org.apache.commons.math3.stat.inference

Class OneWayAnova

java.lang.Object

org.apache.commons.math3.stat.inference.OneWayAnova

public class OneWayAnova
extends java.lang.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

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
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

Modifier and Type	Method and Description
double	anovaFValue(java.util.Collection<double[]> categoryData) Computes the ANOVA F-value for a collection of double[] arrays.
double	anovaPValue(java.util.Collection<double[]> categoryData) Computes the ANOVA P-value for a collection of double[] arrays.
double	anovaPValue(java.util.Collection<SummaryStatistics> categoryData, boolean allowOneElementData) Computes the ANOVA P-value for a collection of SummaryStatistics.
private OneWayAnova.AnovaStats	anovaStats(java.util.Collection<double[]> categoryData) This method calls the method that actually does the calculations (except P-value).
private OneWayAnova.AnovaStats	anovaStats(java.util.Collection<SummaryStatistics> categoryData, boolean allowOneElementData) This method actually does the calculations (except P-value).
boolean	anovaTest(java.util.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(java.util.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(java.util.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(java.util.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

anovaStats

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

This method calls the method that 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

anovaTest

public boolean anovaTest(java.util.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(java.util.Collection<SummaryStatistics> categoryData,
                                boolean allowOneElementData)
                                   throws NullArgumentException,
                                          DimensionMismatchException

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

Parameters:

categoryData - Collection of double[] arrays each containing data for one category

allowOneElementData - if true, allow computation for one catagory only or for one data element per category

Returns:

computed AnovaStats

Throws:

NullArgumentException - if categoryData is null

DimensionMismatchException - if allowOneElementData is false and the number of categories is less than 2 or a contained SummaryStatistics does not contain at least two values