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
Version:
  $Id: OneWayAnova.java 1416643 2012-12-03 19:37:14Z tn $

### Nested Class Summary

Nested Classes
`private static class` `OneWayAnova.AnovaStats` Convenience class to pass dfbg,dfwg,F values around within OneWayAnova.

### Constructor Summary

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

### Method Summary

Methods
`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.
`private OneWayAnova.AnovaStats` `anovaStats(Collection<double[]> categoryData)` This method actually does the calculations (except P-value).
`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

#### 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

#### anovaStats

    private OneWayAnova.AnovaStats anovaStats(Collection<double[]> categoryData)
                                       throws NullArgumentException,
                                              DimensionMismatchException

This method actually does the calculations (except P-value).

Parameters:
  `categoryData` - `Collection` of `double[]` arrays each containing data for one category
Returns:
  computed AnovaStats
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 contain at least two values