org.apache.commons.math3.stat.inference

## Class MannWhitneyUTest

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

public class MannWhitneyUTestextends 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.

### 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

**SCaVis 2.0 © jWork.ORG**