org.apache.commons.math3.stat.inference

## Class OneWayAnova

- java.lang.Object
- - org.apache.commons.math3.stat.inference.OneWayAnova

-     public class OneWayAnova
      extends Object

  Implements one-way ANOVA (analysis of variance) statistics.

  Tests for differences between two or more categories of univariate data (for example, the body mass index of accountants, lawyers, doctors and computer programmers). When two categories are given, this is equivalent to the `TTest`.

  Uses the `commons-math F Distribution implementation` to estimate exact p-values.

  This implementation is based on a description at http://faculty.vassar.edu/lowry/ch13pt1.html

       Abbreviations: bg = between groups,
                      wg = within groups,
                      ss = sum squared deviations

  Since:
    1.2

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `OneWayAnova()` Default constructor.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `anovaFValue(Collection<double[]> categoryData)` Computes the ANOVA F-value for a collection of `double[]` arrays.
    `double` | `anovaPValue(Collection<double[]> categoryData)` Computes the ANOVA P-value for a collection of `double[]` arrays.
    `double` | `anovaPValue(Collection<SummaryStatistics> categoryData, boolean allowOneElementData)` Computes the ANOVA P-value for a collection of `SummaryStatistics`.
    `boolean` | `anovaTest(Collection<double[]> categoryData, double alpha)` Performs an ANOVA test, evaluating the null hypothesis that there is no difference among the means of the data categories.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### OneWayAnova

          public OneWayAnova()

      Default constructor.

  - ### Method Detail

    - #### anovaFValue

          public double anovaFValue(Collection<double[]> categoryData)
                             throws NullArgumentException,
                                    DimensionMismatchException

      Computes the ANOVA F-value for a collection of `double[]` arrays.

      Preconditions:

      - The categoryData `Collection` must contain `double[]` arrays.
      - There must be at least two `double[]` arrays in the `categoryData` collection and each of these arrays must contain at least two values.

      This implementation computes the F statistic using the definitional formula

             F = msbg/mswg

      where

            msbg = between group mean square
            mswg = within group mean square

      are as defined here
      Parameters:
        `categoryData` - `Collection` of `double[]` arrays each containing data for one category
      Returns:
        Fvalue
      Throws:
        `NullArgumentException` - if `categoryData` is `null`
        `DimensionMismatchException` - if the length of the `categoryData` array is less than 2 or a contained `double[]` array does not have at least two values

    - #### anovaPValue

          public double anovaPValue(Collection<double[]> categoryData)
                             throws NullArgumentException,
                                    DimensionMismatchException,
                                    ConvergenceException,
                                    MaxCountExceededException

      Computes the ANOVA P-value for a collection of `double[]` arrays.

      Preconditions:

      - The categoryData `Collection` must contain `double[]` arrays.
      - There must be at least two `double[]` arrays in the `categoryData` collection and each of these arrays must contain at least two values.

      This implementation uses the `commons-math F Distribution implementation` to estimate the exact p-value, using the formula

             p = 1 - cumulativeProbability(F)

      where `F` is the F value and `cumulativeProbability` is the commons-math implementation of the F distribution.
      Parameters:
        `categoryData` - `Collection` of `double[]` arrays each containing data for one category
      Returns:
        Pvalue
      Throws:
        `NullArgumentException` - if `categoryData` is `null`
        `DimensionMismatchException` - if the length of the `categoryData` array is less than 2 or a contained `double[]` array does not have at least two values
        `ConvergenceException` - if the p-value can not be computed due to a convergence error
        `MaxCountExceededException` - if the maximum number of iterations is exceeded

    - #### anovaPValue

          public double anovaPValue(Collection<SummaryStatistics> categoryData,
                           boolean allowOneElementData)
                             throws NullArgumentException,
                                    DimensionMismatchException,
                                    ConvergenceException,
                                    MaxCountExceededException

      Computes the ANOVA P-value for a collection of `SummaryStatistics`.

      Preconditions:

      - The categoryData `Collection` must contain `SummaryStatistics`.
      - There must be at least two `SummaryStatistics` in the `categoryData` collection and each of these statistics must contain at least two values.

      This implementation uses the `commons-math F Distribution implementation` to estimate the exact p-value, using the formula

             p = 1 - cumulativeProbability(F)

      where `F` is the F value and `cumulativeProbability` is the commons-math implementation of the F distribution.
      Parameters:
        `categoryData` - `Collection` of `SummaryStatistics` each containing data for one category
        `allowOneElementData` - if true, allow computation for one catagory only or for one data element per category
      Returns:
        Pvalue
      Throws:
        `NullArgumentException` - if `categoryData` is `null`
        `DimensionMismatchException` - if the length of the `categoryData` array is less than 2 or a contained `SummaryStatistics` does not have at least two values
        `ConvergenceException` - if the p-value can not be computed due to a convergence error
        `MaxCountExceededException` - if the maximum number of iterations is exceeded
      Since:
        3.2

    - #### anovaTest

          public boolean anovaTest(Collection<double[]> categoryData,
                          double alpha)
                            throws NullArgumentException,
                                   DimensionMismatchException,
                                   OutOfRangeException,
                                   ConvergenceException,
                                   MaxCountExceededException

      Performs an ANOVA test, evaluating the null hypothesis that there is no difference among the means of the data categories.

      Preconditions:

      - The categoryData `Collection` must contain `double[]` arrays.
      - There must be at least two `double[]` arrays in the `categoryData` collection and each of these arrays must contain at least two values.
      - alpha must be strictly greater than 0 and less than or equal to 0.5.

      This implementation uses the `commons-math F Distribution implementation` to estimate the exact p-value, using the formula

             p = 1 - cumulativeProbability(F)

      where `F` is the F value and `cumulativeProbability` is the commons-math implementation of the F distribution.

      True is returned iff the estimated p-value is less than alpha.

      Parameters:
        `categoryData` - `Collection` of `double[]` arrays each containing data for one category
        `alpha` - significance level of the test
      Returns:
        true if the null hypothesis can be rejected with confidence 1 - alpha
      Throws:
        `NullArgumentException` - if `categoryData` is `null`
        `DimensionMismatchException` - if the length of the `categoryData` array is less than 2 or a contained `double[]` array does not have at least two values
        `OutOfRangeException` - if `alpha` is not in the range (0, 0.5]
        `ConvergenceException` - if the p-value can not be computed due to a convergence error
        `MaxCountExceededException` - if the maximum number of iterations is exceeded

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