Author: psteitz
Date: Mon Sep 30 20:54:28 2013
New Revision: 1527777
URL: http://svn.apache.org/r1527777
Log:
Added exact binomial test implementation.
Contributed by Thorsten Schaefer
JIRA: MATH-1034
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java
Modified:
commons/proper/math/trunk/src/changes/changes.xml
Modified: commons/proper/math/trunk/src/changes/changes.xml
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/changes/changes.xml?rev=1527777&r1=1527776&r2=1527777&view=diff
==============================================================================
--- commons/proper/math/trunk/src/changes/changes.xml (original)
+++ commons/proper/math/trunk/src/changes/changes.xml Mon Sep 30 20:54:28 2013
@@ -51,6 +51,9 @@ If the output is not quite correct, chec
</properties>
<body>
<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">
Added overloaded constructors for subclasses of "RealDistribution"
implementations
which do not require an explicit "inverseCumulativeAccuracy". The
default accuracy will
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java?rev=1527777&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/AlternativeHypothesis.java
Mon Sep 30 20:54:28 2013
@@ -0,0 +1,41 @@
+/*
+ * 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 ≠ p0
+ */
+ TWO_SIDED,
+
+ /**
+ * Represents a right-sided test. H0: p ≤ p0, H1: p > p0.
+ */
+ GREATER_THAN,
+
+ /**
+ * Represents a left-sided test. H0: p ≥ p0, H1: p < p0.
+ */
+ LESS_THAN
+}
Added:
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java?rev=1527777&view=auto
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java
(added)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math3/stat/inference/BinomialTest.java
Mon Sep 30 20:54:28 2013
@@ -0,0 +1,165 @@
+/*
+ * 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 ≥ 0.</li>
+ * <li>Number of successes must be ≥ 0.</li>
+ * <li>Number of successes must be ≤ number of trials.</li>
+ * <li>Probability must be ≥ 0 and ≤ 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} < {@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 ≥ 0.</li>
+ * <li>Number of successes must be ≥ 0.</li>
+ * <li>Number of successes must be ≤ number of trials.</li>
+ * <li>Probability must be ≥ 0 and ≤ 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} < {@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);
+ }
+ }
+}
Added:
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java?rev=1527777&view=auto
==============================================================================
---
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java
(added)
+++
commons/proper/math/trunk/src/test/java/org/apache/commons/math3/stat/inference/BinomialTestTest.java
Mon Sep 30 20:54:28 2013
@@ -0,0 +1,84 @@
+/*
+ * 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));
+
+ }
+}
