# Ipsos Encyclopedia - Mann-Whitney U Test

For the condition of conducting ANOVA (Analysis of variance), there must be following fundamental assumptions that need to be secured.

## Definition

For the condition of conducting ANOVA (Analysis of variance), there must be following fundamental assumptions that need to be secured:

1. Independence
2. Homogeneity of variance
3. Normality

If the evidence indicates that the assumptions for an analysis of variance or a t-test cannot be maintained, two courses of action are open to us. One is carrying out transformation of the variable to be analysed in a such a manner that the resulting transformed variates meet the assumption, such as logarithmic transformation, square root transformation, Box-Cox transformation, Arcsine transformation etc and the other is carrying out a different test, called as non-parametric method, not requiring the rejected assumptions, such as the distribution-free test in lieu of anova.

As a non-parametric method, when the test is between ONLY two samples (such a design would give rise to a t-test or anova with two classes), there are two non-parametric testes which yield the same statistics and give the same results. Mann-Whitney U-test, and Wilcoxon two-sample test. The null hypothesis is that the two samples come from populations having the same location(not one samples from higher side of population and the other samples from lower side of population).

The Mann-Whitney test is used as an alternative to a t-test when the data are not normally distributed. The test can detect differences in shape and spread as well as just differences in medians. Differences in population medians are often accompanied by equally important differences in shape. The Mann-Whitney test is a test of both location and shape. Given two independent samples, it tests whether one variable tends to have values higher than the other.

Mann-Whitney U-test is the non parametric equivalent of the independent groups T tests (parametric tests) that uses the ranks of the data rather than their raw values to calculate the statistic.

Mann-Whitney U-test converts the original raw values into ranks from entire pooled both groups and then compared the mean ranks (often misunderstood as comparing medians of two groups) with the normalisation of standard error of the mean ranks which yield z-value.

For the comparison with Kolmogorov-smirnov test, please refer to Kolmogorov-Smirnov Two Sample Test.