OneWayAnova (Apache Commons Math 3.6.1 API)

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.

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

Class OneWayAnova

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

OneWayAnova

Method Detail

anovaFValue

anovaPValue

anovaPValue

anovaTest