org.hipparchus.stat.inference

Class WilcoxonSignedRankTest

java.lang.Object

org.hipparchus.stat.inference.WilcoxonSignedRankTest

public class WilcoxonSignedRankTest
extends Object

An implementation of the Wilcoxon signed-rank test. This implementation currently handles only paired (equal length) samples and discards tied pairs from the analysis. The latter behavior differs from the R implementation of wilcox.test and corresponds to the "wilcox" zero_method configurable in scipy.stats.wilcoxon.

Constructor Summary

Constructors

Constructor and Description
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

Modifier and Type	Method and Description
double	wilcoxonSignedRank(double[] x, double[] y) Computes the Wilcoxon signed ranked statistic comparing means 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.

WilcoxonSignedRankTest

public WilcoxonSignedRankTest(NaNStrategy nanStrategy,
                              TiesStrategy tiesStrategy)

Create a test instance using the given strategies for NaN's and ties.

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 MathIllegalArgumentException,
                                 NullArgumentException

Computes the Wilcoxon signed ranked statistic comparing means 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 have 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.

MathIllegalArgumentException - if x or y are zero-length.

MathIllegalArgumentException - if x and y do not have the same length.

wilcoxonSignedRankTest

public double wilcoxonSignedRankTest(double[] x,
                                     double[] y,
                                     boolean exactPValue)
                              throws MathIllegalArgumentException,
                                     NullArgumentException,
                                     MathIllegalStateException

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.

Implementation notes:

• Tied pairs are discarded from the data.
• When exactPValue is false, the normal approximation is used to estimate the p-value including a continuity correction factor. wilcoxonSignedRankTest(x, y, true) should give the same results as wilcox.test(x, y, alternative = "two.sided", mu = 0, paired = TRUE, exact = FALSE, correct = TRUE) in R (as long as there are no tied pairs in the data).

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, MathIllegalArgumentException is thrown)

Returns:

p-value

Throws:

NullArgumentException - if x or y are null.

MathIllegalArgumentException - if x or y are zero-length or for all i, x[i] == y[i]

MathIllegalArgumentException - if x and y do not have the same length.

MathIllegalArgumentException - if exactPValue is true and x.length > 30

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

MathIllegalStateException - if the maximum number of iterations is exceeded