org.apache.commons.math3.stat.inference

## Class MannWhitneyUTest

- java.lang.Object
- - org.apache.commons.math3.stat.inference.MannWhitneyUTest

-     public class MannWhitneyUTest
      extends Object

  An implementation of the Mann-Whitney U test (also called Wilcoxon rank-sum test).

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `MannWhitneyUTest()` Create a test instance using where NaN's are left in place and ties get the average of applicable ranks.
    `MannWhitneyUTest(NaNStrategy nanStrategy, TiesStrategy tiesStrategy)` Create a test instance using the given strategies for NaN's and ties.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `mannWhitneyU(double[] x, double[] y)` Computes the Mann-Whitney U statistic comparing mean for two independent samples possibly of different length.
    `double` | `mannWhitneyUTest(double[] x, double[] y)` Returns the asymptotic observed significance level, or p-value, associated with a Mann-Whitney U statistic comparing mean for two independent samples.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### MannWhitneyUTest

          public MannWhitneyUTest()

      Create a test instance using where NaN's are left in place and ties get the average of applicable ranks. Use this unless you are very sure of what you are doing.

    - #### MannWhitneyUTest

          public MannWhitneyUTest(NaNStrategy nanStrategy,
                          TiesStrategy tiesStrategy)

      Create a test instance using the given strategies for NaN's and ties. Only use this if you are sure of what you are doing.
      Parameters:
        `nanStrategy` - specifies the strategy that should be used for Double.NaN's
        `tiesStrategy` - specifies the strategy that should be used for ties

  - ### Method Detail

    - #### mannWhitneyU

          public double mannWhitneyU(double[] x,
                            double[] y)
                              throws NullArgumentException,
                                     NoDataException

      Computes the Mann-Whitney U statistic comparing mean for two independent samples possibly of different length.

      This statistic can be used to perform a Mann-Whitney U test evaluating the null hypothesis that the two independent samples has equal mean.

      Let Xi denote the i'th individual of the first sample and Yj the j'th individual in the second sample. Note that the samples would often have different length.

      Preconditions:

      - All observations in the two samples are independent.
      - The observations are at least ordinal (continuous are also ordinal).
      Parameters:
        `x` - the first sample
        `y` - the second sample
      Returns:
        Mann-Whitney U statistic (maximum of Ux and Uy)
      Throws:
        `NullArgumentException` - if `x` or `y` are `null`.
        `NoDataException` - if `x` or `y` are zero-length.

    - #### mannWhitneyUTest

          public double mannWhitneyUTest(double[] x,
                                double[] y)
                                  throws NullArgumentException,
                                         NoDataException,
                                         ConvergenceException,
                                         MaxCountExceededException

      Returns the asymptotic observed significance level, or p-value, associated with a Mann-Whitney U statistic comparing mean for two independent samples.

      Let Xi denote the i'th individual of the first sample and Yj the j'th individual in the second sample. Note that the samples would often have different length.

      Preconditions:

      - All observations in the two samples are independent.
      - The observations are at least ordinal (continuous are also ordinal).

      Ties give rise to biased variance at the moment. See e.g. http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf.

      Parameters:
        `x` - the first sample
        `y` - the second sample
      Returns:
        asymptotic p-value
      Throws:
        `NullArgumentException` - if `x` or `y` are `null`.
        `NoDataException` - if `x` or `y` are zero-length.
        `ConvergenceException` - if the p-value can not be computed due to a convergence error
        `MaxCountExceededException` - if the maximum number of iterations is exceeded

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