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

Class ChiSquareTestImpl

    • 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 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.

        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:
        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
        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:
        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
        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:
        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

      • chiSquareDataSetsComparison

        public double chiSquareDataSetsComparison​(long[] observed1,
                                          long[] observed2)
                                   throws java.lang.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:
        java.lang.IllegalArgumentException - if preconditions are not met
        Since:
        1.2

      • chiSquareTestDataSetsComparison

        public double chiSquareTestDataSetsComparison​(long[] observed1,
                                              long[] observed2)
                                       throws java.lang.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:
        java.lang.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 java.lang.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:
        java.lang.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