Package org.apache.commons.statistics.inference

Class MannWhitneyUTest

java.lang.Object

org.apache.commons.statistics.inference.MannWhitneyUTest

public final class MannWhitneyUTest
extends Object

Implements the Mann-Whitney U test (also called Wilcoxon rank-sum test).

Since:

1.1

See Also:

Mann-Whitney U test (Wikipedia)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	MannWhitneyUTest.Result	Result for the Mann-Whitney U test.

Method Summary

Modifier and Type	Method	Description
double	statistic(double[] x, double[] y)	Computes the Mann-Whitney U statistic comparing two independent samples possibly of different length.
MannWhitneyUTest.Result	test(double[] x, double[] y)	Performs a Mann-Whitney U test comparing the location for two independent samples.
MannWhitneyUTest	with(AlternativeHypothesis v)	Return an instance with the configured alternative hypothesis.
MannWhitneyUTest	with(ContinuityCorrection v)	Return an instance with the configured continuity correction.
MannWhitneyUTest	with(PValueMethod v)	Return an instance with the configured p-value method.
static MannWhitneyUTest	withDefaults()	Return an instance using the default options.
MannWhitneyUTest	withMu(double v)	Return an instance with the configured location shift mu.

Methods inherited from class java.lang.Object

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

Method Detail

withDefaults

public static MannWhitneyUTest withDefaults()

Return an instance using the default options.

• AlternativeHypothesis.TWO_SIDED
• PValueMethod.AUTO
• ContinuityCorrection.ENABLED
• mu = 0

Returns:

default instance

with

public MannWhitneyUTest with(AlternativeHypothesis v)

Return an instance with the configured alternative hypothesis.

Parameters:

v - Value.

Returns:

an instance

with

public MannWhitneyUTest with(PValueMethod v)

Return an instance with the configured p-value method.

Parameters:

v - Value.

Returns:

an instance

Throws:

IllegalArgumentException - if the value is not in the allowed options or is null

with

public MannWhitneyUTest with(ContinuityCorrection v)

Return an instance with the configured continuity correction.

If ENABLED, adjust the U rank statistic by 0.5 towards the mean value when computing the z-statistic if a normal approximation is used to compute the p-value.

Parameters:

v - Value.

Returns:

an instance

withMu

public MannWhitneyUTest withMu(double v)

Return an instance with the configured location shift mu.

Parameters:

v - Value.

Returns:

an instance

Throws:

IllegalArgumentException - if the value is not finite

statistic

public double statistic(double[] x,
                        double[] y)

Computes the Mann-Whitney U statistic comparing 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 differ by a location shift of mu.

This returns the U₁ statistic. Compute the U₂ statistic using:

 u2 = (long) x.length * y.length - u1;
 

Parameters:

x - First sample values.

y - Second sample values.

Returns:

Mann-Whitney U₁ statistic

Throws:

IllegalArgumentException - if x or y are zero-length; or contain NaN values.

See Also:

withMu(double)

test

public MannWhitneyUTest.Result test(double[] x,
                                    double[] y)

Performs a Mann-Whitney U test comparing the location for two independent samples. The location is specified using mu.

The test is defined by the AlternativeHypothesis.

• 'two-sided': the distribution underlying (x - mu) is not equal to the distribution underlying y.
• 'greater': the distribution underlying (x - mu) is stochastically greater than the distribution underlying y.
• 'less': the distribution underlying (x - mu) is stochastically less than the distribution underlying y.

If the p-value method is auto an exact p-value is computed if the samples contain less than 50 values; otherwise a normal approximation is used.

Computation of the exact p-value is only valid if there are no tied ranks in the data; otherwise the p-value resorts to the asymptotic approximation using a tie correction and an optional continuity correction.

Note: Exact computation requires tabulation of values not exceeding size (n+1)*(m+1)*(u+1) where u is the minimum of the U₁ and U₂ statistics and n and m are the sample sizes. This may use a very large amount of memory and result in an OutOfMemoryError. Exact computation requires a finite binomial coefficient binom(n+m, m) which is limited to n+m <= 1029 for any n and m, or min(n, m) <= 37 for any max(n, m). An OutOfMemoryError is not expected using the limits configured for the auto p-value computation as the maximum required memory is approximately 23 MiB.

Parameters:

x - First sample values.

y - Second sample values.

Returns:

test result

Throws:

IllegalArgumentException - if x or y are zero-length; or contain NaN values.

OutOfMemoryError - if the exact computation is user-requested for large samples and there is not enough memory.

See Also:

statistic(double[], double[]), withMu(double), with(AlternativeHypothesis), with(ContinuityCorrection)