org.moeaframework.util.statistics
Class MannWhitneyUTest

java.lang.Object
  org.moeaframework.util.statistics.OrdinalStatisticalTest
      org.moeaframework.util.statistics.MannWhitneyUTest

All Implemented Interfaces:

StatisticalTest

public class MannWhitneyUTest
extends OrdinalStatisticalTest

The Mann-Whitney U test determines if two populations have different medians.

• Null Hypothesis: The two populations have the same medians.
• Alternative Hypothesis: The two populations have different medians.

Assumptions:

1. Samples are randomly selected from their corresponding populations
2. Samples are independent
3. The dependent variable (value being sampled) is continuous
4. The underlying distributions of the populations are identical in shape

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

MannWhitneyUTest()
Constructs a Mann-Whitney U test.

Method Summary

void	add(double value, int group) Adds a new observation with the specified value and group.
void	addAll(double[] values, int group) Adds several new observations to the specified group.
boolean	test(double alpha) Returns true if the null hypothesis is rejected; false otherwise.

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

getComparator, getNumberOfGroups, size, update

Methods inherited from class java.lang.Object

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

Constructor Detail

MannWhitneyUTest

public MannWhitneyUTest()

Constructs a Mann-Whitney U test.

Method Detail

add

public void add(double value,
                int group)

Description copied from class: OrdinalStatisticalTest

Adds a new observation with the specified value and group.

Overrides:

add in class OrdinalStatisticalTest

Parameters:

value - the value of the new observation

group - the group to which the new observation belongs

addAll

public void addAll(double[] values,
                   int group)

Description copied from class: OrdinalStatisticalTest

Adds several new observations to the specified group.

Overrides:

addAll in class OrdinalStatisticalTest

Parameters:

values - the values of the new observations

group - the group to which the new observations belong

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 nondirectional) 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