Apache Commons Math 3.6.1 · org.apache.commons.math3.stat.inference.WilcoxonSignedRankTest

Modifier and Type	Field and Description
private NaturalRanking	naturalRanking Ranking algorithm.

Access	Constructor and Description
public	WilcoxonSignedRankTest() Create a test instance where NaN's are left in place and ties get the average of applicable ranks.
public	WilcoxonSignedRankTest(final NaNStrategy specifies the strategy that should be used for Double.NaN's nanStrategy, final TiesStrategy specifies the strategy that should be used for ties tiesStrategy) Create a test instance using the given strategies for NaN's and ties.

Method Summary

Modifier and Type	Method and Description
private double[]	Returns: \|z\| calculateAbsoluteDifferences(final double[] sample z) Calculates \|z[i]\| for all i
private double	Returns: two-sided asymptotic p-value calculateAsymptoticPValue(final double smallest Wilcoxon signed rank value Wmin, final int number of subjects (corresponding to x.length) N)
private double[]	Returns: z = y - x calculateDifferences(final double[] first sample x, final double[] second sample y) Calculates y[i] - x[i] for all i
private double	Returns: two-sided exact p-value calculateExactPValue(final double largest Wilcoxon signed rank value Wmax, final int number of subjects (corresponding to x.length) N) Algorithm inspired by http://www.fon.hum.uva.nl/Service/Statistics/Signed_Rank_Algorihms.html#C by Rob van Son, Institute of Phonetic Sciences & IFOTT, University of Amsterdam
private void	ensureDataConformance(final double[] first sample x, final double[] second sample y) Ensures that the provided arrays fulfills the assumptions.
public double	Returns: wilcoxonSignedRank statistic (the larger of W+ and W-) wilcoxonSignedRank(final double[] the first sample x, final double[] the second sample y) Computes the Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample.
public double	Returns: p-value wilcoxonSignedRankTest(final double[] the first sample x, final double[] the second sample y, final boolean if the exact p-value is wanted (only works for x.length <= 30, if true and x.length > 30, this is ignored because calculations may take too long) exactPValue) Returns the observed significance level, or p-value, associated with a Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

naturalRanking	back to summary
private NaturalRanking naturalRanking Ranking algorithm.

WilcoxonSignedRankTest	back to summary
public WilcoxonSignedRankTest() Create a test instance 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.

WilcoxonSignedRankTest	back to summary
public WilcoxonSignedRankTest(final NaNStrategy nanStrategy, final 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:NaNStrategy specifies the strategy that should be used for Double.NaN's tiesStrategy:TiesStrategy specifies the strategy that should be used for ties

Method Detail

calculateAbsoluteDifferences back to summary

calculateAbsoluteDifferences	back to summary
private double[] calculateAbsoluteDifferences(final double[] z) throws NullArgumentException, NoDataException Calculates \|z[i]\| for all i Parameters z:double[] sample Returns:double[] \|z\| Exceptions NullArgumentException: if `z` is `null` NoDataException: if `z` is zero-length.

private double[] calculateAbsoluteDifferences(final double[] z) throws NullArgumentException, NoDataException

Calculates |z[i]| for all i

Parameters

z:double[]: sample

Returns:double[]

|z|

Exceptions

NullArgumentException:: if z is null
NoDataException:: if z is zero-length.

calculateAsymptoticPValue	back to summary
private double calculateAsymptoticPValue(final double Wmin, final int N) Parameters Wmin:double smallest Wilcoxon signed rank value N:int number of subjects (corresponding to x.length) Returns:double two-sided asymptotic p-value

calculateDifferences	back to summary
private double[] calculateDifferences(final double[] x, final double[] y) Calculates y[i] - x[i] for all i Parameters x:double[] first sample y:double[] second sample Returns:double[] z = y - x

calculateDifferences

back to summary

private double[] calculateDifferences(final double[] x, final double[] y)

Calculates y[i] - x[i] for all i

Parameters

x:double[]: first sample
y:double[]: second sample

Returns:double[]

z = y - x

calculateExactPValue	back to summary
private double calculateExactPValue(final double Wmax, final int N) Algorithm inspired by http://www.fon.hum.uva.nl/Service/Statistics/Signed_Rank_Algorihms.html#C by Rob van Son, Institute of Phonetic Sciences & IFOTT, University of Amsterdam Parameters Wmax:double largest Wilcoxon signed rank value N:int number of subjects (corresponding to x.length) Returns:double two-sided exact p-value

calculateExactPValue

back to summary

private double calculateExactPValue(final double Wmax, final int N)

Algorithm inspired by http://www.fon.hum.uva.nl/Service/Statistics/Signed_Rank_Algorihms.html#C by Rob van Son, Institute of Phonetic Sciences & IFOTT, University of Amsterdam

Parameters

Wmax:double: largest Wilcoxon signed rank value
N:int: number of subjects (corresponding to x.length)

Returns:double

two-sided exact p-value

ensureDataConformance back to summary

ensureDataConformance	back to summary
private void ensureDataConformance(final double[] x, final double[] y) throws NullArgumentException, NoDataException, DimensionMismatchException Ensures that the provided arrays fulfills the assumptions. Parameters x:double[] first sample y:double[] second sample Exceptions NullArgumentException: if `x` or `y` are `null`. NoDataException: if `x` or `y` are zero-length. DimensionMismatchException: if `x` and `y` do not have the same length.

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

Ensures that the provided arrays fulfills the assumptions.

Parameters

x:double[]: first sample
y:double[]: second sample

Exceptions

NullArgumentException:: if x or y are null.
NoDataException:: if x or y are zero-length.
DimensionMismatchException:: if x and y do not have the same length.

wilcoxonSignedRank back to summary

wilcoxonSignedRank	back to summary
public double wilcoxonSignedRank(final double[] x, final double[] y) throws NullArgumentException, NoDataException, DimensionMismatchException Computes the Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample. This statistic can be used to perform a Wilcoxon signed ranked test evaluating the null hypothesis that the two related samples or repeated measurements on a single sample has equal mean. Let X_i denote the i'th individual of the first sample and Y_i the related i'th individual in the second sample. Let Z_i = Y_i - X_i. Preconditions: The differences Z_i must be independent. Each Z_i comes from a continuous population (they must be identical) and is symmetric about a common median. The values that X_i and Y_i represent are ordered, so the comparisons greater than, less than, and equal to are meaningful. Parameters x:double[] the first sample y:double[] the second sample Returns:double wilcoxonSignedRank statistic (the larger of W+ and W-) Exceptions NullArgumentException: if `x` or `y` are `null`. NoDataException: if `x` or `y` are zero-length. DimensionMismatchException: if `x` and `y` do not have the same length.

public double wilcoxonSignedRank(final double[] x, final double[] y) throws NullArgumentException, NoDataException, DimensionMismatchException

Computes the Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample.

This statistic can be used to perform a Wilcoxon signed ranked test evaluating the null hypothesis that the two related samples or repeated measurements on a single sample has equal mean.

Let X_i denote the i'th individual of the first sample and Y_i the related i'th individual in the second sample. Let Z_i = Y_i - X_i.

Preconditions:

The differences Z_i must be independent.
Each Z_i comes from a continuous population (they must be identical) and is symmetric about a common median.
The values that X_i and Y_i represent are ordered, so the comparisons greater than, less than, and equal to are meaningful.

Parameters

x:double[]: the first sample
y:double[]: the second sample

Returns:double

wilcoxonSignedRank statistic (the larger of W+ and W-)

Exceptions

NullArgumentException:: if x or y are null.
NoDataException:: if x or y are zero-length.
DimensionMismatchException:: if x and y do not have the same length.

wilcoxonSignedRankTest back to summary

wilcoxonSignedRankTest	back to summary
public double wilcoxonSignedRankTest(final double[] x, final double[] y, final boolean exactPValue) throws NullArgumentException, NoDataException, DimensionMismatchException, NumberIsTooLargeException, ConvergenceException, MaxCountExceededException Returns the observed significance level, or p-value, associated with a Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample. Let X_i denote the i'th individual of the first sample and Y_i the related i'th individual in the second sample. Let Z_i = Y_i - X_i. Preconditions: The differences Z_i must be independent. Each Z_i comes from a continuous population (they must be identical) and is symmetric about a common median. The values that X_i and Y_i represent are ordered, so the comparisons greater than, less than, and equal to are meaningful. Parameters x:double[] the first sample y:double[] the second sample exactPValue:boolean if the exact p-value is wanted (only works for x.length <= 30, if true and x.length > 30, this is ignored because calculations may take too long) Returns:double p-value Exceptions NullArgumentException: if `x` or `y` are `null`. NoDataException: if `x` or `y` are zero-length. DimensionMismatchException: if `x` and `y` do not have the same length. NumberIsTooLargeException: if `exactPValue` is `true` and `x.length` > 30 ConvergenceException: if the p-value can not be computed due to a convergence error MaxCountExceededException: if the maximum number of iterations is exceeded

public double wilcoxonSignedRankTest(final double[] x, final double[] y, final boolean exactPValue) throws NullArgumentException, NoDataException, DimensionMismatchException, NumberIsTooLargeException, ConvergenceException, MaxCountExceededException

Returns the observed significance level, or p-value, associated with a Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample.

Let X_i denote the i'th individual of the first sample and Y_i the related i'th individual in the second sample. Let Z_i = Y_i - X_i.

Preconditions:

The differences Z_i must be independent.
Each Z_i comes from a continuous population (they must be identical) and is symmetric about a common median.
The values that X_i and Y_i represent are ordered, so the comparisons greater than, less than, and equal to are meaningful.

Parameters

x:double[]: the first sample
y:double[]: the second sample
exactPValue:boolean: if the exact p-value is wanted (only works for x.length <= 30, if true and x.length > 30, this is ignored because calculations may take too long)

Returns:double

p-value

Exceptions

NullArgumentException:: if x or y are null.
NoDataException:: if x or y are zero-length.
DimensionMismatchException:: if x and y do not have the same length.
NumberIsTooLargeException:: if exactPValue is true and x.length > 30
ConvergenceException:: if the p-value can not be computed due to a convergence error
MaxCountExceededException:: if the maximum number of iterations is exceeded

public Class WilcoxonSignedRankTest

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