org.apache.commons.math.stat.inference

## Interface UnknownDistributionChiSquareTest

All Superinterfaces:
  ChiSquareTest

All Known Implementing Classes:
  ChiSquareTestImpl

    public interface UnknownDistributionChiSquareTest
    extends ChiSquareTest

An interface for Chi-Square tests for unknown distributions.

Two samples tests are used when the distribution is unknown a priori but provided by one sample. We compare the second sample against the first.

Since:
  1.2
Version:
  $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $

### Method Summary

Methods
`double` `chiSquareDataSetsComparison(long[] observed1, long[] observed2)` Computes a Chi-Square two sample test statistic comparing bin frequency counts in `observed1` and `observed2`.
`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.

### Methods inherited from interface org.apache.commons.math.stat.inference.ChiSquareTest

`chiSquare, chiSquare, chiSquareTest, chiSquareTest, chiSquareTest, chiSquareTest`

### Method Detail

#### chiSquareDataSetsComparison

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

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.

Parameters:
  `observed1` - array of observed frequency counts of the first data set
  `observed2` - array of observed frequency counts of the second data set
Returns:
  chiSquare statistic
Throws:
  `IllegalArgumentException` - if preconditions are not met

#### chiSquareTestDataSetsComparison

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

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 `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.

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

#### chiSquareTestDataSetsComparison

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

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 `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.

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