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* (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,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math.stat.inference;
import org.apache.commons.math.MathException;
import org.apache.commons.math.distribution.ChiSquaredDistribution;
import org.apache.commons.math.distribution.ChiSquaredDistributionImpl;
import org.apache.commons.math.distribution.DistributionFactory;
/**
* Implements Chi-Square test statistics defined in the
* {@link UnknownDistributionChiSquareTest} interface.
*
* @version $Revision$ $Date$
*/
public class ChiSquareTestImpl implements UnknownDistributionChiSquareTest {
/** Distribution used to compute inference statistics. */
private ChiSquaredDistribution distribution;
/**
* Construct a ChiSquareTestImpl
*/
public ChiSquareTestImpl() {
this(new ChiSquaredDistributionImpl(1.0));
}
/**
* Create a test instance using the given distribution for computing
* inference statistics.
* @param x distribution used to compute inference statistics.
* @since 1.2
*/
public ChiSquareTestImpl(ChiSquaredDistribution x) {
super();
setDistribution(x);
}
/**
* {@inheritDoc}
* Note: This implementation rescales the
* expected array if necessary to ensure that the sum of the
* expected and observed counts are equal.
*
* @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 {
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");
}
double sumExpected = 0d;
double sumObserved = 0d;
for (int i = 0; i < observed.length; i++) {
sumExpected += expected[i];
sumObserved += observed[i];
}
double ratio = 1.0d;
boolean rescale = false;
if (Math.abs(sumExpected - sumObserved) > 10E-6) {
ratio = sumObserved / sumExpected;
rescale = true;
}
double sumSq = 0.0d;
double dev = 0.0d;
for (int i = 0; i < observed.length; i++) {
if (rescale) {
dev = ((double) observed[i] - ratio * expected[i]);
sumSq += dev * dev / (ratio * expected[i]);
} else {
dev = ((double) observed[i] - expected[i]);
sumSq += dev * dev / expected[i];
}
}
return sumSq;
}
/**
* {@inheritDoc}
* Note: This implementation rescales the
* expected array if necessary to ensure that the sum of the
* expected and observed counts are equal.
*
* @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 {
distribution.setDegreesOfFreedom(expected.length - 1.0);
return 1.0 - distribution.cumulativeProbability(
chiSquare(expected, observed));
}
/**
* {@inheritDoc}
* Note: This implementation rescales the
* expected array if necessary to ensure that the sum of the
* expected and observed counts are equal.
*
* @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);
distribution.setDegreesOfFreedom(df);
return 1 - distribution.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);
}
/**
* @param observed1 array of observed frequency counts of the first data set
* @param observed2 array of observed frequency counts of the second data set
* @return chi-square test statistic
* @throws IllegalArgumentException if preconditions are not met
*/
public double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
throws IllegalArgumentException {
// Make sure lengths are same
if ((observed1.length < 2) || (observed1.length != observed2.length)) {
throw new IllegalArgumentException(
"oberved1, observed2 array lengths incorrect");
}
// Ensure non-negative counts
if (!isNonNegative(observed1) || !isNonNegative(observed2)) {
throw new IllegalArgumentException(
"observed counts must be non-negative");
}
// Compute and compare count sums
long countSum1 = 0;
long countSum2 = 0;
boolean unequalCounts = false;
double weight = 0.0;
for (int i = 0; i < observed1.length; i++) {
countSum1 += observed1[i];
countSum2 += observed2[i];
}
// Ensure neither sample is uniformly 0
if (countSum1 * countSum2 == 0) {
throw new IllegalArgumentException(
"observed counts cannot all be 0");
}
// Compare and compute weight only if different
unequalCounts = (countSum1 != countSum2);
if (unequalCounts) {
weight = Math.sqrt((double) countSum1 / (double) countSum2);
}
// Compute ChiSquare statistic
double sumSq = 0.0d;
double dev = 0.0d;
double obs1 = 0.0d;
double obs2 = 0.0d;
for (int i = 0; i < observed1.length; i++) {
if (observed1[i] == 0 && observed2[i] == 0) {
throw new IllegalArgumentException(
"observed counts must not both be zero");
} else {
obs1 = (double) observed1[i];
obs2 = (double) observed2[i];
if (unequalCounts) { // apply weights
dev = obs1/weight - obs2 * weight;
} else {
dev = obs1 - obs2;
}
sumSq += (dev * dev) / (obs1 + obs2);
}
}
return sumSq;
}
/**
* @param observed1 array of observed frequency counts of the first data set
* @param observed2 array of observed frequency counts of the second data set
* @return p-value
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs computing the p-value
*/
public double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
throws IllegalArgumentException, MathException {
distribution.setDegreesOfFreedom((double) observed1.length - 1);
return 1 - distribution.cumulativeProbability(
chiSquareDataSetsComparison(observed1, observed2));
}
/**
* @param observed1 array of observed frequency counts of the first data set
* @param observed2 array of observed frequency counts of the second data set
* @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 chiSquareTestDataSetsComparison(long[] observed1, long[] observed2,
double alpha) throws IllegalArgumentException, MathException {
if ((alpha <= 0) || (alpha > 0.5)) {
throw new IllegalArgumentException(
"bad significance level: " + alpha);
}
return (chiSquareTestDataSetsComparison(observed1, observed2) < 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.
* @deprecated inject ChiSquaredDistribution instances directly instead of
* using a factory.
*/
protected DistributionFactory getDistributionFactory() {
return DistributionFactory.newInstance();
}
//--------------------- 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;
}
/**
* Modify the distribution used to compute inference statistics.
*
* @param value
* the new distribution
* @since 1.2
*/
public void setDistribution(ChiSquaredDistribution value) {
distribution = value;
}
}