/*
* Copyright 2004 The Apache Software Foundation.
*
* Licensed 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.DistributionFactory;
import org.apache.commons.math.distribution.ChiSquaredDistribution;
/**
* Implements Chi-Square test statistics defined in the {@link ChiSquareTest} interface.
*
* @version $Revision: 155427 $ $Date: 2005-02-26 06:11:52 -0700 (Sat, 26 Feb 2005) $
*/
public class ChiSquareTestImpl implements ChiSquareTest {
/** Cached DistributionFactory used to create ChiSquaredDistribution instances */
private DistributionFactory distributionFactory = null;
/**
* Construct a ChiSquareTestImpl
*/
public ChiSquareTestImpl() {
super();
}
/**
* @param observed array of observed frequency counts
* @param expected array of expected frequency counts
* @return chi-square test statistic
* @throws IllegalArgumentException if preconditions are not met
* or length is less than 2
*/
public double chiSquare(double[] expected, long[] observed)
throws IllegalArgumentException {
double sumSq = 0.0d;
double dev = 0.0d;
if ((expected.length < 2) || (expected.length != observed.length)) {
throw new IllegalArgumentException(
"observed, expected array lengths incorrect");
}
if (!isPositive(expected) || !isNonNegative(observed)) {
throw new IllegalArgumentException(
"observed counts must be non-negative and expected counts must be postive");
}
for (int i = 0; i < observed.length; i++) {
dev = ((double) observed[i] - expected[i]);
sumSq += dev * dev / expected[i];
}
return sumSq;
}
/**
* @param observed array of observed frequency counts
* @param expected array of exptected frequency counts
* @return p-value
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs computing the p-value
*/
public double chiSquareTest(double[] expected, long[] observed)
throws IllegalArgumentException, MathException {
ChiSquaredDistribution chiSquaredDistribution =
getDistributionFactory().createChiSquareDistribution(
(double) expected.length - 1);
return 1 - chiSquaredDistribution.cumulativeProbability(
chiSquare(expected, observed));
}
/**
* @param observed array of observed frequency counts
* @param expected array of exptected frequency counts
* @param alpha significance level of the test
* @return true iff null hypothesis can be rejected with confidence
* 1 - alpha
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs performing the test
*/
public boolean chiSquareTest(double[] expected, long[] observed,
double alpha) throws IllegalArgumentException, MathException {
if ((alpha <= 0) || (alpha > 0.5)) {
throw new IllegalArgumentException(
"bad significance level: " + alpha);
}
return (chiSquareTest(expected, observed) < alpha);
}
/**
* @param counts array representation of 2-way table
* @return chi-square test statistic
* @throws IllegalArgumentException if preconditions are not met
*/
public double chiSquare(long[][] counts) throws IllegalArgumentException {
checkArray(counts);
int nRows = counts.length;
int nCols = counts[0].length;
// compute row, column and total sums
double[] rowSum = new double[nRows];
double[] colSum = new double[nCols];
double total = 0.0d;
for (int row = 0; row < nRows; row++) {
for (int col = 0; col < nCols; col++) {
rowSum[row] += (double) counts[row][col];
colSum[col] += (double) counts[row][col];
total += (double) counts[row][col];
}
}
// compute expected counts and chi-square
double sumSq = 0.0d;
double expected = 0.0d;
for (int row = 0; row < nRows; row++) {
for (int col = 0; col < nCols; col++) {
expected = (rowSum[row] * colSum[col]) / total;
sumSq += (((double) counts[row][col] - expected) *
((double) counts[row][col] - expected)) / expected;
}
}
return sumSq;
}
/**
* @param counts array representation of 2-way table
* @return p-value
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs computing the p-value
*/
public double chiSquareTest(long[][] counts)
throws IllegalArgumentException, MathException {
checkArray(counts);
double df = ((double) counts.length -1) * ((double) counts[0].length - 1);
ChiSquaredDistribution chiSquaredDistribution =
getDistributionFactory().createChiSquareDistribution(df);
return 1 - chiSquaredDistribution.cumulativeProbability(chiSquare(counts));
}
/**
* @param counts array representation of 2-way table
* @param alpha significance level of the test
* @return true iff null hypothesis can be rejected with confidence
* 1 - alpha
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs performing the test
*/
public boolean chiSquareTest(long[][] counts, double alpha)
throws IllegalArgumentException, MathException {
if ((alpha <= 0) || (alpha > 0.5)) {
throw new IllegalArgumentException("bad significance level: " + alpha);
}
return (chiSquareTest(counts) < alpha);
}
/**
* Checks to make sure that the input long[][] array is rectangular,
* has at least 2 rows and 2 columns, and has all non-negative entries,
* throwing IllegalArgumentException if any of these checks fail.
*
* @param in input 2-way table to check
* @throws IllegalArgumentException if the array is not valid
*/
private void checkArray(long[][] in) throws IllegalArgumentException {
if (in.length < 2) {
throw new IllegalArgumentException("Input table must have at least two rows");
}
if (in[0].length < 2) {
throw new IllegalArgumentException("Input table must have at least two columns");
}
if (!isRectangular(in)) {
throw new IllegalArgumentException("Input table must be rectangular");
}
if (!isNonNegative(in)) {
throw new IllegalArgumentException("All entries in input 2-way table must be non-negative");
}
}
//--------------------- Protected methods ---------------------------------
/**
* Gets a DistributionFactory to use in creating ChiSquaredDistribution instances.
*
* @return a DistributionFactory
*/
protected DistributionFactory getDistributionFactory() {
if (distributionFactory == null) {
distributionFactory = DistributionFactory.newInstance();
}
return distributionFactory;
}
//--------------------- Private array methods -- should find a utility home for these
/**
* Returns true iff input array is rectangular.
*
* @param in array to be tested
* @return true if the array is rectangular
* @throws NullPointerException if input array is null
* @throws ArrayIndexOutOfBoundsException if input array is empty
*/
private boolean isRectangular(long[][] in) {
for (int i = 1; i < in.length; i++) {
if (in[i].length != in[0].length) {
return false;
}
}
return true;
}
/**
* Returns true iff all entries of the input array are > 0.
* Returns true if the array is non-null, but empty
*
* @param in array to be tested
* @return true if all entries of the array are positive
* @throws NullPointerException if input array is null
*/
private boolean isPositive(double[] in) {
for (int i = 0; i < in.length; i ++) {
if (in[i] <= 0) {
return false;
}
}
return true;
}
/**
* Returns true iff all entries of the input array are >= 0.
* Returns true if the array is non-null, but empty
*
* @param in array to be tested
* @return true if all entries of the array are non-negative
* @throws NullPointerException if input array is null
*/
private boolean isNonNegative(long[] in) {
for (int i = 0; i < in.length; i ++) {
if (in[i] < 0) {
return false;
}
}
return true;
}
/**
* Returns true iff all entries of (all subarrays of) the input array are >= 0.
* Returns true if the array is non-null, but empty
*
* @param in array to be tested
* @return true if all entries of the array are non-negative
* @throws NullPointerException if input array is null
*/
private boolean isNonNegative(long[][] in) {
for (int i = 0; i < in.length; i ++) {
for (int j = 0; j < in[i].length; j++) {
if (in[i][j] < 0) {
return false;
}
}
}
return true;
}
}