Package org.apache.commons.math.stat.inference

Class ChiSquareTestImpl

java.lang.Object

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

All Implemented Interfaces:

ChiSquareTest, UnknownDistributionChiSquareTest

public class ChiSquareTestImpl
extends Object
implements UnknownDistributionChiSquareTest

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

Constructor Summary

Constructors

Constructor	Description
ChiSquareTestImpl()	Construct a ChiSquareTestImpl
ChiSquareTestImpl(ChiSquaredDistribution x)	Create a test instance using the given distribution for computing inference statistics.

Method Summary

Modifier and Type	Method	Description
double	chiSquare(double[] expected, long[] observed)	Computes the Chi-Square statistic comparing observed and expected frequency 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	chiSquareDataSetsComparison(long[] observed1, long[] observed2)	Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2.
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.
double	chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)	Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and observed2.
boolean	chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)	Performs a Chi-Square two sample test comparing two binned data sets.
void	setDistribution(ChiSquaredDistribution value)	Modify the distribution used to compute inference statistics.

Methods inherited from class java.lang.Object

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

Constructor Detail

ChiSquareTestImpl

public ChiSquareTestImpl()

Construct a ChiSquareTestImpl

ChiSquareTestImpl

public ChiSquareTestImpl(ChiSquaredDistribution x)

Create a test instance using the given distribution for computing inference statistics.

Parameters:

x - distribution used to compute inference statistics.

Since:

1.2

Method Detail

chiSquare

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

Computes the Chi-Square statistic comparing observed and expected frequency 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.

Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

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:

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

chiSquareTest

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

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.

Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

observed - array of observed frequency counts

expected - array of expected frequency counts

Returns:

p-value

Throws:

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 IllegalArgumentException,
                             MathException

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.

Note: This implementation rescales the expected array if necessary to ensure that the sum of the expected and observed counts are equal.

Specified by:

chiSquareTest in interface ChiSquareTest

Parameters:

observed - array of observed frequency counts

expected - array of expected frequency counts

alpha - significance level of the test

Returns:

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

Throws:

IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

chiSquare

public double chiSquare(long[][] counts)
                 throws 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:

IllegalArgumentException - if preconditions are not met

chiSquareTest

public double chiSquareTest(long[][] counts)
                     throws 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:

IllegalArgumentException - if preconditions are not met

MathException - if an error occurs computing the p-value

chiSquareTest

public boolean chiSquareTest(long[][] counts,
                             double alpha)
                      throws 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:

IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

chiSquareDataSetsComparison

public double chiSquareDataSetsComparison(long[] observed1,
                                          long[] observed2)
                                   throws IllegalArgumentException

Description copied from interface: UnknownDistributionChiSquareTest

Computes a Chi-Square two sample test statistic comparing bin frequency counts in observed1 and observed2. The sums of frequency counts in the two samples are not required to be the same. The formula used to compute the test statistic is

∑[(K * observed1[i] - observed2[i]/K)2 / (observed1[i] + observed2[i])] where
K = &sqrt;[&sum(observed2 / ∑(observed1)]

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

Preconditions:

• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 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:

chiSquareDataSetsComparison in interface UnknownDistributionChiSquareTest

Parameters:

observed1 - array of observed frequency counts of the first data set

observed2 - array of observed frequency counts of the second data set

Returns:

chi-square test statistic

Throws:

IllegalArgumentException - if preconditions are not met

Since:

1.2

chiSquareTestDataSetsComparison

public double chiSquareTestDataSetsComparison(long[] observed1,
                                              long[] observed2)
                                       throws IllegalArgumentException,
                                              MathException

Description copied from interface: UnknownDistributionChiSquareTest

Returns the observed significance level, or p-value, associated with a Chi-Square two sample test comparing bin frequency counts in observed1 and observed2.

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

See UnknownDistributionChiSquareTest.chiSquareDataSetsComparison(long[], long[]) for details on the formula used to compute the test statistic. The degrees of of freedom used to perform the test is one less than the common length of the input observed count arrays.

Preconditions:

• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 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:

chiSquareTestDataSetsComparison in interface UnknownDistributionChiSquareTest

Parameters:

observed1 - array of observed frequency counts of the first data set

observed2 - array of observed frequency counts of the second data set

Returns:

p-value

Throws:

IllegalArgumentException - if preconditions are not met

MathException - if an error occurs computing the p-value

Since:

1.2

chiSquareTestDataSetsComparison

public boolean chiSquareTestDataSetsComparison(long[] observed1,
                                               long[] observed2,
                                               double alpha)
                                        throws IllegalArgumentException,
                                               MathException

Description copied from interface: UnknownDistributionChiSquareTest

Performs a Chi-Square two sample test comparing two binned data sets. The test evaluates the null hypothesis that the two lists of observed counts conform to the same frequency distribution, with significance level alpha. Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent confidence.

See UnknownDistributionChiSquareTest.chiSquareDataSetsComparison(long[], long[]) for details on the formula used to compute the Chisquare statistic used in the test. The degrees of of freedom used to perform the test is one less than the common length of the input observed count arrays.

Preconditions:

• Observed counts must be non-negative.
• Observed counts for a specific bin must not both be zero.
• Observed counts for a specific sample must not all be 0.
• The arrays observed1 and observed2 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:

chiSquareTestDataSetsComparison in interface UnknownDistributionChiSquareTest

Parameters:

observed1 - array of observed frequency counts of the first data set

observed2 - array of observed frequency counts of the second data set

alpha - significance level of the test

Returns:

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

Throws:

IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

Since:

1.2

setDistribution

public void setDistribution(ChiSquaredDistribution value)

Modify the distribution used to compute inference statistics.

Parameters:

value - the new distribution

Since:

1.2