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/*
* File: HolmCorrection.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Jun 21, 2011, 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.matrix.Matrix;
import gov.sandia.cognition.math.matrix.MatrixFactory;
import gov.sandia.cognition.util.ArrayIndexSorter;
import java.util.Collection;
/**
* The Holm correction is a uniformly tighter bound than the Bonferroni/Sidak
* correction by first sorting the pair-wide p-values and then adjusting the
* p-values by the number of remaining hypotheses. To reject the first p-value,
* the smallest pair-wise p-value must be smaller than the Bonferroni corrected
* value (alpha/N), then the next smallest p-value must be smaller than
* (alpha/(N-1)) and so forth. This is a uniformly looser bound than the
* Shaffer static correction. However, the computational complexity of the Holm
* algorithm is quadratic in the number of treatments, meaning its linear
* in the number of actual comparisons.
* So, for treatments above 100 (4950 comparisons), the Holm correction may be
* the most appropriate choice. This implementation uses the slightly tighter
* Sidak correction, as opposed to the standard Bonferroni correction.
*
* @author Kevin R. Dixon
* @since 3.3.0
*/
@PublicationReference(
author="Wikipedia",
title="Holm–Bonferroni method",
type=PublicationType.WebPage,
url="http://en.wikipedia.org/wiki/Holm%E2%80%93Bonferroni_method",
year=2011
)
public class HolmCorrection
extends AbstractPairwiseMultipleHypothesisComparison
{
/**
* Default constructor
*/
public HolmCorrection()
{
this( DEFAULT_PAIRWISE_TEST );
}
/**
* Creates a new instance of BonferroniCorrection
* @param pairwiseTest
* Confidence test used for pair-wise null-hypothesis tests.
*/
public HolmCorrection(
final NullHypothesisEvaluator> pairwiseTest)
{
super( pairwiseTest );
}
@Override
public HolmCorrection clone()
{
return (HolmCorrection) super.clone();
}
@Override
public HolmCorrection.Statistic evaluateNullHypotheses(
final Collection> data,
final double uncompensatedAlpha)
{
return new HolmCorrection.Statistic(
data, uncompensatedAlpha, this.getPairwiseTest() );
}
/**
* Test statistic from the Shaffer static multiple-comparison test
*/
public static class Statistic
extends AbstractPairwiseMultipleHypothesisComparison.Statistic
{
/**
* Matrix of adjusted alphas (p-value thresholds) for each comparison
*/
protected Matrix adjustedAlphas;
/**
* Creates a new instance of Statistic
* @param data
* Data from each treatment to consider
* @param uncompensatedAlpha
* Uncompensated alpha (p-value threshold) for the multiple comparison
* test
* @param pairwiseTest
* Confidence test used for pair-wise null-hypothesis tests.
*/
public Statistic(
final Collection> data,
final double uncompensatedAlpha,
final NullHypothesisEvaluator> pairwiseTest )
{
super( data, uncompensatedAlpha, pairwiseTest );
final int numComparisons =
this.treatmentCount * (this.treatmentCount-1) / 2;
this.computePairwiseTestResults(data, pairwiseTest );
double[] pvalues = new double[ numComparisons ];
int index = 0;
for( int i = 0; i < this.treatmentCount; i++ )
{
for( int j = i+1; j < this.treatmentCount; j++ )
{
pvalues[index] =
this.nullHypothesisProbabilities.getElement(i, j);
index++;
}
}
// Sort the p-values from smallest to largest
int[] sortedIndices =
ArrayIndexSorter.sortArrayAscending(pvalues);
double[] adjustedAlpha = new double[ numComparisons ];
int hypothesesRemaining = numComparisons;
for( int i = 0; i < numComparisons; i++ )
{
// adjustedAlpha[sortedIndices[i]] = BonferroniCorrection.adjust(
// this.uncompensatedAlpha, maxPossibleTrueHypotheses );
adjustedAlpha[sortedIndices[i]] = SidakCorrection.adjust(
this.uncompensatedAlpha, hypothesesRemaining );
hypothesesRemaining--;
}
// Stuff the adjusted alphas back into the adjustedAlphas matrix
Matrix alphaMatrix = MatrixFactory.getDefault().createMatrix(
this.treatmentCount,this.treatmentCount);
index = 0;
for( int i = 0; i < this.treatmentCount; i++ )
{
for( int j = i+1; j < this.treatmentCount; j++ )
{
alphaMatrix.setElement(i, j, adjustedAlpha[index]);
alphaMatrix.setElement(j, i, adjustedAlpha[index]);
index++;
}
}
this.adjustedAlphas = alphaMatrix;
}
@Override
public double getAdjustedAlpha(
int i,
int j)
{
return this.adjustedAlphas.getElement(i, j);
}
}
}