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
+ }
+ }
+}
