org.apache.commons.math.stat.inference
Class ChiSquareTestImpl

java.lang.Object
  org.apache.commons.math.stat.inference.ChiSquareTestImpl

All Implemented Interfaces:

ChiSquareTest

public class ChiSquareTestImpl
extends java.lang.Object
implements ChiSquareTest

Implements Chi-Square test statistics defined in the ChiSquareTest interface.

Version:

$Revision: 155427 $ $Date: 2005-02-26 06:11:52 -0700 (Sat, 26 Feb 2005) $

Field Summary

private DistributionFactory

distributionFactory Cached DistributionFactory used to create ChiSquaredDistribution instances

Constructor Summary

ChiSquareTestImpl()
Construct a ChiSquareTestImpl

Method Summary

private void	checkArray(long[][] in) Checks to make sure that the input long[][] array is rectangular, has at least 2 rows and 2 columns, and has all non-negative entries, throwing IllegalArgumentException if any of these checks fail.
double	chiSquare(double[] expected, long[] observed) Computes the Chi-Square statistic comparing observed and expected freqeuncy counts.
double	chiSquare(long[][] counts) Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
double	chiSquareTest(double[] expected, long[] observed) Returns the observed significance level, or p-value, associated with a Chi-square goodness of fit test comparing the observed frequency counts to those in the expected array.
boolean	chiSquareTest(double[] expected, long[] observed, double alpha) Performs a Chi-square goodness of fit test evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha.
double	chiSquareTest(long[][] counts) Returns the observed significance level, or p-value, associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.
boolean	chiSquareTest(long[][] counts, double alpha) Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha.
protected DistributionFactory	getDistributionFactory() Gets a DistributionFactory to use in creating ChiSquaredDistribution instances.
private boolean	isNonNegative(long[] in) Returns true iff all entries of the input array are >= 0.
private boolean	isNonNegative(long[][] in) Returns true iff all entries of (all subarrays of) the input array are >= 0.
private boolean	isPositive(double[] in) Returns true iff all entries of the input array are > 0.
private boolean	isRectangular(long[][] in) Returns true iff input array is rectangular.

Methods inherited from class java.lang.Object

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

Field Detail

distributionFactory

private DistributionFactory distributionFactory

Cached DistributionFactory used to create ChiSquaredDistribution instances

Constructor Detail

ChiSquareTestImpl

public ChiSquareTestImpl()

Construct a ChiSquareTestImpl

Method Detail

chiSquare

public double chiSquare(double[] expected,
                        long[] observed)
                 throws java.lang.IllegalArgumentException

Description copied from interface: ChiSquareTest

Computes the Chi-Square statistic comparing observed and expected freqeuncy counts.

This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that the observed counts follow the expected distribution.

Preconditions:

• Expected counts must all be positive.
• Observed counts must all be >= 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquare in interface ChiSquareTest

Parameters:

observed - array of observed frequency counts

expected - array of expected frequency counts

Returns:

chi-square test statistic

Throws:

java.lang.IllegalArgumentException - if preconditions are not met or length is less than 2

chiSquareTest

public double chiSquareTest(double[] expected,
                            long[] observed)
                     throws java.lang.IllegalArgumentException,
                            MathException

Description copied from interface: ChiSquareTest

Returns the observed significance level, or p-value, associated with a Chi-square goodness of fit test comparing the observed frequency counts to those in the expected array.

The number returned is the smallest significance level at which one can reject the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts.

Preconditions:

• Expected counts must all be positive.
• Observed counts must all be >= 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

observed - array of observed frequency counts

expected - array of exptected frequency counts

Returns:

p-value

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs computing the p-value

chiSquareTest

public boolean chiSquareTest(double[] expected,
                             long[] observed,
                             double alpha)
                      throws java.lang.IllegalArgumentException,
                             MathException

Description copied from interface: ChiSquareTest

Performs a Chi-square goodness of fit test evaluating the null hypothesis that the observed counts conform to the frequency distribution described by the expected counts, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.

Example:
To test the hypothesis that observed follows expected at the 99% level, use

chiSquareTest(expected, observed, 0.01)

Preconditions:

• Expected counts must all be positive.
• Observed counts must all be >= 0.
• The observed and expected arrays must have the same length and their common length must be at least 2.
• 0 < alpha < 0.5

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

observed - array of observed frequency counts

expected - array of exptected frequency counts

alpha - significance level of the test

Returns:

true iff null hypothesis can be rejected with confidence 1 - alpha

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

chiSquare

public double chiSquare(long[][] counts)
                 throws java.lang.IllegalArgumentException

Description copied from interface: ChiSquareTest

Computes the Chi-Square statistic associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.

The rows of the 2-way table are count[0], ... , count[count.length - 1]

Preconditions:

• All counts must be >= 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquare in interface ChiSquareTest

Parameters:

counts - array representation of 2-way table

Returns:

chi-square test statistic

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

chiSquareTest

public double chiSquareTest(long[][] counts)
                     throws java.lang.IllegalArgumentException,
                            MathException

Description copied from interface: ChiSquareTest

Returns the observed significance level, or p-value, associated with a chi-square test of independence based on the input counts array, viewed as a two-way table.

The rows of the 2-way table are count[0], ... , count[count.length - 1]

Preconditions:

• All counts must be >= 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

counts - array representation of 2-way table

Returns:

p-value

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs computing the p-value

chiSquareTest

public boolean chiSquareTest(long[][] counts,
                             double alpha)
                      throws java.lang.IllegalArgumentException,
                             MathException

Description copied from interface: ChiSquareTest

Performs a chi-square test of independence evaluating the null hypothesis that the classifications represented by the counts in the columns of the input 2-way table are independent of the rows, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.

The rows of the 2-way table are count[0], ... , count[count.length - 1]

Example:
To test the null hypothesis that the counts in count[0], ... , count[count.length - 1] all correspond to the same underlying probability distribution at the 99% level, use

chiSquareTest(counts, 0.01)

Preconditions:

• All counts must be >= 0.
• The count array must be rectangular (i.e. all count[i] subarrays must have the same length).
• The 2-way table represented by counts must have at least 2 columns and at least 2 rows.

If any of the preconditions are not met, an IllegalArgumentException is thrown.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

counts - array representation of 2-way table

alpha - significance level of the test

Returns:

true iff null hypothesis can be rejected with confidence 1 - alpha

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

checkArray

private void checkArray(long[][] in)
                 throws java.lang.IllegalArgumentException

Checks to make sure that the input long[][] array is rectangular, has at least 2 rows and 2 columns, and has all non-negative entries, throwing IllegalArgumentException if any of these checks fail.

Parameters:

in - input 2-way table to check

Throws:

java.lang.IllegalArgumentException - if the array is not valid

getDistributionFactory

protected DistributionFactory getDistributionFactory()

Gets a DistributionFactory to use in creating ChiSquaredDistribution instances.

Returns:

a DistributionFactory

isRectangular

private boolean isRectangular(long[][] in)

Returns true iff input array is rectangular.

Parameters:

in - array to be tested

Returns:

true if the array is rectangular

Throws:

java.lang.NullPointerException - if input array is null

java.lang.ArrayIndexOutOfBoundsException - if input array is empty

isPositive

private boolean isPositive(double[] in)

Returns true iff all entries of the input array are > 0. Returns true if the array is non-null, but empty

Parameters:

in - array to be tested

Returns:

true if all entries of the array are positive

Throws:

java.lang.NullPointerException - if input array is null

isNonNegative

private boolean isNonNegative(long[] in)

Returns true iff all entries of the input array are >= 0. Returns true if the array is non-null, but empty

Parameters:

in - array to be tested

Returns:

true if all entries of the array are non-negative

Throws:

java.lang.NullPointerException - if input array is null

isNonNegative

private boolean isNonNegative(long[][] in)

Returns true iff all entries of (all subarrays of) the input array are >= 0. Returns true if the array is non-null, but empty

Parameters:

in - array to be tested

Returns:

true if all entries of the array are non-negative

Throws:

java.lang.NullPointerException - if input array is null