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## 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 Object
implements ChiSquareTest

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

Version:
  $Revision: 1.11 $ $Date: 2004/12/04 20:47:46 $

Constructor Summary
`ChiSquareTestImpl()` Construct a ChiSquareTestImpl

Method Summary
`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.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### ChiSquareTestImpl

    public ChiSquareTestImpl()

  Construct a ChiSquareTestImpl

Method Detail

### chiSquare

    public double chiSquare(double[] expected,
                            long[] observed)
                     throws 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:
    `IllegalArgumentException` - if preconditions are not met or length is less than 2

### chiSquareTest

    public double chiSquareTest(double[] expected,
                                long[] observed)
                         throws 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:
    `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

  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:
    `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

### getDistributionFactory

    protected DistributionFactory getDistributionFactory()

  Gets a DistributionFactory to use in creating ChiSquaredDistribution instances.

  Returns:
    a DistributionFactory

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