gov.sandia.cognition.statistics.method

Class ChiSquareConfidence

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.method.ChiSquareConfidence

All Implemented Interfaces:

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

@ConfidenceTestAssumptions(name="Chi-Squre test",
                           alsoKnownAs="Pearson\'s Chi-Square test",
                           description="The chi-square test determines if the given data were generated from the same discrete distributions.",
                           assumptions={"A large sample, typically above 30.","Typically, each bin from the discrete distribution must have at least 5 samples.","The underlying discrete distribution must obey the weak law of large numbers.","The observations are assumed to be independent."},
                           nullHypothesis="The frequency of events in the two datasets is consistent.",
                           dataPaired=true,
                           dataSameSize=true,
                           distribution=ChiSquareDistribution.CDF.class,
                           reference=@PublicationReference(author="Wikipedia",title="Pearson\'s chi-square test",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test"))
public class ChiSquareConfidence
extends AbstractCloneableSerializable
implements NullHypothesisEvaluator<java.util.Collection<? extends java.lang.Number>>

This is the chi-square goodness-of-fit test. This test allows us to compare observations against expected results, where the observations and expectations are recorded for discrete groups/conditions/bins. The null hypothesis is that the observed values were drawn from the same distribution as the expected values.

The chi-square goodness-of-fit test is a discrete version of the more general Kolmogorov-Smirnov test. If your data were drawn from a continuous distribution, I would recommend the K-S test instead.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ChiSquareConfidence.Statistic Confidence Statistic for a chi-square test

Field Summary

Fields

Modifier and Type	Field and Description
static ChiSquareConfidence	INSTANCE Default instance variable since the class has no members.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
static <DomainType> ChiSquareConfidence.Statistic	evaluateNullHypothesis(java.util.Collection<? extends DomainType> data, ProbabilityMassFunction<DomainType> pmf) Computes the chi-square test between a collection of data and a Probability Mass Function that may have create the observed data.
ChiSquareConfidence.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 ChiSquareConfidence INSTANCE

Default instance variable since the class has no members.

Constructor Detail

ChiSquareConfidence

public ChiSquareConfidence()

Creates a new instance of ChiSquareConfidence

Method Detail

evaluateNullHypothesis

public static <DomainType> ChiSquareConfidence.Statistic evaluateNullHypothesis(java.util.Collection<? extends DomainType> data,
                                                                                ProbabilityMassFunction<DomainType> pmf)

Computes the chi-square test between a collection of data and a Probability Mass Function that may have create the observed data.

Type Parameters:

DomainType - Domain type of the PMF.

Parameters:

data - Data observed from some discrete distribution.

pmf - Probability mass function that may have created the observed data.

Returns:

Chi-square test results.

evaluateNullHypothesis

public ChiSquareConfidence.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.