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

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

Nested Class Summary

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

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

java.lang.String	alternativeHypothesis() Get a description of the alternative hypothesis.
static Matrix	expectedContingencyTable(int[] rowSums, int[] colSums) Assume the null hypothesis of independence, we compute the expected frequency of each category.
java.lang.String	nullHypothesis() 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

oneSidedPvalue, pValue, rejectNull, testStatistics

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

nullHypothesis

public java.lang.String nullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

nullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

alternativeHypothesis

public java.lang.String alternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

alternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

expectedContingencyTable

public static Matrix expectedContingencyTable(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 iff to minus 0.5 for each observation in the test statistics

Returns:

the Pearson's cumulative test statistic