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From m...@apache.org
Subject svn commit: r1053836 - in /commons/proper/math/trunk/src: main/java/org/apache/commons/math/stat/inference/ test/java/org/apache/commons/math/stat/inference/
Date Thu, 30 Dec 2010 09:52:00 GMT
Author: mikl
Date: Thu Dec 30 09:52:00 2010
New Revision: 1053836

URL: http://svn.apache.org/viewvc?rev=1053836&view=rev
Log:
Starting point for fixing MATH-431. Still some validation tests and documentation are missing.

Added:
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTest.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTestImpl.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTest.java
    commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestImpl.java
    commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/MannWhitneyUTestTest.java
    commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestTest.java

Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTest.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTest.java
(added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTest.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,96 @@
+/*
+ * 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 org.apache.commons.math.MathException;
+
+/**
+ * An interface for Mann-Whitney U test (also called Wilcoxon rank-sum test).
+ * 
+ * @version $Revision: $ $Date: $
+ */
+public interface MannWhitneyUTest {
+
+    /**
+     * Computes the <a
+     * href="http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U"> Mann-Whitney
+     * U statistic</a> comparing mean for two independent samples possibly of
+     * different length.
+     * <p>
+     * This statistic can be used to perform a Mann-Whitney U test evaluating
+     * the null hypothesis that the two independent samples has equal mean.
+     * </p>
+     * <p>
+     * Let X<sub>i</sub> denote the i'th individual of the first sample and
+     * Y<sub>j</sub> the j'th individual in the second sample. Note that the
+     * samples would often have different length.
+     * </p>
+     * <p>
+     * <strong>Preconditions</strong>:
+     * <ul>
+     * <li>All observations in the two samples are independent.</li>
+     * <li>The observations are at least ordinal (continuous are also ordinal).</li>
+     * </ul>
+     * </p>
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @return mannWhitneyU statistic
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     */
+    double mannWhitneyU(final double[] x, final double[] y)
+            throws IllegalArgumentException;
+
+    /**
+     * Returns the asymptotic <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/Mann%E2%80%93Whitney_U"> Mann-Whitney
+     * U statistic</a> comparing mean for two independent samples.
+     * <p>
+     * Let X<sub>i</sub> denote the i'th individual of the first sample and
+     * Y<sub>j</sub> the j'th individual in the second sample. Note that the
+     * samples would often have different length.
+     * </p>
+     * <p>
+     * <strong>Preconditions</strong>:
+     * <ul>
+     * <li>All observations in the two samples are independent.</li>
+     * <li>The observations are at least ordinal (continuous are also ordinal).</li>
+     * </ul>
+     * </p>
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @param exactPValue
+     *            if the exact p-value is wanted (only works for x.length <= 30,
+     *            if true and x.length > 30, this is ignored because
+     *            calculations may take too long)
+     * @return asymptotic p-value
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     * @throws MathException
+     *             if an error occurs computing the p-value
+     */
+    double mannWhitneyUTest(final double[] x, final double[] y)
+            throws IllegalArgumentException, MathException;
+}

Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTestImpl.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTestImpl.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTestImpl.java
(added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/MannWhitneyUTestImpl.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,199 @@
+/*
+ * 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 org.apache.commons.math.MathException;
+import org.apache.commons.math.distribution.NormalDistributionImpl;
+import org.apache.commons.math.stat.ranking.NaNStrategy;
+import org.apache.commons.math.stat.ranking.NaturalRanking;
+import org.apache.commons.math.stat.ranking.TiesStrategy;
+import org.apache.commons.math.util.FastMath;
+
+/**
+ * An implementation of the Mann-Whitney U test (also called Wilcoxon rank-sum
+ * test).
+ * 
+ * @version $Revision: $ $Date: $
+ */
+public class MannWhitneyUTestImpl implements MannWhitneyUTest {
+    private NaturalRanking naturalRanking;
+
+    /**
+     * Create a test instance using where NaN's are left in place and ties get
+     * the average of applicable ranks. Use this unless you are very sure of
+     * what you are doing.
+     */
+    public MannWhitneyUTestImpl() {
+        naturalRanking = new NaturalRanking(NaNStrategy.FIXED,
+                TiesStrategy.AVERAGE);
+    }
+
+    /**
+     * Create a test instance using the given strategies for NaN's and ties.
+     * Only use this if you are sure of what you are doing.
+     * 
+     * @param nanStrategy
+     *            specifies the strategy that should be used for Double.NaN's
+     * @param tiesStrategy
+     *            specifies the strategy that should be used for ties
+     */
+    public MannWhitneyUTestImpl(NaNStrategy nanStrategy,
+            TiesStrategy tiesStrategy) {
+        naturalRanking = new NaturalRanking(nanStrategy, tiesStrategy);
+    }
+
+    /**
+     * Ensures that the provided arrays fulfills the assumptions.
+     * 
+     * @param x
+     * @param y
+     * @throws IllegalArgumentException
+     *             if assumptions are not met
+     */
+    private void ensureDataConformance(final double[] x, final double[] y)
+            throws IllegalArgumentException {
+        if (x == null) {
+            throw new IllegalArgumentException("x must not be null");
+        }
+
+        if (y == null) {
+            throw new IllegalArgumentException("y must not be null");
+        }
+
+        if (x.length == 0) {
+            throw new IllegalArgumentException(
+                    "x must contain at least one element");
+        }
+
+        if (y.length == 0) {
+            throw new IllegalArgumentException(
+                    "y must contain at least one element");
+        }
+    }
+
+    private double[] concatinateSamples(final double[] x, final double[] y) {
+        final double[] z = new double[x.length + y.length];
+
+        System.arraycopy(x, 0, z, 0, x.length);
+        System.arraycopy(y, 0, z, x.length, y.length);
+
+        return z;
+    }
+
+    /**
+     * {@inheritDoc}
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @return mannWhitneyU statistic U (maximum of U<sup>x</sup> and U<sup>y</sup>)
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     */
+    public double mannWhitneyU(final double[] x, final double[] y)
+            throws IllegalArgumentException {
+
+        ensureDataConformance(x, y);
+
+        final double[] z = concatinateSamples(x, y);
+        final double[] ranks = naturalRanking.rank(z);
+
+        double sumRankX = 0;
+
+        /*
+         * The ranks for x is in the first x.length entries in ranks because x
+         * is in the first x.length entries in z
+         */
+        for (int i = 0; i < x.length; ++i) {
+            sumRankX += ranks[i];
+        }
+
+        /*
+         * U1 = R1 - (n1 * (n1 + 1)) / 2 where R1 is sum of ranks for sample 1,
+         * e.g. x, n1 is the number of observations in sample 1.
+         */
+        final double U1 = sumRankX - (x.length * (x.length + 1)) / 2;
+
+        /*
+         * It can be shown that U1 + U2 = n1 * n2
+         */
+        final double U2 = x.length * y.length - U1;
+
+        return FastMath.max(U1, U2);
+    }
+
+    /**
+     * @param Umin
+     *            smallest Mann-Whitney U value
+     * @param N
+     *            number of subjects (corresponding to x.length)
+     * @return two-sided asymptotic p-value
+     * @throws MathException
+     *             if an error occurs computing the p-value
+     */
+    private double calculateAsymptoticPValue(final double Umin, final int n1,
+            final int n2) throws MathException {
+        
+        final int n1n2prod = n1 * n2;
+
+        // http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U#Normal_approximation
+        final double EU = (double) n1n2prod / 2.0;
+        final double VarU = (double) (n1n2prod * (n1 + n2 + 1)) / 12.0;
+
+        final double z = (Umin - EU) / FastMath.sqrt(VarU);
+
+        final NormalDistributionImpl standardNormal = new NormalDistributionImpl(
+                0, 1);
+
+        return 2 * standardNormal.cumulativeProbability(z);
+    }
+
+    /**
+     * Ties give rise to biased variance at the moment. See e.g. <a
+     * href="http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf"
+     * >http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf</a>.
+     * 
+     * {@inheritDoc}
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @param exactPValue
+     *            if the exact p-value is wanted (only for x.length <= 50)
+     * @return asymptotic p-value (biased for samples with ties)
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     * @throws MathException
+     *             if an error occurs computing the p-value
+     */
+    public double mannWhitneyUTest(final double[] x, final double[] y)
+            throws IllegalArgumentException, MathException {
+
+        ensureDataConformance(x, y);
+        
+        final double Umax = mannWhitneyU(x, y);
+        
+        /*
+         * It can be shown that U1 + U2 = n1 * n2
+         */
+        final double Umin = x.length * y.length - Umax; 
+
+        return calculateAsymptoticPValue(Umin, x.length, y.length);
+    }
+}

Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTest.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTest.java
(added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTest.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,107 @@
+/*
+ * 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 org.apache.commons.math.MathException;
+
+/**
+ * An interface for Wilcoxon signed-rank test.
+ * 
+ * @version $Revision: $ $Date: $
+ */
+public interface WilcoxonSignedRankTest {
+
+    /**
+     * Computes the <a
+     * href="http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test">
+     * Wilcoxon signed ranked statistic</a> comparing mean for two related
+     * samples or repeated measurements on a single sample.
+     * <p>
+     * This statistic can be used to perform a Wilcoxon signed ranked test
+     * evaluating the null hypothesis that the two related samples or repeated
+     * measurements on a single sample has equal mean.
+     * </p>
+     * <p>
+     * Let X<sub>i</sub> denote the i'th individual of the first sample and
+     * Y<sub>i</sub> the related i'th individual in the second sample. Let
+     * Z<sub>i</sub> = Y<sub>i</sub> - X<sub>i</sub>.
+     * </p>
+     * <p>
+     * <strong>Preconditions</strong>:
+     * <ul>
+     * <li>The differences Z<sub>i</sub> must be independent.</li>
+     * <li>Each Z<sub>i</sub> comes from a continuous population (they
must be
+     * identical) and is symmetric about a common median.</li>
+     * <li>The values that X<sub>i</sub> and Y<sub>i</sub>
represent are
+     * ordered, so the comparisons greater than, less than, and equal to are
+     * meaningful.</li>
+     * </ul>
+     * </p>
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @return wilcoxonSignedRank statistic
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     */
+    double wilcoxonSignedRank(final double[] x, final double[] y)
+            throws IllegalArgumentException;
+
+    /**
+     * 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/Wilcoxon_signed-rank_test">
+     * Wilcoxon signed ranked statistic</a> comparing mean for two related
+     * samples or repeated measurements on a single sample.
+     * <p>
+     * Let X<sub>i</sub> denote the i'th individual of the first sample and
+     * Y<sub>i</sub> the related i'th individual in the second sample. Let
+     * Z<sub>i</sub> = Y<sub>i</sub> - X<sub>i</sub>.
+     * </p>
+     * <p>
+     * <strong>Preconditions</strong>:
+     * <ul>
+     * <li>The differences Z<sub>i</sub> must be independent.</li>
+     * <li>Each Z<sub>i</sub> comes from a continuous population (they
must be
+     * identical) and is symmetric about a common median.</li>
+     * <li>The values that X<sub>i</sub> and Y<sub>i</sub>
represent are
+     * ordered, so the comparisons greater than, less than, and equal to are
+     * meaningful.</li>
+     * </ul>
+     * </p>
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @param exactPValue
+     *            if the exact p-value is wanted (only works for x.length <= 30,
+     *            if true and x.length > 30, this is ignored because
+     *            calculations may take too long)
+     * @return p-value
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     * @throws MathException
+     *             if an error occurs computing the p-value
+     */
+    double wilcoxonSignedRankTest(final double[] x, final double[] y,
+            boolean exactPValue) throws IllegalArgumentException,
+            MathException;
+}

Added: commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestImpl.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestImpl.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestImpl.java
(added)
+++ commons/proper/math/trunk/src/main/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestImpl.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,271 @@
+/*
+ * 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 org.apache.commons.math.MathException;
+import org.apache.commons.math.distribution.NormalDistributionImpl;
+import org.apache.commons.math.stat.ranking.NaNStrategy;
+import org.apache.commons.math.stat.ranking.NaturalRanking;
+import org.apache.commons.math.stat.ranking.TiesStrategy;
+import org.apache.commons.math.util.FastMath;
+
+/**
+ * An implementation of the Wilcoxon signed-rank test.
+ * 
+ * @version $Revision: $ $Date: $
+ */
+public class WilcoxonSignedRankTestImpl implements WilcoxonSignedRankTest {
+    private NaturalRanking naturalRanking;
+
+    /**
+     * Create a test instance where NaN's are left in place and ties get
+     * the average of applicable ranks. Use this unless you are very sure
+     * of what you are doing.
+     */
+    public WilcoxonSignedRankTestImpl() {
+        naturalRanking = new NaturalRanking(NaNStrategy.FIXED,
+                TiesStrategy.AVERAGE);
+    }
+
+    /**
+     * Create a test instance using the given strategies for NaN's and ties.
+     * Only use this if you are sure of what you are doing.
+     * 
+     * @param nanStrategy
+     *            specifies the strategy that should be used for Double.NaN's
+     * @param tiesStrategy
+     *            specifies the strategy that should be used for ties
+     */
+    public WilcoxonSignedRankTestImpl(NaNStrategy nanStrategy,
+            TiesStrategy tiesStrategy) {
+        naturalRanking = new NaturalRanking(nanStrategy, tiesStrategy);
+    }
+
+    /**
+     * Ensures that the provided arrays fulfills the assumptions.
+     * 
+     * @param x
+     * @param y
+     * @throws IllegalArgumentException
+     *             if assumptions are not met
+     */
+    private void ensureDataConformance(final double[] x, final double[] y)
+            throws IllegalArgumentException {
+        if (x == null) {
+            throw new IllegalArgumentException("x must not be null");
+        }
+
+        if (y == null) {
+            throw new IllegalArgumentException("y must not be null");
+        }
+
+        if (x.length != y.length) {
+            throw new IllegalArgumentException(
+                    "x and y must contain the same number of elements");
+        }
+
+        if (x.length == 0) {
+            throw new IllegalArgumentException(
+                    "x and y must contain at least one element");
+        }
+    }
+
+    /**
+     * Calculates y[i] - x[i] for all i
+     * 
+     * @param x
+     * @param y
+     * @throws IllegalArgumentException
+     *             if assumptions are not met
+     */
+    private double[] calculateDifferences(final double[] x, final double[] y)
+            throws IllegalArgumentException {
+
+        final double[] z = new double[x.length];
+
+        for (int i = 0; i < x.length; ++i) {
+            z[i] = y[i] - x[i];
+        }
+
+        return z;
+    }
+
+    /**
+     * Calculates |z[i]| for all i
+     * 
+     * @param z
+     * @throws IllegalArgumentException
+     *             if assumptions are not met
+     */
+    private double[] calculateAbsoluteDifferences(final double[] z)
+            throws IllegalArgumentException {
+        if (z == null) {
+            throw new IllegalArgumentException("z must not be null");
+        }
+
+        if (z.length == 0) {
+            throw new IllegalArgumentException(
+                    "z must contain at least one element");
+        }
+
+        final double[] zAbs = new double[z.length];
+
+        for (int i = 0; i < z.length; ++i) {
+            zAbs[i] = FastMath.abs(z[i]);
+        }
+
+        return zAbs;
+    }
+
+    /**
+     * {@inheritDoc}
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @return wilcoxonSignedRank statistic (the larger of W+ and W-)
+     * @throws IllegalArgumentException
+     *             if preconditions are not met
+     */
+    public double wilcoxonSignedRank(final double[] x, final double[] y)
+            throws IllegalArgumentException {
+        
+        ensureDataConformance(x, y);
+
+        // throws IllegalArgumentException if x and y are not correctly
+        // specified
+        final double[] z = calculateDifferences(x, y);
+        final double[] zAbs = calculateAbsoluteDifferences(z);
+
+        final double[] ranks = naturalRanking.rank(zAbs);
+
+        double Wplus = 0;
+
+        for (int i = 0; i < z.length; ++i) {
+            if (z[i] > 0) {
+                Wplus += ranks[i];
+            }
+        }
+
+        final int N = x.length;
+        final double Wminus = (((double) (N * (N + 1))) / 2.0) - Wplus;
+
+        return FastMath.max(Wplus, Wminus);
+    }
+
+    /**
+     * Algorithm inspired by
+     * http://www.fon.hum.uva.nl/Service/Statistics/Signed_Rank_Algorihms.html#C
+     * by Rob van Son, Institute of Phonetic Sciences & IFOTT, 
+     * University of Amsterdam
+     * 
+     * @param Wmax largest Wilcoxon signed rank value
+     * @param N number of subjects (corresponding to x.length)
+     * @return two-sided exact p-value 
+     */
+    private double calculateExactPValue(final double Wmax, final int N) {
+
+        // Total number of outcomes (equal to 2^N but a lot faster)
+        final int m = 1 << N;
+
+        int largerRankSums = 0;
+
+        for (int i = 0; i < m; ++i) {
+            int rankSum = 0;
+
+            // Generate all possible rank sums
+            for (int j = 0; j < N; ++j) {
+
+                // (i >> j) & 1 extract i's j-th bit from the right
+                if (((i >> j) & 1) == 1) {
+                    rankSum += j + 1;
+                }
+            }
+
+            if (rankSum >= Wmax) {
+                ++largerRankSums;
+            }
+        }
+
+        /*
+         * largerRankSums / m gives the one-sided p-value, so it's multiplied
+         * with 2 to get the two-sided p-value
+         */
+        return 2 * ((double) largerRankSums) / ((double) m);
+    }
+    
+    /**
+     * @param Wmin smallest Wilcoxon signed rank value
+     * @param N number of subjects (corresponding to x.length)
+     * @return two-sided asymptotic p-value 
+     * @throws MathException if an error occurs computing the p-value
+     */
+    private double calculateAsymptoticPValue(final double Wmin, final int N) throws MathException
{
+        
+        final double ES = (double) (N * (N + 1)) / 4.0;
+        
+        /* Same as (but saves computations): 
+         * final double VarW = ((double) (N * (N + 1) * (2*N + 1))) / 24;
+         */
+        final double VarS = ES * ((double) (2 * N + 1) / 6.0);
+        
+        // - 0.5 is a continuity correction
+        final double z = (Wmin - ES - 0.5) / FastMath.sqrt(VarS);
+
+        final NormalDistributionImpl standardNormal = new NormalDistributionImpl(0, 1);
+
+        return 2*standardNormal.cumulativeProbability(z);
+    }
+
+    /**
+     * {@inheritDoc}
+     * 
+     * @param x
+     *            the first sample
+     * @param y
+     *            the second sample
+     * @param exactPValue
+     *            if the exact p-value is wanted (only for x.length <= 30)
+     * @return p-value
+     * @throws IllegalArgumentException
+     *             if preconditions are not met or exact p-value is wanted for
+     *             when x.length > 30
+     * @throws MathException
+     *             if an error occurs computing the p-value
+     */
+    public double wilcoxonSignedRankTest(final double[] x, final double[] y,
+            boolean exactPValue) throws IllegalArgumentException,
+            MathException {
+        
+        ensureDataConformance(x, y);
+
+        final int N = x.length;
+        final double Wmax = wilcoxonSignedRank(x, y);
+        
+        if (exactPValue && N > 30) {
+            throw new IllegalArgumentException("Exact test can only be made for N <= 30.");
+        }
+        
+        if (exactPValue) {
+            return calculateExactPValue(Wmax, N);
+        } else {
+            final double Wmin = ( (double)(N*(N+1)) / 2.0 ) - Wmax;
+            return calculateAsymptoticPValue(Wmin, N);
+        }
+    }
+}

Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/MannWhitneyUTestTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/MannWhitneyUTestTest.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/MannWhitneyUTestTest.java
(added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/MannWhitneyUTestTest.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,101 @@
+/*
+ * 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.TestCase;
+
+/**
+ * Test cases for the ChiSquareTestImpl class.
+ *
+ * @version $Revision: $ $Date: $
+ */
+
+public class MannWhitneyUTestTest extends TestCase {
+
+    protected MannWhitneyUTest testStatistic = new MannWhitneyUTestImpl();
+
+    public MannWhitneyUTestTest(String name) {
+        super(name);
+    }
+
+    public void testMannWhitneyUSimple() throws Exception {
+        /* Target values computed using R version 2.11.1
+         * x <- c(19, 22, 16, 29, 24)
+         * y <- c(20, 11, 17, 12)
+         * wilcox.test(x, y, alternative = "two.sided", mu = 0, paired = FALSE, exact = FALSE,
correct = FALSE)
+         * W = 17, p-value = 0.08641 
+         */
+        final double x[] = {19, 22, 16, 29, 24};
+        final double y[] = {20, 11, 17, 12};
+        
+        assertEquals(17, testStatistic.mannWhitneyU(x, y), 1e-10);
+        assertEquals(0.08641, testStatistic.mannWhitneyUTest(x, y), 1e-5);
+    }
+
+
+    public void testMannWhitneyUInputValidation() throws Exception {
+        /* Samples must be present, i.e. length > 0
+         */
+        try {
+            testStatistic.mannWhitneyUTest(new double[] { }, new double[] { 1.0 });
+            fail("x does not contain samples (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        try {
+            testStatistic.mannWhitneyUTest(new double[] { 1.0 }, new double[] { });
+            fail("y does not contain samples (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        /*
+         * x and y is null
+         */
+        try {
+            testStatistic.mannWhitneyUTest(null, null);
+            fail("x and y is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.mannWhitneyUTest(null, null);
+            fail("x and y is null (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        /*
+         * x or y is null
+         */
+        try {
+            testStatistic.mannWhitneyUTest(null, new double[] { 1.0 });
+            fail("x is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.mannWhitneyUTest(new double[] { 1.0 }, null);
+            fail("y is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+    }
+}

Added: commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestTest.java
URL: http://svn.apache.org/viewvc/commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestTest.java?rev=1053836&view=auto
==============================================================================
--- commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestTest.java
(added)
+++ commons/proper/math/trunk/src/test/java/org/apache/commons/math/stat/inference/WilcoxonSignedRankTestTest.java
Thu Dec 30 09:52:00 2010
@@ -0,0 +1,180 @@
+/*
+ * 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.TestCase;
+
+/**
+ * Test cases for the ChiSquareTestImpl class.
+ *
+ * @version $Revision: $ $Date: $
+ */
+
+public class WilcoxonSignedRankTestTest extends TestCase {
+
+    protected WilcoxonSignedRankTest testStatistic = new WilcoxonSignedRankTestImpl();
+
+    public WilcoxonSignedRankTestTest(String name) {
+        super(name);
+    }
+
+    public void testWilcoxonSignedRankSimple() throws Exception {
+        /* Target values computed using R version 2.11.1
+         * x <- c(1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
+         * y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
+         */
+        final double x[] = {1.83, 0.50, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.30};
+        final double y[] = {0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29};
+        
+        /* EXACT:
+         * wilcox.test(x, y, alternative = "two.sided", mu = 0, paired = TRUE, exact = TRUE,
correct = FALSE)
+         * V = 40, p-value = 0.03906
+         * 
+         * Corresponds to the value obtained in R.
+         */
+        assertEquals(40, testStatistic.wilcoxonSignedRank(x, y), 1e-10);
+        assertEquals(0.03906, testStatistic.wilcoxonSignedRankTest(x, y, true), 1e-5);  
     
+        
+        /* ASYMPTOTIC:
+         * wilcox.test(x, y, alternative = "two.sided", mu = 0, paired = TRUE, exact = FALSE,
correct = FALSE)
+         * V = 40, p-value = 0.03815
+         * 
+         * This is not entirely the same due to different corrects, 
+         * e.g. http://mlsc.lboro.ac.uk/resources/statistics/wsrt.pdf
+         * and src/library/stats/R/wilcox.test.R in the R source
+         */
+        assertEquals(40, testStatistic.wilcoxonSignedRank(x, y), 1e-10);
+        assertEquals(0.0329693812, testStatistic.wilcoxonSignedRankTest(x, y, false), 1e-10);
+    }
+    
+    public void testWilcoxonSignedRankInputValidation() throws Exception {
+        /*
+         * Exact only for sample size <= 30
+         */
+        final double[] x1 = new double[30];
+        final double[] x2 = new double[31];
+        final double[] y1 = new double[30];
+        final double[] y2 = new double[31];
+        for (int i = 0; i < 30; ++i) {
+            x1[i] = x2[i] = y1[i] = y2[i] = i;            
+        }
+        
+        // Exactly 30 is okay
+        testStatistic.wilcoxonSignedRankTest(x1, y1, true);            
+        
+        try {
+            testStatistic.wilcoxonSignedRankTest(x2, y2, true);
+            fail("More than 30 samples and exact chosen, IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        /* Samples must be present, i.e. length > 0
+         */
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { }, new double[] { 1.0 },
true);
+            fail("x does not contain samples (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { }, new double[] { 1.0 },
false);
+            fail("x does not contain samples (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0 }, new double[] { },
true);
+            fail("y does not contain samples (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0 }, new double[] { },
false);
+            fail("y does not contain samples (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        /* Samples not same size, i.e. cannot be pairred
+         */
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0, 2.0 }, new double[]
{ 3.0 }, true);
+            fail("x and y not same size (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0, 2.0 }, new double[]
{ 3.0 }, false);
+            fail("x and y not same size (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        /*
+         * x and y is null
+         */
+        try {
+            testStatistic.wilcoxonSignedRankTest(null, null, true);
+            fail("x and y is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.wilcoxonSignedRankTest(null, null, false);
+            fail("x and y is null (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        /*
+         * x or y is null
+         */
+        try {
+            testStatistic.wilcoxonSignedRankTest(null, new double[] { 1.0 }, true);
+            fail("x is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.wilcoxonSignedRankTest(null, new double[] { 1.0 }, false);
+            fail("x is null (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0 }, null, true);
+            fail("y is null (exact), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+        
+        try {
+            testStatistic.wilcoxonSignedRankTest(new double[] { 1.0 }, null, false);
+            fail("y is null (asymptotic), IllegalArgumentException expected");
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+    }
+}



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