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).

Field Summary

Fields

Modifier and Type	Field	Description
private NaturalRanking	naturalRanking	Ranking algorithm.

Constructor Summary

Constructors

Constructor	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

Modifier and Type	Method	Description
private double	calculateAsymptoticPValue(double Umin, int n1, int n2)
private double[]	concatenateSamples(double[] x, double[] y)	Concatenate the samples into one array.
private void	ensureDataConformance(double[] x, double[] y)	Ensures that the provided arrays fulfills the assumptions.
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 Object

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

Field Details

naturalRanking

private NaturalRanking naturalRanking

Ranking algorithm.

Constructor Details

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 Details

ensureDataConformance

private void ensureDataConformance(double[] x,
 double[] y)
                            throws NullArgumentException,
NoDataException

Ensures that the provided arrays fulfills the assumptions.

Parameters:

x - first sample

y - second sample

Throws:

NullArgumentException - if x or y are null.

NoDataException - if x or y are zero-length.

concatenateSamples

private double[] concatenateSamples(double[] x,
 double[] y)

Concatenate the samples into one array.

Parameters:

x - first sample

y - second sample

Returns:

concatenated array

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.

calculateAsymptoticPValue

private double calculateAsymptoticPValue(double Umin,
 int n1,
 int n2)
                                  throws ConvergenceException,
MaxCountExceededException

Parameters:

Umin - smallest Mann-Whitney U value

n1 - number of subjects in first sample

n2 - number of subjects in second sample

Returns:

two-sided asymptotic p-value

Throws:

ConvergenceException - if the p-value can not be computed due to a convergence error

MaxCountExceededException - if the maximum number of iterations is exceeded

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