gov.sandia.cognition.statistics.method

## Class MannWhitneyUConfidence

• All Implemented Interfaces:
NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

```@ConfidenceTestAssumptions(name="Mann-Whitney U-test",
alsoKnownAs={"Mann-Whitney-Wolcoxon","Wilcoxon rank-sum test","Wilcoxon-Mann-Whitney test","U-test"},
description="A nonparameteric test to determine is two groups of data were drawn from the same underlying distribution.",
assumptions={"The groups were sampled independently.","The data are orginal and we can determine which of two samples is greater than the other.","Although the two populations don\'t have to follow any particular distribution, the two distributions must have a similar shape."},
nullHypothesis="The data were drawn from the same distribution.",
dataPaired=false,
dataSameSize=false,
distribution=UnivariateGaussian.CDF.class,
reference=@PublicationReference(author="Wikipedia",title="Mann-Whitney U",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Mann-Whitney_U"))
public class MannWhitneyUConfidence
extends AbstractCloneableSerializable
implements NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>```
Performs a Mann-Whitney U-test on the given data (usually simply called a "U-test", sometimes called a Wilcoxon-Mann-Whitney U-test, or Wilcoxon rank-sum test).
Since:
2.0
Author:
Kevin R. Dixon
See Also:
Serialized Form
• ### Nested Class Summary

Nested Classes
Modifier and Type Class and Description
`static class ` `MannWhitneyUConfidence.Statistic`
Statistics from the Mann-Whitney U-test
• ### Constructor Summary

Constructors
Constructor and Description
`MannWhitneyUConfidence()`
Creates a new instance of MannWhitneyUConfidence
• ### Method Summary

All Methods
Modifier and Type Method and Description
`MannWhitneyUConfidence.Statistic` `evaluateNullHypothesis(java.util.Collection<? extends InputOutputPair<? extends java.lang.Number,java.lang.Boolean>> scoreClassPairs)`
Performs a U-test on the score-class pairs.
`MannWhitneyUConfidence.Statistic` ```evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1, java.util.Collection<? extends java.lang.Number> data2)```
Computes the probability that two data were generated by the same distribution.
• ### Methods inherited from class gov.sandia.cognition.util.AbstractCloneableSerializable

`clone`
• ### Methods inherited from class java.lang.Object

`equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Methods inherited from interface gov.sandia.cognition.util.CloneableSerializable

`clone`
• ### Constructor Detail

• #### MannWhitneyUConfidence

`public MannWhitneyUConfidence()`
Creates a new instance of MannWhitneyUConfidence
• ### Method Detail

• #### evaluateNullHypothesis

`public MannWhitneyUConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends InputOutputPair<? extends java.lang.Number,java.lang.Boolean>> scoreClassPairs)`
Performs a U-test on the score-class pairs. The first element in the pair is a score, the second is a flag to determine which group the score belongs to. For example {, means that data1=1.0 and data2=0.9 and so forth. This is useful for computing that classified data partitions data better than chance.
Parameters:
`scoreClassPairs` - Pairs of scores with the corresponding class "label" for the score
Returns:
Statistics from the Mann-Whitney U-test
• #### evaluateNullHypothesis

```public MannWhitneyUConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1,
java.util.Collection<? extends java.lang.Number> data2)```
Description copied from interface: `NullHypothesisEvaluator`
Computes the probability that two data were generated by the same distribution. NullHypothesisProbability=1 means that the distributions are likely the same, NullHypothesisProbability=0 means they are likely NOT the same, and NullHypothesisProbability less than 0.05 is the standard statistical significance test. This is the "p-value" that social scientists like to use.
Specified by:
`evaluateNullHypothesis` in interface `NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>`
Parameters:
`data1` - First dataset to consider
`data2` - Second dataset to consider
Returns:
Probability that the two data were generated by the same source. A value of NullHypothesisProbability less than 0.05 is the standard point at which social scientists say two distributions were generated by different sources.