gov.sandia.cognition.statistics.method

Class FriedmanConfidence

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.FriedmanConfidence

All Implemented Interfaces:

BlockExperimentComparison<java.lang.Number>, NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

@ConfidenceTestAssumptions(name="Friedman\'s test",alsoKnownAs="",description={"Friedman\'s test determines if the rankings associated with various treatments are equal.","This is a nonparametric rank-based alternative to ANOVA, a multiple comparison generalization similar to the difference between Student\'s t-test and Wilcoxon rank-signed test.","Friedman\'s test tends to have as much power as ANOVA, but without ANOVA\'s parameteric assumptions"},assumptions={"All data came from same distribution, without considering treatment effects.","Measurements are independent and equivalent within a treatment.","All observations are independent."},nullHypothesis="The treatments have no effect on experimental observations.",dataPaired=true,dataSameSize=true,distribution=SnedecorFDistribution.class,reference={@PublicationReference(author="Janez Demsar",title="Statistical Comparisons of Classifiers over Multiple Data Sets",type=Journal,publication="Journal of Machine Learning Research",year=2006,url="http://www.jmlr.org/papers/volume7/demsar06a/demsar06a.pdf"),@PublicationReference(author="Wikipedia",title="Friedman test",type=WebPage,year=2011,url="http://en.wikipedia.org/wiki/Friedman_test",notes="Our test uses the tighter F-statistic rather than the original chi-square statistic")})
public class FriedmanConfidence
extends AbstractCloneableSerializable
implements BlockExperimentComparison<java.lang.Number>

The Friedman test determines if the rankings associated with various treatments are equal. This is a nonparametric alternative to ANOVA.

Since:

3.1

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	FriedmanConfidence.Statistic Confidence statistic associated with the Friedman test using the tighter F-statistic.

Field Summary

Fields

Modifier and Type	Field and Description
static FriedmanConfidence	INSTANCE Default instance.

Constructor Summary

Constructors

Constructor and Description
FriedmanConfidence() Creates a new instance of FriedmanConfidence

Method Summary

Modifier and Type	Method and Description
static java.util.ArrayList<java.lang.Double>	computeTreatmentRankMeans(java.util.Collection<? extends java.util.Collection<? extends java.lang.Number>> data) Computes the mean rank of the treatments
FriedmanConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends java.util.Collection<? extends java.lang.Number>> data) Evaluates the null hypothesis for the given block-design treatments
FriedmanConfidence.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

Field Detail

INSTANCE

public static final FriedmanConfidence INSTANCE

Default instance.

Constructor Detail

FriedmanConfidence

public FriedmanConfidence()

Creates a new instance of FriedmanConfidence

Method Detail

evaluateNullHypothesis

public FriedmanConfidence.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.

evaluateNullHypothesis

public FriedmanConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.util.Collection<? extends java.lang.Number>> data)

Description copied from interface: BlockExperimentComparison

Evaluates the null hypothesis for the given block-design treatments

Specified by:

evaluateNullHypothesis in interface BlockExperimentComparison<java.lang.Number>

Parameters:

data - Collection of treatments for the block-design experiment, where each treatment contains

Returns:

The confidence for the null hypothesis.

computeTreatmentRankMeans

public static java.util.ArrayList<java.lang.Double> computeTreatmentRankMeans(java.util.Collection<? extends java.util.Collection<? extends java.lang.Number>> data)

Computes the mean rank of the treatments

Parameters:

data - Collection of treatments, where each treatment must have the same number of subjects in each treatment

Returns:

An mean rank for each of the treatments