org.apache.commons.math.stat.inference

Interface ChiSquareTest

All Known Subinterfaces:

UnknownDistributionChiSquareTest

All Known Implementing Classes:

ChiSquareTestImpl

public interface ChiSquareTest

An interface for Chi-Square tests.

This interface handles only known distributions. If the distribution is unknown and should be provided by a sample, then the UnknownDistributionChiSquareTest extended interface should be used instead.

Method Summary

Modifier and Type	Method and 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	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.

Method Detail

chiSquare

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

Parameters:

observed - array of observed frequency counts

expected - array of expected frequency counts

Returns:

chiSquare statistic

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

chiSquareTest

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

Parameters:

observed - array of observed frequency counts

expected - array of expected frequency counts

Returns:

p-value

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs computing the p-value

chiSquareTest

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

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:

java.lang.IllegalArgumentException - if preconditions are not met

MathException - if an error occurs performing the test

chiSquare

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

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.

Parameters:

counts - array representation of 2-way table

Returns:

chiSquare statistic

Throws:

java.lang.IllegalArgumentException - if preconditions are not met

chiSquareTest

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

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.

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

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

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.

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