Class ChiSquareTest

java.lang.Object
org.apache.commons.statistics.inference.ChiSquareTest

public final class ChiSquareTest extends Object
Implements chi-square test statistics.

This implementation handles both known and unknown distributions.

Two samples tests can be used when the distribution is unknown a priori but provided by one sample, or when the hypothesis under test is that the two samples come from the same underlying distribution.

Since:
1.1
See Also:
  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    private static final String
    Name for the column.
    private static final ChiSquareTest
    Default instance.
    private final int
    Degrees of freedom adjustment.
    private static final String
    Name for the row.
  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    private
    ChiSquareTest(int degreesOfFreedomAdjustment)
     
  • Method Summary

    Modifier and Type
    Method
    Description
    private static void
    checkNonZero(double value, String name, int index)
    Check the array value is non-zero.
    private static double
    computeP(double chi2, double degreesOfFreedom)
    Compute the chi-square test p-value.
    double
    statistic(double[] expected, long[] observed)
    Computes the chi-square goodness-of-fit statistic comparing observed and expected frequency counts.
    double
    statistic(long[] observed)
    Computes the chi-square goodness-of-fit statistic comparing the observed counts to a uniform expected value (each category is equally likely).
    double
    statistic(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 in row-major format.
    double
    statistic(long[] observed1, long[] observed2)
    Computes a chi-square statistic associated with a chi-square test of independence of frequency counts in observed1 and observed2.
    test(double[] expected, long[] observed)
    Perform a chi-square goodness-of-fit test evaluating the null hypothesis that the observed counts conform to the expected counts.
    test(long[] observed)
    Perform a chi-square goodness-of-fit test evaluating the null hypothesis that the observed counts conform to a uniform distribution (each category is equally likely).
    test(long[][] counts)
    Perform a chi-square test of independence based on the input counts array, viewed as a two-way table.
    test(long[] observed1, long[] observed2)
    Perform a chi-square test of independence of frequency counts in observed1 and observed2.
    Return an instance using the default options.
    Return an instance with the configured degrees of freedom adjustment.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
  • Field Details

    • ROW

      private static final String ROW
      Name for the row.
      See Also:
    • COLUMN

      private static final String COLUMN
      Name for the column.
      See Also:
    • DEFAULT

      private static final ChiSquareTest DEFAULT
      Default instance.
    • degreesOfFreedomAdjustment

      private final int degreesOfFreedomAdjustment
      Degrees of freedom adjustment.
  • Constructor Details

    • ChiSquareTest

      private ChiSquareTest(int degreesOfFreedomAdjustment)
      Parameters:
      degreesOfFreedomAdjustment - Degrees of freedom adjustment.
  • Method Details

    • withDefaults

      public static ChiSquareTest withDefaults()
      Return an instance using the default options.
      Returns:
      default instance
    • withDegreesOfFreedomAdjustment

      public ChiSquareTest withDegreesOfFreedomAdjustment(int v)
      Return an instance with the configured degrees of freedom adjustment.

      The default degrees of freedom for a sample of length n are n - 1. An intrinsic null hypothesis is one where you estimate one or more parameters from the data in order to get the numbers for your null hypothesis. For a distribution with p parameters where up to p parameters have been estimated from the data the degrees of freedom is in the range [n - 1 - p, n - 1].

      Parameters:
      v - Value.
      Returns:
      an instance
      Throws:
      IllegalArgumentException - if the value is negative
    • statistic

      public double statistic(long[] observed)
      Computes the chi-square goodness-of-fit statistic comparing the observed counts to a uniform expected value (each category is equally likely).

      Note: This is a specialized version of a comparison of observed with an expected array of uniform values. The result is faster than calling statistic(double[], long[]) and the statistic is the same, with an allowance for accumulated floating-point error due to the optimized routine.

      Parameters:
      observed - Observed frequency counts.
      Returns:
      Chi-square statistic
      Throws:
      IllegalArgumentException - if the sample size is less than 2; observed has negative entries; or all the observations are zero.
      See Also:
    • statistic

      public double statistic(double[] expected, long[] observed)
      Computes the chi-square goodness-of-fit statistic comparing observed and expected frequency counts.

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

      Parameters:
      expected - Expected frequency counts.
      observed - Observed frequency counts.
      Returns:
      Chi-square statistic
      Throws:
      IllegalArgumentException - if the sample size is less than 2; the array sizes do not match; expected has entries that are not strictly positive; observed has negative entries; or all the observations are zero.
      See Also:
    • statistic

      public double statistic(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 in row-major format.
      Parameters:
      counts - 2-way table.
      Returns:
      Chi-square statistic
      Throws:
      IllegalArgumentException - if the number of rows or columns is less than 2; the array is non-rectangular; the array has negative entries; or the sum of a row or column is zero.
      See Also:
    • statistic

      public double statistic(long[] observed1, long[] observed2)
      Computes a chi-square statistic associated with a chi-square test of independence of 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:

      \[ \sum_i{ \frac{(K * a_i - b_i / K)^2}{a_i + b_i} } \]

      where

      \[ K = \sqrt{ \sum_i{a_i} / \sum_i{b_i} } \]

      Note: This is a specialized version of a 2-by-n contingency table. The result is faster than calling statistic(long[][]) with the table composed as new long[][]{observed1, observed2}. The statistic is the same, with an allowance for accumulated floating-point error due to the optimized routine.

      Parameters:
      observed1 - Observed frequency counts of the first data set.
      observed2 - Observed frequency counts of the second data set.
      Returns:
      Chi-square statistic
      Throws:
      IllegalArgumentException - if the sample size is less than 2; the array sizes do not match; either array has entries that are negative; either all counts of observed1 or observed2 are zero; or if the count at some index is zero for both arrays.
      See Also:
    • test

      public SignificanceResult test(long[] observed)
      Perform a chi-square goodness-of-fit test evaluating the null hypothesis that the observed counts conform to a uniform distribution (each category is equally likely).
      Parameters:
      observed - Observed frequency counts.
      Returns:
      test result
      Throws:
      IllegalArgumentException - if the sample size is less than 2; observed has negative entries; or all the observations are zero
      See Also:
    • test

      public SignificanceResult test(double[] expected, long[] observed)
      Perform a chi-square goodness-of-fit test evaluating the null hypothesis that the observed counts conform to the expected counts.

      The test can be configured to apply an adjustment to the degrees of freedom if the observed data has been used to create the expected counts.

      Parameters:
      expected - Expected frequency counts.
      observed - Observed frequency counts.
      Returns:
      test result
      Throws:
      IllegalArgumentException - if the sample size is less than 2; the array sizes do not match; expected has entries that are not strictly positive; observed has negative entries; all the observations are zero; or the adjusted degrees of freedom are not strictly positive
      See Also:
    • test

      public SignificanceResult test(long[][] counts)
      Perform a chi-square test of independence based on the input counts array, viewed as a two-way table.
      Parameters:
      counts - 2-way table.
      Returns:
      test result
      Throws:
      IllegalArgumentException - if the number of rows or columns is less than 2; the array is non-rectangular; the array has negative entries; or the sum of a row or column is zero.
      See Also:
    • test

      public SignificanceResult test(long[] observed1, long[] observed2)
      Perform a chi-square test of independence of frequency counts in observed1 and observed2.

      Note: This is a specialized version of a 2-by-n contingency table.

      Parameters:
      observed1 - Observed frequency counts of the first data set.
      observed2 - Observed frequency counts of the second data set.
      Returns:
      test result
      Throws:
      IllegalArgumentException - if the sample size is less than 2; the array sizes do not match; either array has entries that are negative; either all counts of observed1 or observed2 are zero; or if the count at some index is zero for both arrays.
      See Also:
    • computeP

      private static double computeP(double chi2, double degreesOfFreedom)
      Compute the chi-square test p-value.
      Parameters:
      chi2 - Chi-square statistic.
      degreesOfFreedom - Degrees of freedom.
      Returns:
      p-value
    • checkNonZero

      private static void checkNonZero(double value, String name, int index)
      Check the array value is non-zero.
      Parameters:
      value - Value
      name - Name of the array
      index - Index in the array
      Throws:
      IllegalArgumentException - if the value is zero