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Java example source code file (OneWayAnova.java)

This example Java source code file (OneWayAnova.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

anovastats, collection, convergenceexception, dimensionmismatchexception, fdistribution, maxcountexceededexception, nullargumentexception, onewayanova, outofrangeexception, summarystatistics, util

The OneWayAnova.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.stat.inference;

import java.util.ArrayList;
import java.util.Collection;

import org.apache.commons.math3.distribution.FDistribution;
import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.stat.descriptive.SummaryStatistics;
import org.apache.commons.math3.util.MathUtils;

/**
 * Implements one-way ANOVA (analysis of variance) statistics.
 *
 * <p> 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 {@link org.apache.commons.math3.stat.inference.TTest}.
 * </p>

* Uses the {@link org.apache.commons.math3.distribution.FDistribution * commons-math F Distribution implementation} to estimate exact p-values.</p> * <p>This implementation is based on a description at * http://faculty.vassar.edu/lowry/ch13pt1.html</p> * <pre> * Abbreviations: bg = between groups, * wg = within groups, * ss = sum squared deviations * </pre> * * @since 1.2 */ public class OneWayAnova { /** * Default constructor. */ public OneWayAnova() { } /** * Computes the ANOVA F-value for a collection of <code>double[] * arrays. * * <p>Preconditions:

    * <li>The categoryData Collection must contain * <code>double[] arrays. * <li> There must be at least two double[] arrays in the * <code>categoryData collection and each of these arrays must * contain at least two values.</li>

* This implementation computes the F statistic using the definitional * formula<pre> * F = msbg/mswg</pre> * where<pre> * msbg = between group mean square * mswg = within group mean square</pre> * are as defined <a href="http://faculty.vassar.edu/lowry/ch13pt1.html"> * here</a>

* * @param categoryData <code>Collection of double[] * arrays each containing data for one category * @return Fvalue * @throws NullArgumentException if <code>categoryData is null * @throws DimensionMismatchException if the length of the <code>categoryData * array is less than 2 or a contained <code>double[] array does not have * at least two values */ public double anovaFValue(final Collection<double[]> categoryData) throws NullArgumentException, DimensionMismatchException { AnovaStats a = anovaStats(categoryData); return a.F; } /** * Computes the ANOVA P-value for a collection of <code>double[] * arrays. * * <p>Preconditions:
    * <li>The categoryData Collection must contain * <code>double[] arrays. * <li> There must be at least two double[] arrays in the * <code>categoryData collection and each of these arrays must * contain at least two values.</li>

* This implementation uses the * {@link org.apache.commons.math3.distribution.FDistribution * commons-math F Distribution implementation} to estimate the exact * p-value, using the formula<pre> * p = 1 - cumulativeProbability(F)</pre> * where <code>F is the F value and cumulativeProbability * is the commons-math implementation of the F distribution.</p> * * @param categoryData <code>Collection of double[] * arrays each containing data for one category * @return Pvalue * @throws NullArgumentException if <code>categoryData is null * @throws DimensionMismatchException if the length of the <code>categoryData * array is less than 2 or a contained <code>double[] array does not have * at least two values * @throws ConvergenceException if the p-value can not be computed due to a convergence error * @throws MaxCountExceededException if the maximum number of iterations is exceeded */ public double anovaPValue(final Collection<double[]> categoryData) throws NullArgumentException, DimensionMismatchException, ConvergenceException, MaxCountExceededException { final AnovaStats a = anovaStats(categoryData); // No try-catch or advertised exception because args are valid // pass a null rng to avoid unneeded overhead as we will not sample from this distribution final FDistribution fdist = new FDistribution(null, a.dfbg, a.dfwg); return 1.0 - fdist.cumulativeProbability(a.F); } /** * Computes the ANOVA P-value for a collection of {@link SummaryStatistics}. * * <p>Preconditions:

    * <li>The categoryData Collection must contain * {@link SummaryStatistics}.</li> * <li> There must be at least two {@link SummaryStatistics} in the * <code>categoryData collection and each of these statistics must * contain at least two values.</li>

* This implementation uses the * {@link org.apache.commons.math3.distribution.FDistribution * commons-math F Distribution implementation} to estimate the exact * p-value, using the formula<pre> * p = 1 - cumulativeProbability(F)</pre> * where <code>F is the F value and cumulativeProbability * is the commons-math implementation of the F distribution.</p> * * @param categoryData <code>Collection of {@link SummaryStatistics} * each containing data for one category * @param allowOneElementData if true, allow computation for one catagory * only or for one data element per category * @return Pvalue * @throws NullArgumentException if <code>categoryData is null * @throws DimensionMismatchException if the length of the <code>categoryData * array is less than 2 or a contained {@link SummaryStatistics} does not have * at least two values * @throws ConvergenceException if the p-value can not be computed due to a convergence error * @throws MaxCountExceededException if the maximum number of iterations is exceeded * @since 3.2 */ public double anovaPValue(final Collection<SummaryStatistics> categoryData, final boolean allowOneElementData) throws NullArgumentException, DimensionMismatchException, ConvergenceException, MaxCountExceededException { final AnovaStats a = anovaStats(categoryData, allowOneElementData); // pass a null rng to avoid unneeded overhead as we will not sample from this distribution final FDistribution fdist = new FDistribution(null, a.dfbg, a.dfwg); return 1.0 - fdist.cumulativeProbability(a.F); } /** * This method calls the method that actually does the calculations (except * P-value). * * @param categoryData * <code>Collection of double[] arrays each * containing data for one category * @return computed AnovaStats * @throws NullArgumentException * if <code>categoryData is null * @throws DimensionMismatchException * if the length of the <code>categoryData array is less * than 2 or a contained <code>double[] array does not * contain at least two values */ private AnovaStats anovaStats(final Collection<double[]> categoryData) throws NullArgumentException, DimensionMismatchException { MathUtils.checkNotNull(categoryData); final Collection<SummaryStatistics> categoryDataSummaryStatistics = new ArrayList<SummaryStatistics>(categoryData.size()); // convert arrays to SummaryStatistics for (final double[] data : categoryData) { final SummaryStatistics dataSummaryStatistics = new SummaryStatistics(); categoryDataSummaryStatistics.add(dataSummaryStatistics); for (final double val : data) { dataSummaryStatistics.addValue(val); } } return anovaStats(categoryDataSummaryStatistics, false); } /** * Performs an ANOVA test, evaluating the null hypothesis that there * is no difference among the means of the data categories. * * <p>Preconditions:

    * <li>The categoryData Collection must contain * <code>double[] arrays. * <li> There must be at least two double[] arrays in the * <code>categoryData collection and each of these arrays must * contain at least two values.</li> * <li>alpha must be strictly greater than 0 and less than or equal to 0.5. * </li>

* This implementation uses the * {@link org.apache.commons.math3.distribution.FDistribution * commons-math F Distribution implementation} to estimate the exact * p-value, using the formula<pre> * p = 1 - cumulativeProbability(F)</pre> * where <code>F is the F value and cumulativeProbability * is the commons-math implementation of the F distribution.</p> * <p>True is returned iff the estimated p-value is less than alpha.

* * @param categoryData <code>Collection of double[] * arrays each containing data for one category * @param alpha significance level of the test * @return true if the null hypothesis can be rejected with * confidence 1 - alpha * @throws NullArgumentException if <code>categoryData is null * @throws DimensionMismatchException if the length of the <code>categoryData * array is less than 2 or a contained <code>double[] array does not have * at least two values * @throws OutOfRangeException if <code>alpha is not in the range (0, 0.5] * @throws ConvergenceException if the p-value can not be computed due to a convergence error * @throws MaxCountExceededException if the maximum number of iterations is exceeded */ public boolean anovaTest(final Collection<double[]> categoryData, final double alpha) throws NullArgumentException, DimensionMismatchException, OutOfRangeException, ConvergenceException, MaxCountExceededException { if ((alpha <= 0) || (alpha > 0.5)) { throw new OutOfRangeException( LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, alpha, 0, 0.5); } return anovaPValue(categoryData) < alpha; } /** * This method actually does the calculations (except P-value). * * @param categoryData <code>Collection of double[] * arrays each containing data for one category * @param allowOneElementData if true, allow computation for one catagory * only or for one data element per category * @return computed AnovaStats * @throws NullArgumentException if <code>categoryData is null * @throws DimensionMismatchException if <code>allowOneElementData is false and the number of * categories is less than 2 or a contained SummaryStatistics does not contain * at least two values */ private AnovaStats anovaStats(final Collection<SummaryStatistics> categoryData, final boolean allowOneElementData) throws NullArgumentException, DimensionMismatchException { MathUtils.checkNotNull(categoryData); if (!allowOneElementData) { // check if we have enough categories if (categoryData.size() < 2) { throw new DimensionMismatchException(LocalizedFormats.TWO_OR_MORE_CATEGORIES_REQUIRED, categoryData.size(), 2); } // check if each category has enough data for (final SummaryStatistics array : categoryData) { if (array.getN() <= 1) { throw new DimensionMismatchException(LocalizedFormats.TWO_OR_MORE_VALUES_IN_CATEGORY_REQUIRED, (int) array.getN(), 2); } } } int dfwg = 0; double sswg = 0; double totsum = 0; double totsumsq = 0; int totnum = 0; for (final SummaryStatistics data : categoryData) { final double sum = data.getSum(); final double sumsq = data.getSumsq(); final int num = (int) data.getN(); totnum += num; totsum += sum; totsumsq += sumsq; dfwg += num - 1; final double ss = sumsq - ((sum * sum) / num); sswg += ss; } final double sst = totsumsq - ((totsum * totsum) / totnum); final double ssbg = sst - sswg; final int dfbg = categoryData.size() - 1; final double msbg = ssbg / dfbg; final double mswg = sswg / dfwg; final double F = msbg / mswg; return new AnovaStats(dfbg, dfwg, F); } /** Convenience class to pass dfbg,dfwg,F values around within OneWayAnova. No get/set methods provided. */ private static class AnovaStats { /** Degrees of freedom in numerator (between groups). */ private final int dfbg; /** Degrees of freedom in denominator (within groups). */ private final int dfwg; /** Statistic. */ private final double F; /** * Constructor * @param dfbg degrees of freedom in numerator (between groups) * @param dfwg degrees of freedom in denominator (within groups) * @param F statistic */ private AnovaStats(int dfbg, int dfwg, double F) { this.dfbg = dfbg; this.dfwg = dfwg; this.F = F; } } }

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