Added one-way ANOVA implementation.
JIRA: MATH-173 Contributed by Bob MacCallum. git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@615531 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz
parent
39c77b17fd
commit
41eb3cb7b7
3
pom.xml
3
pom.xml
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@ -118,6 +118,9 @@
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<contributor>
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<contributor>
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<name>Piotr Kochanski</name>
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<name>Piotr Kochanski</name>
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</contributor>
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</contributor>
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<contributor>
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<name>Bob MacCallum</name>
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</contributor>
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<contributor>
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<contributor>
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<name>Fredrik Norin</name>
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<name>Fredrik Norin</name>
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</contributor>
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</contributor>
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.stat.inference;
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import org.apache.commons.math.MathException;
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import java.util.Collection;
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/**
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* An interface for one-way ANOVA (analysis of variance).
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*
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* <p> Tests for differences between two or more categories of univariate data
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* (for example, the body mass index of accountants, lawyers, doctors and
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* computer programmers). When two categories are given, this is equivalent to
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* the {@link org.apache.commons.math.stat.inference.TTest}.
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* </p>
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*
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* @since 1.2
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* @version $Revision$ $Date$
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*/
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public interface OneWayAnova {
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/**
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* Computes the ANOVA F-value for a collection of <code>double[]</code>
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* arrays.
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*
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* <p><strong>Preconditions</strong>: <ul>
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* <li>The categoryData <code>Collection</code> must contain
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* <code>double[]</code> arrays.</li>
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* <li> There must be at least two <code>double[]</code> arrays in the
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* <code>categoryData</code> collection and each of these arrays must
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* contain at least two values.</li></ul></p>
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*
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* @param categoryData <code>Collection</code> of <code>double[]</code>
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* arrays each containing data for one category
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* @return Fvalue
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* @throws IllegalArgumentException if the preconditions are not met
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* @throws MathException if the statistic can not be computed do to a
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* convergence or other numerical error.
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*/
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public double anovaFValue(Collection categoryData)
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throws IllegalArgumentException, MathException;
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/**
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* Computes the ANOVA P-value for a collection of <code>double[]</code>
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* arrays.
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*
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* <p><strong>Preconditions</strong>: <ul>
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* <li>The categoryData <code>Collection</code> must contain
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* <code>double[]</code> arrays.</li>
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* <li> There must be at least two <code>double[]</code> arrays in the
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* <code>categoryData</code> collection and each of these arrays must
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* contain at least two values.</li></ul></p>
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*
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* @param categoryData <code>Collection</code> of <code>double[]</code>
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* arrays each containing data for one category
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* @return Pvalue
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* @throws IllegalArgumentException if the preconditions are not met
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* @throws MathException if the statistic can not be computed do to a
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* convergence or other numerical error.
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*/
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public double anovaPValue(Collection categoryData)
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throws IllegalArgumentException, MathException;
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/**
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* Performs an ANOVA test, evaluating the null hypothesis that there
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* is no difference among the means of the data categories.
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*
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* <p><strong>Preconditions</strong>: <ul>
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* <li>The categoryData <code>Collection</code> must contain
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* <code>double[]</code> arrays.</li>
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* <li> There must be at least two <code>double[]</code> arrays in the
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* <code>categoryData</code> collection and each of these arrays must
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* contain at least two values.</li>
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* <li>alpha must be strictly greater than 0 and less than or equal to 0.5.
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* </li></ul></p>
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*
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* @param categoryData <code>Collection</code> of <code>double[]</code>
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* arrays each containing data for one category
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* @param alpha significance level of the test
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* @return true if the null hypothesis can be rejected with
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* confidence 1 - alpha
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* @throws IllegalArgumentException if the preconditions are not met
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* @throws MathException if the statistic can not be computed do to a
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* convergence or other numerical error.
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*/
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public boolean anovaTest(Collection categoryData, double alpha)
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throws IllegalArgumentException, MathException;
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}
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@ -0,0 +1,208 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.stat.inference;
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import org.apache.commons.math.MathException;
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import org.apache.commons.math.stat.descriptive.summary.Sum;
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import org.apache.commons.math.stat.descriptive.summary.SumOfSquares;
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import org.apache.commons.math.distribution.FDistribution;
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import org.apache.commons.math.distribution.FDistributionImpl;
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import java.util.Collection;
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import java.util.Iterator;
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/**
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* Implements one-way ANOVA statistics defined in the {@link OneWayAnovaImpl}
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* interface.
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*
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* <p>Uses the
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* {@link org.apache.commons.math.distribution.FDistribution
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* commons-math F Distribution implementation} to estimate exact p-values.</p>
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*
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* <p>This implementation is based on a description at
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* http://faculty.vassar.edu/lowry/ch13pt1.html</p>
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* <pre>
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* Abbreviations: bg = between groups,
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* wg = within groups,
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* ss = sum squared deviations
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* </pre>
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*
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* @since 1.2
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* @version $Revision$ $Date$
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*/
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public class OneWayAnovaImpl implements OneWayAnova {
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/**
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* Default constructor.
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*/
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public OneWayAnovaImpl() {
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}
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/**
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* {@inheritDoc}<p>
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* This implementation computes the F statistic using the definitional
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* formula<pre>
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* F = msbg/mswg</pre>
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* where<pre>
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* msbg = between group mean square
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* mswg = within group mean square</pre>
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* are as defined <a href="http://faculty.vassar.edu/lowry/ch13pt1.html">
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* here</a></p>
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*/
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public double anovaFValue(Collection categoryData)
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throws IllegalArgumentException, MathException {
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AnovaStats a = anovaStats(categoryData);
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return a.F;
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}
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/**
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* {@inheritDoc}<p>
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* This implementation uses the
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* {@link org.apache.commons.math.distribution.FDistribution
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* commons-math F Distribution implementation} to estimate the exact
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* p-value, using the formula<pre>
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* p = 1 - cumulativeProbability(F)</pre>
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* where <code>F</code> is the F value and <code>cumulativeProbability</code>
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* is the commons-math implementation of the F distribution.</p>
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*/
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public double anovaPValue(Collection categoryData)
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throws IllegalArgumentException, MathException {
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AnovaStats a = anovaStats(categoryData);
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FDistribution fdist = new FDistributionImpl(a.dfbg, a.dfwg);
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return 1.0 - fdist.cumulativeProbability(a.F);
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}
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/**
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* {@inheritDoc}<p>
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* This implementation uses the
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* {@link org.apache.commons.math.distribution.FDistribution
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* commons-math F Distribution implementation} to estimate the exact
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* p-value, using the formula<pre>
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* p = 1 - cumulativeProbability(F)</pre>
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* where <code>F</code> is the F value and <code>cumulativeProbability</code>
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* is the commons-math implementation of the F distribution.</p>
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* <p>True is returned iff the estimated p-value is less than alpha.</p>
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*/
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public boolean anovaTest(Collection categoryData, double alpha)
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throws IllegalArgumentException, MathException {
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if ((alpha <= 0) || (alpha > 0.5)) {
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throw new IllegalArgumentException("bad significance level: " + alpha);
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}
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return (anovaPValue(categoryData) < alpha);
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}
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/**
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* This method actually does the calculations (except P-value).
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*
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* @param categoryData <code>Collection</code> of <code>double[]</code>
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* arrays each containing data for one category
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* @return computed AnovaStats
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* @throws IllegalArgumentException if categoryData does not meet
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* preconditions specified in the interface definition
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* @throws MathException if an error occurs computing the Anova stats
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*/
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private AnovaStats anovaStats(Collection categoryData)
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throws IllegalArgumentException, MathException {
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// check if we have enough categories
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if (categoryData.size() < 2) {
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throw new IllegalArgumentException(
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"ANOVA: two or more categories required");
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}
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// check if each category has enough data and all is double[]
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for (Iterator iterator = categoryData.iterator(); iterator.hasNext();) {
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double[] array;
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try {
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array = (double[])iterator.next();
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} catch (Exception ex) {
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throw new IllegalArgumentException(
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"ANOVA: categoryData contains non-double[] elements.", ex);
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}
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if (array.length <= 1) {
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throw new IllegalArgumentException(
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"ANOVA: one element of categoryData has fewer than 2 values.");
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}
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}
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int dfwg = 0;
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double sswg = 0;
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Sum totsum = new Sum();
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SumOfSquares totsumsq = new SumOfSquares();
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int totnum = 0;
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for (Iterator iterator = categoryData.iterator(); iterator.hasNext();) {
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double[] data = (double[])iterator.next();
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Sum sum = new Sum();
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SumOfSquares sumsq = new SumOfSquares();
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int num = 0;
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for (int i = 0; i < data.length; i++) {
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double val = data[i];
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// within category
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num++;
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sum.increment(val);
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sumsq.increment(val);
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// for all categories
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totnum++;
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totsum.increment(val);
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totsumsq.increment(val);
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}
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dfwg += num - 1;
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double ss = sumsq.getResult() - sum.getResult() * sum.getResult() / num;
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sswg += ss;
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}
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double sst = totsumsq.getResult() - totsum.getResult() *
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totsum.getResult()/totnum;
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double ssbg = sst - sswg;
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int dfbg = categoryData.size() - 1;
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double msbg = ssbg/dfbg;
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double mswg = sswg/dfwg;
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double F = msbg/mswg;
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return new AnovaStats(dfbg, dfwg, F);
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}
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/**
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Convenience class to pass dfbg,dfwg,F values around within AnovaImpl.
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No get/set methods provided.
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*/
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private static class AnovaStats {
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private int dfbg;
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private int dfwg;
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private double F;
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/**
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* Constructor
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* @param dfbg degrees of freedom in numerator (between groups)
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* @param dfwg degrees of freedom in denominator (within groups)
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* @param F statistic
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*/
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AnovaStats(int dfbg, int dfwg, double F) {
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this.dfbg = dfbg;
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this.dfwg = dfwg;
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this.F = F;
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}
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}
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}
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@ -0,0 +1,72 @@
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# Licensed to the Apache Software Foundation (ASF) under one or more
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# contributor license agreements. See the NOTICE file distributed with
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# this work for additional information regarding copyright ownership.
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# The ASF licenses this file to You under the Apache License, Version 2.0
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# (the "License"); you may not use this file except in compliance with
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# the License. You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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#
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#------------------------------------------------------------------------------
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# R source file to validate Binomial distribution tests in
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# org.apache.commons.math.distribution.BinomialDistributionTest
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#
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# To run the test, install R, put this file and testFunctions
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# into the same directory, launch R from this directory and then enter
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# source("<name-of-this-file>")
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#
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# R functions used
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# anova(model) <- anova
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# lm(frame) <- linear model
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#------------------------------------------------------------------------------
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tol <- 1E-12 # error tolerance for tests
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#------------------------------------------------------------------------------
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# Function definitions
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source("testFunctions") # utility test functions
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options(digits=16) # override number of digits displayed
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# function to verify anova computations
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verifyAnova <- function(frame, expectedP, expectedF, frameName) {
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a <- anova(lm(frame))
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p <- a$"Pr(>F)"[1]
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f <- a$"F value"[1]
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output <- c("P-value test frame = ", frameName)
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if (assertEquals(expectedP,p,tol,"P value")) {
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displayPadded(output, SUCCEEDED, WIDTH)
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} else {
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displayPadded(output, FAILED, WIDTH)
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}
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output <- c("F-value test frame = ", frameName)
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if (assertEquals(expectedF,f,tol,"F value")) {
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displayPadded(output, SUCCEEDED, WIDTH)
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} else {
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displayPadded(output, FAILED, WIDTH)
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}
|
||||||
|
}
|
||||||
|
|
||||||
|
#--------------------------------------------------------------------------
|
||||||
|
cat("Anova test cases\n")
|
||||||
|
classA <- c(93.0, 103.0, 95.0, 101.0, 91.0, 105.0, 96.0, 94.0, 101.0)
|
||||||
|
classB <- c(99.0, 92.0, 102.0, 100.0, 102.0, 89.0)
|
||||||
|
classC <- c(110.0, 115.0, 111.0, 117.0, 128.0, 117.0)
|
||||||
|
|
||||||
|
threeClasses = data.frame(val = c(classA, classB, classC),
|
||||||
|
class=c(rep("classA", length(classA)),
|
||||||
|
rep("classB", length(classB)),
|
||||||
|
rep("classC", length(classC))))
|
||||||
|
|
||||||
|
verifyAnova(threeClasses,6.959446e-06, 24.67361709460624, "Three classes")
|
||||||
|
|
||||||
|
twoClasses = data.frame(val = c(classA, classB),
|
||||||
|
class=c(rep("classA", length(classA)), rep("classB", length(classB))))
|
||||||
|
verifyAnova(twoClasses, 0.904212960464, 0.0150579150579, "Two classes")
|
||||||
|
|
||||||
|
displayDashes(WIDTH)
|
||||||
|
|
@ -39,6 +39,7 @@ source("regressionTestCases")
|
||||||
|
|
||||||
# inference
|
# inference
|
||||||
source("chiSquareTestCases")
|
source("chiSquareTestCases")
|
||||||
|
source("anovaTestCases")
|
||||||
|
|
||||||
# descriptive
|
# descriptive
|
||||||
source("descriptiveTestCases")
|
source("descriptiveTestCases")
|
||||||
|
|
|
||||||
|
|
@ -0,0 +1,143 @@
|
||||||
|
/*
|
||||||
|
* 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.math.stat.inference;
|
||||||
|
|
||||||
|
import junit.framework.Test;
|
||||||
|
import junit.framework.TestCase;
|
||||||
|
import junit.framework.TestSuite;
|
||||||
|
|
||||||
|
import java.util.ArrayList;
|
||||||
|
import java.util.List;
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Test cases for the OneWayAnovaImpl class.
|
||||||
|
*
|
||||||
|
* @version $Revision$ $Date$
|
||||||
|
*/
|
||||||
|
|
||||||
|
public class OneWayAnovaTest extends TestCase {
|
||||||
|
|
||||||
|
protected OneWayAnova testStatistic = new OneWayAnovaImpl();
|
||||||
|
|
||||||
|
private char[] wrongArray = { 'a', 'b', 'c' };
|
||||||
|
private double[] emptyArray = {};
|
||||||
|
|
||||||
|
private double[] classA =
|
||||||
|
{93.0, 103.0, 95.0, 101.0, 91.0, 105.0, 96.0, 94.0, 101.0 };
|
||||||
|
private double[] classB =
|
||||||
|
{99.0, 92.0, 102.0, 100.0, 102.0, 89.0 };
|
||||||
|
private double[] classC =
|
||||||
|
{110.0, 115.0, 111.0, 117.0, 128.0, 117.0 };
|
||||||
|
|
||||||
|
public OneWayAnovaTest(String name) {
|
||||||
|
super(name);
|
||||||
|
}
|
||||||
|
|
||||||
|
public void setUp() {
|
||||||
|
}
|
||||||
|
|
||||||
|
public static Test suite() {
|
||||||
|
TestSuite suite = new TestSuite(OneWayAnovaTest.class);
|
||||||
|
suite.setName("TestStatistic Tests");
|
||||||
|
return suite;
|
||||||
|
}
|
||||||
|
|
||||||
|
public void testAnovaFValue() throws Exception {
|
||||||
|
// Target comparison values computed using R version 2.6.0 (Linux version)
|
||||||
|
List threeClasses = new ArrayList();
|
||||||
|
threeClasses.add(classA);
|
||||||
|
threeClasses.add(classB);
|
||||||
|
threeClasses.add(classC);
|
||||||
|
|
||||||
|
assertEquals("ANOVA F-value", 24.67361709460624,
|
||||||
|
testStatistic.anovaFValue(threeClasses), 1E-12);
|
||||||
|
|
||||||
|
List twoClasses = new ArrayList();
|
||||||
|
twoClasses.add(classA);
|
||||||
|
twoClasses.add(classB);
|
||||||
|
|
||||||
|
assertEquals("ANOVA F-value", 0.0150579150579,
|
||||||
|
testStatistic.anovaFValue(twoClasses), 1E-12);
|
||||||
|
|
||||||
|
// now try some input hashes which should fail
|
||||||
|
List wrongContents = new ArrayList();
|
||||||
|
wrongContents.add(classC);
|
||||||
|
wrongContents.add(wrongArray);
|
||||||
|
try {
|
||||||
|
double bad = testStatistic.anovaFValue(wrongContents);
|
||||||
|
fail("non double[] hash value for key classX, IllegalArgumentException expected");
|
||||||
|
} catch (IllegalArgumentException ex) {
|
||||||
|
// expected
|
||||||
|
}
|
||||||
|
|
||||||
|
List emptyContents = new ArrayList();
|
||||||
|
emptyContents.add(emptyArray);
|
||||||
|
emptyContents.add(classC);
|
||||||
|
try {
|
||||||
|
double bad = testStatistic.anovaFValue(emptyContents);
|
||||||
|
fail("empty array for key classX, IllegalArgumentException expected");
|
||||||
|
} catch (IllegalArgumentException ex) {
|
||||||
|
// expected
|
||||||
|
}
|
||||||
|
|
||||||
|
List tooFew = new ArrayList();
|
||||||
|
tooFew.add(classA);
|
||||||
|
try {
|
||||||
|
double bad = testStatistic.anovaFValue(tooFew);
|
||||||
|
fail("less than two classes, IllegalArgumentException expected");
|
||||||
|
} catch (IllegalArgumentException ex) {
|
||||||
|
// expected
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
public void testAnovaPValue() throws Exception {
|
||||||
|
// Target comparison values computed using R version 2.6.0 (Linux version)
|
||||||
|
List threeClasses = new ArrayList();
|
||||||
|
threeClasses.add(classA);
|
||||||
|
threeClasses.add(classB);
|
||||||
|
threeClasses.add(classC);
|
||||||
|
|
||||||
|
assertEquals("ANOVA P-value", 6.959446E-06,
|
||||||
|
testStatistic.anovaPValue(threeClasses), 1E-12);
|
||||||
|
|
||||||
|
List twoClasses = new ArrayList();
|
||||||
|
twoClasses.add(classA);
|
||||||
|
twoClasses.add(classB);
|
||||||
|
|
||||||
|
assertEquals("ANOVA P-value", 0.904212960464,
|
||||||
|
testStatistic.anovaPValue(twoClasses), 1E-12);
|
||||||
|
|
||||||
|
}
|
||||||
|
|
||||||
|
public void testAnovaTest() throws Exception {
|
||||||
|
// Target comparison values computed using R version 2.3.1 (Linux version)
|
||||||
|
List threeClasses = new ArrayList();
|
||||||
|
threeClasses.add(classA);
|
||||||
|
threeClasses.add(classB);
|
||||||
|
threeClasses.add(classC);
|
||||||
|
|
||||||
|
assertTrue("ANOVA Test P<0.01", testStatistic.anovaTest(threeClasses, 0.01));
|
||||||
|
|
||||||
|
List twoClasses = new ArrayList();
|
||||||
|
twoClasses.add(classA);
|
||||||
|
twoClasses.add(classB);
|
||||||
|
|
||||||
|
assertFalse("ANOVA Test P>0.01", testStatistic.anovaTest(twoClasses, 0.01));
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
|
|
@ -130,6 +130,9 @@ Commons Math Release Notes</title>
|
||||||
<action dev="luc" type="update" issue="MATH-179" due-to="Niall Pemberton">
|
<action dev="luc" type="update" issue="MATH-179" due-to="Niall Pemberton">
|
||||||
Add tests for Fraction constructor using double parameter.
|
Add tests for Fraction constructor using double parameter.
|
||||||
</action>
|
</action>
|
||||||
|
<action dev="psteitz" type="update" issue="MATH-173" due-to="Bob MacCallum">
|
||||||
|
Added one-way ANOVA implementation.
|
||||||
|
</action>
|
||||||
</release>
|
</release>
|
||||||
<release version="1.1" date="2005-12-17"
|
<release version="1.1" date="2005-12-17"
|
||||||
description="This is a maintenance release containing bug fixes and enhancements.
|
description="This is a maintenance release containing bug fixes and enhancements.
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue