Class MannWhitneyUTest
java.lang.Object
org.apache.commons.math3.stat.inference.MannWhitneyUTest
An implementation of the Mann-Whitney U test (also called Wilcoxon rank-sum test).
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Field Summary
Fields -
Constructor Summary
ConstructorsConstructorDescriptionCreate 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 TypeMethodDescriptionprivate 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.
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Field Details
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naturalRanking
Ranking algorithm.
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Constructor Details
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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
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'stiesStrategy
- specifies the strategy that should be used for ties
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Method Details
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ensureDataConformance
private void ensureDataConformance(double[] x, double[] y) throws NullArgumentException, NoDataException Ensures that the provided arrays fulfills the assumptions.- Parameters:
x
- first sampley
- second sample- Throws:
NullArgumentException
- ifx
ory
arenull
.NoDataException
- ifx
ory
are zero-length.
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concatenateSamples
private double[] concatenateSamples(double[] x, double[] y) Concatenate the samples into one array.- Parameters:
x
- first sampley
- second sample- Returns:
- concatenated array
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mannWhitneyU
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 sampley
- the second sample- Returns:
- Mann-Whitney U statistic (maximum of Ux and Uy)
- Throws:
NullArgumentException
- ifx
ory
arenull
.NoDataException
- ifx
ory
are zero-length.
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calculateAsymptoticPValue
private double calculateAsymptoticPValue(double Umin, int n1, int n2) throws ConvergenceException, MaxCountExceededException - Parameters:
Umin
- smallest Mann-Whitney U valuen1
- number of subjects in first samplen2
- 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 errorMaxCountExceededException
- if the maximum number of iterations is exceeded
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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 sampley
- the second sample- Returns:
- asymptotic p-value
- Throws:
NullArgumentException
- ifx
ory
arenull
.NoDataException
- ifx
ory
are zero-length.ConvergenceException
- if the p-value can not be computed due to a convergence errorMaxCountExceededException
- if the maximum number of iterations is exceeded
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