org.apache.commons.math.stat.inference
Class OneWayAnovaImpl

java.lang.Object
  org.apache.commons.math.stat.inference.OneWayAnovaImpl

All Implemented Interfaces:

OneWayAnova

public class OneWayAnovaImpl
extends Object
implements OneWayAnova

Implements one-way ANOVA statistics defined in the OneWayAnovaImpl interface.

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:

$Revision: 825917 $ $Date: 2009-10-16 10:47:27 -0400 (Fri, 16 Oct 2009) $

Nested Class Summary

private static class

OneWayAnovaImpl.AnovaStats Convenience class to pass dfbg,dfwg,F values around within AnovaImpl.

Constructor Summary

OneWayAnovaImpl()
Default constructor.

Method Summary

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 OneWayAnovaImpl.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

OneWayAnovaImpl

public OneWayAnovaImpl()

Default constructor.

Method Detail

anovaFValue

public double anovaFValue(Collection<double[]> categoryData)
                   throws IllegalArgumentException,
                          MathException

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

Specified by:

anovaFValue in interface OneWayAnova

Parameters:

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

Returns:

Fvalue

Throws:

IllegalArgumentException - if the preconditions are not met

MathException - if the statistic can not be computed do to a convergence or other numerical error.

anovaPValue

public double anovaPValue(Collection<double[]> categoryData)
                   throws IllegalArgumentException,
                          MathException

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.

Specified by:

anovaPValue in interface OneWayAnova

Parameters:

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

Returns:

Pvalue

Throws:

IllegalArgumentException - if the preconditions are not met

MathException - if the statistic can not be computed do to a convergence or other numerical error.

anovaTest

public boolean anovaTest(Collection<double[]> categoryData,
                         double alpha)
                  throws IllegalArgumentException,
                         MathException

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.

Specified by:

anovaTest in interface OneWayAnova

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:

IllegalArgumentException - if the preconditions are not met

MathException - if the statistic can not be computed do to a convergence or other numerical error.

anovaStats

private OneWayAnovaImpl.AnovaStats anovaStats(Collection<double[]> categoryData)
                                       throws IllegalArgumentException,
                                              MathException

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:

IllegalArgumentException - if categoryData does not meet preconditions specified in the interface definition

MathException - if an error occurs computing the Anova stats