Mann-Whitney U Test

Mann-Whitney U Test

Description

  • The Mann-Whitney U test is used to compare differences between the two independent groups.
  • The test is a Non-Parametric version of the two-sample T-test.

Why to use

To determine if the population median of the two groups differs or not.

When to use

When the dependent variable is continuous but not normally distributed.

When not to use

  • When the distributions of the two samples are very different.
  • When the data consists of missing values. In which case, missing value imputation needs to be performed.

Prerequisites

  • Both the variables must be continuous and numeric.
  • Group 1 and group 2 must be independent of each other.
  • Observations are not normally distributed.
  • Number of observations in both groups must be equal.

Input

Two numeric data groups.

Output

  • U statistic
  • p Value

Statistical Methods Used

  • U statistic
  • Alpha (α)

Limitations

The difference in sample sizes results in reduced power of the statistical test.


The system calculates the p value in this test and compares it with the alpha value.

Criteria

Interpretation

When the p-value is greater than alpha an alternative hypothesis can either be "Two-sided" or "One-sided (less than)" or "One-sided (greater than)"

As the p-value is greater than alpha, the population median of the first group equals the population median of the second group. (η1=η2)

When the p-value is less than alpha and the alternative hypothesis is equal "Two-sided"

As the p-value is less than or equal to alpha, the population median of the first group is not equal to the population median of the second group. (η1≠η2)

When the p value is less than alpha and the alternative hypothesis is equal "One-sided (less than)"

As the p value is less than or equal to alpha, the population median of the first group is less than the population median of the second group. (η1<η2)

When the p value is less than alpha and the alternative hypothesis is equal to "One-sided (greater than)"

As the p value is less than or equal to alpha, the population median of the first group is greater than the population median of the second group. (η1>η2)

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