In statistics, the<unk>  test (also called the<unk><unk> -Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon-Mann-Whitney test) is a non-parametric test for assessing whether two samples of observations come from the same distribution. The null hypothesis is that the two samples are drawn from a single population, and therefore that their probability distributions are equal.  It requires the two samples to be independent, and the observations to be ordinal or continuous measurements, i.e. one can at least say, of any two observations, which is the greater.  More generally, the Wilcoxon-Mann-Whitney two-sample test may be thought of as testing the null hypothesis that the probability of an observation from one population exceeding an observation from the second population is equal to 0.5.  Another alternative interpretation is that the test assesses whether the Hodges-Lehmann estimate of the difference in central tendency between the two populations is zero.  The Hodges-Lehmann estimate for this two-sample problem is the median of all possible differences between an observation in the first sample and an observation in the second sample.  It is commonly thought that the MWW test tests for differences in medians but this is not strictly true.
It is one of the best-known non-parametric significance tests.  It was proposed initially by Wilcoxon (1945), for equal sample sizes, and extended to arbitrary sample sizes and in other ways by<unk>  and<unk>  (1947).  MWW is virtually identical to performing an ordinary parametric two-sample t test on the data after ranking over the combined samples.
Mann-Whitney U
Shapiro-Wilk test
Wilcoxon signed-rank test
Kendall tau rank correlation coefficient
ANOVA-simultaneous component analysis
Brown-Forsythe test
Chi-square test
Binomial test