Mann–Whitney–Wilcoxon (MWW) rank-sum test statistics. [1] Ranklets achieve similar response to Haar wavelets as they share the same pattern of orientation-selectivity, multi-scale nature and a suitable notion of completeness. [2]
kruskal.test (Ozone ~ Month, data = airquality) Kruskal-Wallis rank sum test data: Ozone by Month Kruskal-Wallis chi-squared = 29.267, df = 4, p-value = 6.901e-06 To determine which months differ, post-hoc tests may be performed using a Wilcoxon test for each pair of months, with a Bonferroni (or other) correction for multiple hypothesis testing.