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Added exact binomial test implementation. 

Contributed by Thorsten Schaefer
JIRA: MATH-1034


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1527777 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Phil Steitz 2013-09-30 20:54:28 +00:00
parent 7cc91e9f22
commit 22cad3d1a9
4 changed files with 293 additions and 0 deletions
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3
src/changes/changes.xml
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@ -51,6 +51,9 @@ If the output is not quite correct, check for invisible trailing spaces!
</properties> </properties>
<body> <body>
<release version="x.y" date="TBD" description="TBD"> <release version="x.y" date="TBD" description="TBD">
<action dev="psteitz" type="add" issue="MATH-1034" due-to="Thorsten Schaefer">
Added exact binomial test implementation.
</action>
<action dev="tn" type="add" issue="MATH-1018" due-to="Ajo Fod"> <action dev="tn" type="add" issue="MATH-1018" due-to="Ajo Fod">
Added overloaded constructors for subclasses of "RealDistribution" implementations Added overloaded constructors for subclasses of "RealDistribution" implementations
which do not require an explicit "inverseCumulativeAccuracy". The default accuracy will which do not require an explicit "inverseCumulativeAccuracy". The default accuracy will

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src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java Normal file
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/*
* 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;
/**
* Represents an alternative hypothesis for a hypothesis test.
*
* @version $Id$
* @since 3.3
*/
public enum AlternativeHypothesis {
/**
* Represents a two-sided test. H0: p=p0, H1: p &ne; p0
*/
TWO_SIDED,
/**
* Represents a right-sided test. H0: p &le; p0, H1: p &gt; p0.
*/
GREATER_THAN,
/**
* Represents a left-sided test. H0: p &ge; p0, H1: p &lt; p0.
*/
LESS_THAN
}

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src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java Normal file
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/*
* 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 org.apache.commons.math3.distribution.BinomialDistribution;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MathInternalError;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
/**
* Implements binomial test statistics.
*
* <p>
* Exact test for the statistical significance of deviations from a
* theoretically expected distribution of observations into two categories.
* </p>
*
* @see <a href="http://en.wikipedia.org/wiki/Binomial_test">Binomial test (Wikipedia)</a>
* @version $Id$
* @since 3.3
*/
public class BinomialTest {
/**
* Returns whether the null hypothesis can be rejected with the given
* confidence level.
*
* <p>
* <strong>Preconditions</strong>:
* <ul>
* <li>Number of trials must be &ge; 0.</li>
* <li>Number of successes must be &ge; 0.</li>
* <li>Number of successes must be &le; number of trials.</li>
* <li>Probability must be &ge; 0 and &le; 1.
* </ul>
* </p>
*
* @param numberOfTrials number of trials performed
* @param numberOfSuccesses number of successes observed
* @param probability assumed probability of a single trial under the null hypothesis
* @param alternativeHypothesis type of hypothesis being evaluated (one- or two-sided)
* @param confidenceLevel confidence level of the test
* @return true if the null hypothesis can be rejected with confidence {@code confidenceLevel}
* @throws NotPositiveException if {@code numberOfTrials} or {@code numberOfSuccesses}
* is negative
* @throws OutOfRangeException if {@code probability} is not between 0 and 1
* @throws MathIllegalArgumentException if
* {@code numberOfTrials} &lt; {@code numberOfSuccesses} or if {@code alternateHypothesis}
* is null.
* @see AlternativeHypothesis
*/
public boolean binomialTest(int numberOfTrials, int numberOfSuccesses, double probability,
AlternativeHypothesis alternativeHypothesis, double confidenceLevel) {
double pValue = binomialTest(numberOfTrials, numberOfSuccesses, probability, alternativeHypothesis);
return pValue < 1 - confidenceLevel;
}
/**
* Returns the <i>observed significance level</i>, or <a href=
* "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
* p-value</a>, associated with a <a
* href="http://en.wikipedia.org/wiki/Binomial_test"> Binomial test</a>.
* <p>
* The number returned is the smallest significance level at which one can
* reject the null hypothesis. The form of the hypothesis depends on
* {@code alternativeHypothesis}.
* </p>
* <p>
* <strong>Preconditions</strong>:
* <ul>
* <li>Number of trials must be &ge; 0.</li>
* <li>Number of successes must be &ge; 0.</li>
* <li>Number of successes must be &le; number of trials.</li>
* <li>Probability must be &ge; 0 and &le; 1.
* </ul>
* </p>
*
* @param numberOfTrials number of trials performed
* @param numberOfSuccesses number of successes observed
* @param probability assumed probability of a single trial under the null hypothesis
* @param alternativeHypothesis type of hypothesis being evaluated (one- or two-sided)
* @return p-value
* @throws NotPositiveException if {@code numberOfTrials} or {@code numberOfSuccesses}
* is negative
* @throws OutOfRangeException if {@code probability} is not between 0 and 1
* @throws MathIllegalArgumentException if
* {@code numberOfTrials} &lt; {@code numberOfSuccesses} or if {@code alternateHypothesis}
* is null.
* @see AlternativeHypothesis
*/
public double binomialTest(int numberOfTrials, int numberOfSuccesses, double probability,
AlternativeHypothesis alternativeHypothesis) {
if (numberOfTrials < 0) {
throw new NotPositiveException(numberOfTrials);
}
if (numberOfSuccesses < 0) {
throw new NotPositiveException(numberOfSuccesses);
}
if (probability < 0 || probability > 1) {
throw new OutOfRangeException(probability, 0, 1);
}
if (numberOfTrials < numberOfSuccesses) {
throw new MathIllegalArgumentException(
LocalizedFormats.BINOMIAL_INVALID_PARAMETERS_ORDER,
numberOfTrials, numberOfSuccesses);
}
if (alternativeHypothesis == null) {
throw new NullArgumentException();
}
final BinomialDistribution distribution = new BinomialDistribution(numberOfTrials, probability);
switch (alternativeHypothesis) {
case GREATER_THAN:
return 1 - distribution.cumulativeProbability(numberOfSuccesses - 1);
case LESS_THAN:
return distribution.cumulativeProbability(numberOfSuccesses);
case TWO_SIDED:
int criticalValueLow = 0;
int criticalValueHigh = numberOfTrials;
double pTotal = 0;
while (true) {
double pLow = distribution.probability(criticalValueLow);
double pHigh = distribution.probability(criticalValueHigh);
if (pLow == pHigh) {
pTotal += 2 * pLow;
criticalValueLow++;
criticalValueHigh--;
} else if (pLow < pHigh) {
pTotal += pLow;
criticalValueLow++;
} else {
pTotal += pHigh;
criticalValueHigh--;
}
if (criticalValueLow > numberOfSuccesses || criticalValueHigh < numberOfSuccesses) {
break;
}
}
return pTotal;
default:
throw new MathInternalError(LocalizedFormats. OUT_OF_RANGE_SIMPLE, alternativeHypothesis,
AlternativeHypothesis.TWO_SIDED, AlternativeHypothesis.LESS_THAN);
}
}
}

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src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java Normal file
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/*
* 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 org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for the BinomialTest class.
*/
public class BinomialTestTest {
protected BinomialTest testStatistic = new BinomialTest();
private static int successes = 51;
private static int trials = 235;
private static double probability = 1.0 / 6.0;
@Test
public void testBinomialTestPValues() {
Assert.assertEquals(0.04375, testStatistic.binomialTest(
trials, successes, probability, AlternativeHypothesis.TWO_SIDED), 1E-4);
Assert.assertEquals(0.02654, testStatistic.binomialTest(
trials, successes, probability, AlternativeHypothesis.GREATER_THAN), 1E-4);
Assert.assertEquals(0.982, testStatistic.binomialTest(
trials, successes, probability, AlternativeHypothesis.LESS_THAN), 1E-4);
}
@Test
public void testBinomialTestExceptions() {
try {
testStatistic.binomialTest(10, -1, 0.5, AlternativeHypothesis.TWO_SIDED);
Assert.fail("Expected not positive exception");
} catch (NotPositiveException e) {
// expected exception;
}
try {
testStatistic.binomialTest(10, 11, 0.5, AlternativeHypothesis.TWO_SIDED);
Assert.fail("Expected illegal argument exception");
} catch (MathIllegalArgumentException e) {
// expected exception;
}
try {
testStatistic.binomialTest(10, 11, 0.5, null);
Assert.fail("Expected illegal argument exception");
} catch (MathIllegalArgumentException e) {
// expected exception;
}
}
@Test
public void testBinomialTestAcceptReject() {
double confidenceLevel95 = 0.95;
double confidenceLevel99 = 0.99;
Assert.assertTrue(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.TWO_SIDED, confidenceLevel95));
Assert.assertTrue(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.GREATER_THAN, confidenceLevel95));
Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.LESS_THAN, confidenceLevel95));
Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.TWO_SIDED, confidenceLevel99));
Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.GREATER_THAN, confidenceLevel99));
Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.LESS_THAN, confidenceLevel95));
}
}