Package org.moeaframework.util.statistics

Class WilcoxonSignedRanksTest

java.lang.Object

org.moeaframework.util.statistics.OrdinalStatisticalTest

org.moeaframework.util.statistics.WilcoxonSignedRanksTest

All Implemented Interfaces:

StatisticalTest

public class WilcoxonSignedRanksTest
extends OrdinalStatisticalTest

The Wilcoxon Signed-Ranks test determines if the population median is equal to a specified value.

• Null Hypothesis: The population median equals X.
• Alternative Hypothesis: The population median does not equal X.

Assumptions:

1. Samples are randomly selected from the population
2. The underlying population distribution is symmetrical

References:

1. Sheskin, D.J. "Handbook of Parametric and Nonparametric Statistical Procedures, Third Edition." Chapman & Hall/CRC. 2004.

Field Summary

Fields inherited from class org.moeaframework.util.statistics.OrdinalStatisticalTest

comparator, data, numberOfGroups

Constructor Summary

Constructors

Constructor	Description
WilcoxonSignedRanksTest(double median)	Constructs a Wilcoxon signed ranks test with the specified median.

Method Summary

Modifier and Type	Method	Description
void	add(double value)	Adds a new observation with the specified value.
void	addAll(double[] values)	Adds several new observations with the specified values.
double	getMedian()	Returns the value being tested against the population median.
org.apache.commons.math3.stat.descriptive.DescriptiveStatistics	getStatistics()	Returns the descriptive statistics for the recorded data.
boolean	test(double alpha)	Returns true if the null hypothesis is rejected; false otherwise.

Methods inherited from class org.moeaframework.util.statistics.OrdinalStatisticalTest

add, addAll, getComparator, getNumberOfGroups, getStatistics, size, update

Methods inherited from class java.lang.Object

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

Constructor Details

WilcoxonSignedRanksTest

public WilcoxonSignedRanksTest(double median)

Constructs a Wilcoxon signed ranks test with the specified median.

Parameters:

median - the value being tested against the population median

Method Details

getMedian

public double getMedian()

Returns the value being tested against the population median.

Returns:

the value being tested against the population median

add

public void add(double value)

Adds a new observation with the specified value.

Parameters:

value - the value of the new observation

addAll

public void addAll(double[] values)

Adds several new observations with the specified values.

Parameters:

values - the values of the new observations

getStatistics

public org.apache.commons.math3.stat.descriptive.DescriptiveStatistics getStatistics()

Returns the descriptive statistics for the recorded data.

Returns:

the descriptive statistics

test

public boolean test(double alpha)

Returns true if the null hypothesis is rejected; false otherwise. The meaning of the null hypothesis and alternative hypothesis depends on the specific test.

The prespecified level of confidence, alpha, can be used for either one-tailed or two-tailed (directional or non-directional) distributions, depending on the specific test. Some tests may only support specific values for alpha.

When the samples from both populations are less than 20, only alpha values of 0.05 and 0.01 are valid. This is because a table is used to accurately determine the critical values. When more than 20 samples are available, the normal approximation is used allowing any value for alpha.

Parameters:

alpha - the prespecified level of confidence

Returns:

true if the null hypothesis is rejected; false otherwise

Throws:

IllegalArgumentException - if an insufficient sampling size is provided, or if an invalid alpha value is provided