/*
* File: AnalysisOfVarianceOneWay.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright August 16, 2007, Sandia Corporation. Under the terms of Contract
* DE-AC04-94AL85000, there is a non-exclusive license for use of this work by
* or on behalf of the U.S. Government. Export of this program may require a
* license from the United States Government. See CopyrightHistory.txt for
* complete details.
*
*/
package gov.sandia.cognition.statistics.method;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.math.UnivariateStatisticsUtil;
import gov.sandia.cognition.statistics.distribution.SnedecorFDistribution;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.Pair;
import java.util.Arrays;
import java.util.Collection;
/**
* Analysis of Variance single-factor null-hypothesis testing procedure,
* usually called "1-way ANOVA".
* ANOVA evaluates the probability of the null hypothesis for a Collection of
* treatment cases. Each "treatment" is an experiment with a Collection of
* results from a given population. You can have different population sizes
* in each treatment. The null hypothesis is that there are no differences
* between the populations and that observed differences are due to chance.
*
* @author Kevin R. Dixon
* @since 2.0
*
*/
@ConfidenceTestAssumptions(
name="One-Way Analysis of Variance",
alsoKnownAs={
"1-way ANOVA",
"Fixed-effects 1-way ANOVA",
"F test"
},
description={
"ANOVA tests to determine if the means between the various treatments are equal.",
"ANOVA is a generalization of the paired Student t-test, where there can be multiple treatments.",
"When there are two groups, a control group and a treatment group, ANOVA is equivalent to the unpaired t-test."
},
assumptions={
"The data are sampled from a Gaussian distribution.",
"The variance within the different groups is equal.",
"The data from each group is collected independently of each other."
},
nullHypothesis="The means from all groups are equal.",
dataPaired=false,
dataSameSize=false,
distribution=SnedecorFDistribution.CDF.class,
reference=@PublicationReference(
author="Wikipedia",
title="Analysis of Variance",
type=PublicationType.WebPage,
year=2009,
url="http://en.wikipedia.org/wiki/Analysis_of_variance"
)
)
public class AnalysisOfVarianceOneWay
extends AbstractCloneableSerializable
implements BlockExperimentComparison<Number>
{
/**
* Default instance.
*/
public static final AnalysisOfVarianceOneWay INSTANCE =
new AnalysisOfVarianceOneWay();
/**
* Creates a new instance of AnalysisOfVarianceOneWay
*/
public AnalysisOfVarianceOneWay()
{
}
@PublicationReference(
author={
"Frederick J. Gravetter",
"Larry B. Wallnau"
},
title="Statistics for the Behavioral Sciences",
type=PublicationType.Book,
year=2003,
pages={406,412},
notes="Chapter 13.3"
)
@Override
public AnalysisOfVarianceOneWay.Statistic evaluateNullHypothesis(
final Collection<? extends Collection<? extends Number>> data )
{
// I apologize for this clunky notation... it comes from a social
// science text book: "Statistics for the Behavioral Sciences" by
// Gravetter & Wallnau, Chapter 13.3, p. 406-412
// number of treatments
int k = data.size();
// total number of samples
int N = 0;
double G = 0.0;
double Sxx = 0.0;
double SSwithin = 0.0;
double SSbetween = 0.0;
for( Collection<? extends Number> treatment : data )
{
int n = treatment.size();
Pair<Double,Double> result =
UnivariateStatisticsUtil.computeMeanAndVariance(treatment);
double SS = result.getSecond() * (n-1);
SSwithin += SS;
double T = result.getFirst() * n;
SSbetween += ((T*T) / n);
N += n;
for( Number value : treatment )
{
final double x = value.doubleValue();
G += x;
Sxx += x*x;
}
}
SSbetween -= ((G*G) / N);
//double SStotal = Sxx - ((G*G)/N);
int dfbetween = k-1;
int dfwithin = N-k;
double MSbetween = SSbetween / dfbetween;
double MSwithin = SSwithin / dfwithin;
double F = MSbetween / MSwithin;
return new AnalysisOfVarianceOneWay.Statistic( F, dfbetween, dfwithin );
}
/**
* Evaluates the ANOVA statistics for the two given treatments, each
* treatment can have a different number of samples
* @param data1 First treatment
* @param data2 Second treatment
* @return ANOVA Confidence statistics
*/
@SuppressWarnings("unchecked")
@Override
public AnalysisOfVarianceOneWay.Statistic evaluateNullHypothesis(
final Collection<? extends Number> data1,
final Collection<? extends Number> data2)
{
return this.evaluateNullHypothesis(
Arrays.asList( data1, data2 ) );
}
/**
* Returns the confidence statistic for an ANOVA test
*/
public static class Statistic
extends AbstractConfidenceStatistic
{
/**
* Input to the Snedecor F-distribution
*/
private double F;
/**
* Degrees of freedom between the treatments
*/
private double DFbetween;
/**
* Degrees of freedom within the treatments
*/
private double DFwithin;
/**
* Creates a new instance of Statistic
* @param F
* Input to the Snedecor F-distribution
* @param DFbetween
* Degrees of freedom between the treatments
* @param DFwithin
* Degrees of freedom within the treatments
*/
public Statistic(
final double F,
final double DFbetween,
final double DFwithin )
{
super( 1 - SnedecorFDistribution.CDF.evaluate( F, DFbetween, DFwithin ) );
this.setF( F );
this.setDFbetween( DFbetween );
this.setDFwithin( DFwithin );
}
@Override
public Statistic clone()
{
return (Statistic) super.clone();
}
/**
* Getter for F
* @return
* Input to the Snedecor F-distribution
*/
public double getF()
{
return this.F;
}
/**
* Setter for F
* @param F
* Input to the Snedecor F-distribution
*/
protected void setF(
final double F)
{
this.F = F;
}
/**
* Getter for DFbetween
* @return
* Degrees of freedom between the treatments
*/
public double getDFbetween()
{
return this.DFbetween;
}
/**
* Setter for DFbetween
* @param DFbetween
* Degrees of freedom between the treatments
*/
protected void setDFbetween(
final double DFbetween)
{
this.DFbetween = DFbetween;
}
/**
* Getter for DFwithin
* @return
* Degrees of freedom within the treatments
*/
public double getDFwithin()
{
return this.DFwithin;
}
/**
* Setter for DFwithin
* @param DFwithin
* Degrees of freedom within the treatments
*/
protected void setDFwithin(
final double DFwithin)
{
this.DFwithin = DFwithin;
}
@Override
public double getTestStatistic()
{
return this.getF();
}
}
}