org.apache.commons.math3.stat.inference
Class WilcoxonSignedRankTest

java.lang.Object
  org.apache.commons.math3.stat.inference.WilcoxonSignedRankTest

public class WilcoxonSignedRankTest
extends Object

An implementation of the Wilcoxon signed-rank test.

Version:

$Id: WilcoxonSignedRankTest.java 7721 2013-02-14 14:07:13Z CardosoP $

Constructor Summary

WilcoxonSignedRankTest()
Create a test instance where NaN's are left in place and ties get the average of applicable ranks.

WilcoxonSignedRankTest(NaNStrategy nanStrategy, TiesStrategy tiesStrategy)
Create a test instance using the given strategies for NaN's and ties.

Method Summary

double	wilcoxonSignedRank(double[] x, double[] y) Computes the Wilcoxon signed ranked statistic comparing mean for two related samples or repeated measurements on a single sample.
double	wilcoxonSignedRankTest(double[] x, double[] y, boolean 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.

Methods inherited from class java.lang.Object

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

Constructor Detail

WilcoxonSignedRankTest

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

public WilcoxonSignedRankTest(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

wilcoxonSignedRank

public double wilcoxonSignedRank(double[] x,
                                 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 - the first sample

y - the second sample

Returns:

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

Throws:

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

public double wilcoxonSignedRankTest(double[] x,
                                     double[] y,
                                     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 - the first sample

y - the second sample

exactPValue - 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:

p-value

Throws:

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