com.numericalmethod.suanshu.stats.test.distribution.pearson

Class ChiSquare4Independence

java.lang.Object

com.numericalmethod.suanshu.stats.test.HypothesisTest

com.numericalmethod.suanshu.stats.test.distribution.pearson.ChiSquare4Independence

All Implemented Interfaces:

java.io.Serializable

public class ChiSquare4Independence
extends HypothesisTest

Pearson's chi-square test of independence assesses whether paired observations on two variables, expressed in a contingency table, are independent of each other.

See Also:

Wikipedia: Pearson's chi-square test, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ChiSquare4Independence.Type the distribution used for the test

Field Summary

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Constructor Summary

Constructors

Constructor and Description
ChiSquare4Independence(Matrix sample) Assess whether the two random variable in the contingency table is independent.
ChiSquare4Independence(Matrix sample, int nSim, ChiSquare4Independence.Type type) Assess whether the two random variable in the contingency table is independent.

Method Summary

Modifier and Type	Method and Description
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
static Matrix	getExpectedContingencyTable(int[] rowSums, int[] colSums) Assume the null hypothesis of independence, we compute the expected frequency of each category.
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
static double	pearsonStat(Matrix O, Matrix E, boolean YatesContinuityCorrection) Compute the Pearson's cumulative test statistic, which asymptotically approaches a χ2 distribution.

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

isNullRejected, oneSidedPvalue, pValue, statistics

Methods inherited from class java.lang.Object

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

Constructor Detail

ChiSquare4Independence

public ChiSquare4Independence(Matrix sample,
                              int nSim,
                              ChiSquare4Independence.Type type)

Assess whether the two random variable in the contingency table is independent.

Parameters:

sample - a contingency table

nSim - number of simulation when EXACT distribution is used

type - the type of distribution

ChiSquare4Independence

public ChiSquare4Independence(Matrix sample)

Assess whether the two random variable in the contingency table is independent.

Parameters:

sample - a contingency table

Method Detail

getNullHypothesis

public java.lang.String getNullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

getNullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

getExpectedContingencyTable

public static Matrix getExpectedContingencyTable(int[] rowSums,
                                                 int[] colSums)

Assume the null hypothesis of independence, we compute the expected frequency of each category.

Parameters:

rowSums - row totals

colSums - column totals

Returns:

a table of expected frequency under the null hypothesis

pearsonStat

public static double pearsonStat(Matrix O,
                                 Matrix E,
                                 boolean YatesContinuityCorrection)

Compute the Pearson's cumulative test statistic, which asymptotically approaches a χ2 distribution.

Parameters:

O - the observation matrix

E - the expectation matrix

YatesContinuityCorrection - true if to minus 0.5 for each observation in the test statistics

Returns:

the Pearson's cumulative test statistic