Mann Whitney U Test - SoojungHong/StatisticalMind GitHub Wiki

Reference :

http://www.statisticssolutions.com/mann-whitney-u-test/

Mann-Whitney U test is the non-parametric alternative test to the independent sample t-test. It is a non-parametric test that is used to compare two sample means that come from the same population, and used to test whether two sample means are equal or not. Usually, the Mann-Whitney U test is used when the data is ordinal or when the assumptions of the t-test are not met.

In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample. Unlike the t-test it does not require the assumption of normal distributions. It is nearly as efficient as the t-test on normal distributions. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution. A Wilcoxon rank sum test is a nonparametric test that can be used to determine whether two independent samples were selected from populations having the same distribution.

Assumptions of the Mann-Whitney: Mann-Whitney U test is a non-parametric test, so it does not assume any assumptions related to the distribution of scores. There are, however, some assumptions that are assumed

  1. The sample drawn from the population is random.
  2. Independence within the samples and mutual independence is assumed. That means that an observation is in one group or the other (it cannot be in both).
  3. Ordinal measurement scale is assumed. Calculation of the Mann-Whitney U: U = (n1 * n2) + n2(n2 +1)/2 - (sum of Ri where i starts from n1+1 to n2)

Where: U=Mann-Whitney U test N1 = sample size one N2= Sample size two Ri = Rank of the sample size Use of Mann-Whitney: Mann-Whitney U test is used for every field, but is frequently used in psychology, healthcare, nursing, business, and many other disciplines. For example, in psychology, it is used to compare attitude or behavior, etc. In medicine, it is used to know the effect of two medicines and whether they are equal or not. It is also used to know whether or not a particular medicine cures the ailment or not. In business, it can be used to know the preferences of different people and it can be used to see if that changes depending on location.

  • nonparameteric test : Nonparametric statistics are statistics not based on parameterized families of probability distributions. They include both descriptive and inferential statistics. The typical parameters are the mean, variance, etc. Unlike parametric statistics, nonparametric statistics make no assumptions about the probability distributions of the variables being assessed. The difference between parametric models and non-parametric models is that the former has a fixed number of parameters, while the latter grows the number of parameters with the amount of training data.