gov.sandia.cognition.statistics.method

Class KolmogorovSmirnovConfidence

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.KolmogorovSmirnovConfidence

All Implemented Interfaces:

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

@ConfidenceTestAssumptions(name="Kolmogorov-Smirnov test",
                           alsoKnownAs="K-S test",
                           description={"Determines if two datasets were drawn from the same univariate distribution.","Robust, nonparameteric test that makes no assumptions on the underlying distribution (continuous, discrete, etc.)."},
                           assumptions="The data were sampled independently from each other.",
                           nullHypothesis="The data were drawn from the same distribution.",
                           dataPaired=false,
                           dataSameSize=false,
                           distribution=KolmogorovDistribution.CDF.class,
                           reference=@PublicationReference(author="Wikipedia",title="Kolmogorov-Smirnov test",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test"))
public class KolmogorovSmirnovConfidence
extends AbstractCloneableSerializable
implements NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>

Performs a Kolmogorov-Smirnov Confidence Test. This is often simply called the "K-S test". This is a powerful nonparametric test that determines the probability that two distributions were generated by the same distribution. There are minimal (no?) assumptions on the underlying data or distributions. That is, the distributions are NOT assumed to be Gaussian, etc.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	KolmogorovSmirnovConfidence.Statistic Computes the ConfidenceStatistic associated with a K-S test

Field Summary

Fields

Modifier and Type	Field and Description
static KolmogorovSmirnovConfidence	INSTANCE Default instance of the K-S test.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
protected static double[]	computeAscendingArray(java.util.Collection<? extends java.lang.Number> data) Returns an array of ascending sorted values from the given Collection
static KolmogorovSmirnovConfidence.Statistic	evaluateGaussianHypothesis(java.util.Collection<java.lang.Double> data) Evaluates the Hypothesis that the given data were generated according to a UnivariateGaussian distribution.
static <DomainType extends java.lang.Number> KolmogorovSmirnovConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends DomainType> data1, CumulativeDistributionFunction<DomainType> function) This is the standard K-S test for determining if the given data were generated by the given CDF.
KolmogorovSmirnovConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1, java.util.Collection<? extends java.lang.Number> data2) This is the standard K-S test for two distributions of data.

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 KolmogorovSmirnovConfidence INSTANCE

Default instance of the K-S test.

Constructor Detail

KolmogorovSmirnovConfidence

public KolmogorovSmirnovConfidence()

Creates a new instance of KolmogorovSmirnovConfidence

Method Detail

computeAscendingArray

protected static double[] computeAscendingArray(java.util.Collection<? extends java.lang.Number> data)

Returns an array of ascending sorted values from the given Collection

Parameters:

data - Collection of doubles to sort into ascending order

Returns:

Array of ascending sorted values

evaluateNullHypothesis

@PublicationReference(author={"William H. Press","Saul A. Teukolsky","William T. Vetterling","Brian P. Flannery"},
                      title="Numerical Recipes in C, Second Edition",
                      type=Book,
                      year=1992,
                      pages={625,626},
                      notes={"Section 14.3","Function kstwo()"},
                      url="http://www.nrbook.com/a/bookcpdf.php")
public KolmogorovSmirnovConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends java.lang.Number> data1,
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         java.util.Collection<? extends java.lang.Number> data2)

This is the standard K-S test for two distributions of data. Determines the probability that the two distributions of data were generated by the same underlying distributions. This is a parameter-free test, so the assumptions on the underlying data are minimal (inexistent?).

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:

ConfidenceStatistic from the K-S test.

evaluateNullHypothesis

@PublicationReference(author={"William H. Press","Saul A. Teukolsky","William T. Vetterling","Brian P. Flannery"},
                      title="Numerical Recipes in C, Second Edition",
                      type=Book,
                      year=1992,
                      pages=625,
                      notes={"Section 14.3","Function ksone()"})
public static <DomainType extends java.lang.Number> KolmogorovSmirnovConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends DomainType> data1,
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              CumulativeDistributionFunction<DomainType> function)

This is the standard K-S test for determining if the given data were generated by the given CDF. Computes the probability that the two distributions of data are actually the same underlying distributions. This is a parameter-free test, so the assumptions on the underlying data are minimal (inexistent?). For example, to test if a dataset is normally distribution, call computeNullHypothesisProbability( data, new UnivariateGaussian.CumulativeDistribution() ).

Type Parameters:

DomainType - Type of Number to consider

Parameters:

data1 - Dataset to consider

function - CDF to compare against the given data

Returns:

ConfidenceStatistic from the K-S test.

evaluateGaussianHypothesis

public static KolmogorovSmirnovConfidence.Statistic evaluateGaussianHypothesis(java.util.Collection<java.lang.Double> data)

Evaluates the Hypothesis that the given data were generated according to a UnivariateGaussian distribution. A high null-hypothesis probability is not conclusive proof that the data were generated by a Gaussian. However, a low null-hypothesis probability is conclusive that the data were NOT likely generated by a Gaussian

Parameters:

data - Data to evaluate the possibility that they were generated according to a Gaussian Distribution

Returns:

Confidence statistic from the K-S test