MannWhitneyUTest (Apache Commons Math 3.3 API)

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).

Version:

$Id: MannWhitneyUTest.java 1416643 2012-12-03 19:37:14Z tn $

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 X_i denote the i'th individual of the first sample and Y_j 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 U^x and U^y)
    
    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 X_i denote the i'th individual of the first sample and Y_j 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

Class MannWhitneyUTest

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MannWhitneyUTest

MannWhitneyUTest

Method Detail

mannWhitneyU

mannWhitneyUTest