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Java example source code file (ChiSquareTest.java)

This example Java source code file (ChiSquareTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

chisquareddistribution, chisquaretest, dimensionmismatchexception, maxcountexceededexception, notpositiveexception, notstrictlypositiveexception, nullargumentexception, outofrangeexception, zeroexception

The ChiSquareTest.java Java example source code

/*
 * 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
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 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
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package org.apache.commons.math3.stat.inference;

import org.apache.commons.math3.distribution.ChiSquaredDistribution;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NotPositiveException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.ZeroException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;

/**
 * Implements Chi-Square test statistics.
 *
 * <p>This implementation handles both known and unknown distributions.

* * <p>Two samples tests can be used when the distribution is unknown a priori * but provided by one sample, or when the hypothesis under test is that the two * samples come from the same underlying distribution.</p> * */ public class ChiSquareTest { /** * Construct a ChiSquareTest */ public ChiSquareTest() { super(); } /** * Computes the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> * Chi-Square statistic</a> comparing observed and expected * frequency counts. * <p> * This statistic can be used to perform a Chi-Square test evaluating the null * hypothesis that the observed counts follow the expected distribution.</p> * <p> * <strong>Preconditions:
    * <li>Expected counts must all be positive. * </li> * <li>Observed counts must all be ≥ 0. * </li> * <li>The observed and expected arrays must have the same length and * their common length must be at least 2. * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* <p>Note: This implementation rescales the * <code>expected array if necessary to ensure that the sum of the * expected and observed counts are equal.</p> * * @param observed array of observed frequency counts * @param expected array of expected frequency counts * @return chiSquare test statistic * @throws NotPositiveException if <code>observed has negative entries * @throws NotStrictlyPositiveException if <code>expected has entries that are * not strictly positive * @throws DimensionMismatchException if the arrays length is less than 2 */ public double chiSquare(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException { if (expected.length < 2) { throw new DimensionMismatchException(expected.length, 2); } if (expected.length != observed.length) { throw new DimensionMismatchException(expected.length, observed.length); } MathArrays.checkPositive(expected); MathArrays.checkNonNegative(observed); 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 (FastMath.abs(sumExpected - sumObserved) > 10E-6) { ratio = sumObserved / sumExpected; rescale = true; } double sumSq = 0.0d; for (int i = 0; i < observed.length; i++) { if (rescale) { final double dev = observed[i] - ratio * expected[i]; sumSq += dev * dev / (ratio * expected[i]); } else { final double dev = observed[i] - expected[i]; sumSq += dev * dev / expected[i]; } } return sumSq; } /** * Returns the <i>observed significance level, or observed * frequency counts to those in the <code>expected array. * <p> * The number returned is the smallest significance level at which one can reject * the null hypothesis that the observed counts conform to the frequency distribution * described by the expected counts.</p> * <p> * <strong>Preconditions:
    * <li>Expected counts must all be positive. * </li> * <li>Observed counts must all be ≥ 0. * </li> * <li>The observed and expected arrays must have the same length and * their common length must be at least 2. * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* <p>Note: This implementation rescales the * <code>expected array if necessary to ensure that the sum of the * expected and observed counts are equal.</p> * * @param observed array of observed frequency counts * @param expected array of expected frequency counts * @return p-value * @throws NotPositiveException if <code>observed has negative entries * @throws NotStrictlyPositiveException if <code>expected has entries that are * not strictly positive * @throws DimensionMismatchException if the arrays length is less than 2 * @throws MaxCountExceededException if an error occurs computing the p-value */ public double chiSquareTest(final double[] expected, final long[] observed) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, MaxCountExceededException { // pass a null rng to avoid unneeded overhead as we will not sample from this distribution final ChiSquaredDistribution distribution = new ChiSquaredDistribution(null, expected.length - 1.0); return 1.0 - distribution.cumulativeProbability(chiSquare(expected, observed)); } /** * Performs a <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"> * Chi-square goodness of fit test</a> evaluating the null hypothesis that the * observed counts conform to the frequency distribution described by the expected * counts, with significance level <code>alpha. Returns true iff the null * hypothesis can be rejected with 100 * (1 - alpha) percent confidence. * <p> * <strong>Example:
* To test the hypothesis that <code>observed follows * <code>expected at the 99% level, use

* <code>chiSquareTest(expected, observed, 0.01)

* <p> * <strong>Preconditions:
    * <li>Expected counts must all be positive. * </li> * <li>Observed counts must all be ≥ 0. * </li> * <li>The observed and expected arrays must have the same length and * their common length must be at least 2. * <li> 0 < alpha < 0.5 * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* <p>Note: This implementation rescales the * <code>expected array if necessary to ensure that the sum of the * expected and observed counts are equal.</p> * * @param observed array of observed frequency counts * @param expected array of expected frequency counts * @param alpha significance level of the test * @return true iff null hypothesis can be rejected with confidence * 1 - alpha * @throws NotPositiveException if <code>observed has negative entries * @throws NotStrictlyPositiveException if <code>expected has entries that are * not strictly positive * @throws DimensionMismatchException if the arrays length is less than 2 * @throws OutOfRangeException if <code>alpha is not in the range (0, 0.5] * @throws MaxCountExceededException if an error occurs computing the p-value */ public boolean chiSquareTest(final double[] expected, final long[] observed, final double alpha) throws NotPositiveException, NotStrictlyPositiveException, DimensionMismatchException, OutOfRangeException, MaxCountExceededException { if ((alpha <= 0) || (alpha > 0.5)) { throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, alpha, 0, 0.5); } return chiSquareTest(expected, observed) < alpha; } /** * Computes the Chi-Square statistic associated with a * <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> * chi-square test of independence</a> based on the input counts * array, viewed as a two-way table. * <p> * The rows of the 2-way table are * <code>count[0], ... , count[count.length - 1]

* <p> * <strong>Preconditions:
    * <li>All counts must be ≥ 0. * </li> * <li>The count array must be rectangular (i.e. all count[i] subarrays * must have the same length). * </li> * <li>The 2-way table represented by counts must have at * least 2 columns and at least 2 rows. * </li> * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @param counts array representation of 2-way table * @return chiSquare test statistic * @throws NullArgumentException if the array is null * @throws DimensionMismatchException if the array is not rectangular * @throws NotPositiveException if {@code counts} has negative entries */ public double chiSquare(final long[][] counts) throws NullArgumentException, NotPositiveException, DimensionMismatchException { 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] += counts[row][col]; colSum[col] += counts[row][col]; total += 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 += ((counts[row][col] - expected) * (counts[row][col] - expected)) / expected; } } return sumSq; } /** * Returns the <i>observed significance level, or
counts * array, viewed as a two-way table. * <p> * The rows of the 2-way table are * <code>count[0], ... , count[count.length - 1]

* <p> * <strong>Preconditions:
    * <li>All counts must be ≥ 0. * </li> * <li>The count array must be rectangular (i.e. all count[i] subarrays must have * the same length). * </li> * <li>The 2-way table represented by counts must have at least 2 * columns and at least 2 rows. * </li> * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @param counts array representation of 2-way table * @return p-value * @throws NullArgumentException if the array is null * @throws DimensionMismatchException if the array is not rectangular * @throws NotPositiveException if {@code counts} has negative entries * @throws MaxCountExceededException if an error occurs computing the p-value */ public double chiSquareTest(final long[][] counts) throws NullArgumentException, DimensionMismatchException, NotPositiveException, MaxCountExceededException { checkArray(counts); double df = ((double) counts.length -1) * ((double) counts[0].length - 1); // pass a null rng to avoid unneeded overhead as we will not sample from this distribution final ChiSquaredDistribution distribution = new ChiSquaredDistribution(df); return 1 - distribution.cumulativeProbability(chiSquare(counts)); } /** * Performs a <a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"> * chi-square test of independence</a> evaluating the null hypothesis that the * classifications represented by the counts in the columns of the input 2-way table * are independent of the rows, with significance level <code>alpha. * Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent * confidence. * <p> * The rows of the 2-way table are * <code>count[0], ... , count[count.length - 1]

* <p> * <strong>Example:
* To test the null hypothesis that the counts in * <code>count[0], ... , count[count.length - 1] * all correspond to the same underlying probability distribution at the 99% level, use</p> * <p>chiSquareTest(counts, 0.01)

* <p> * <strong>Preconditions:
    * <li>All counts must be ≥ 0. * </li> * <li>The count array must be rectangular (i.e. all count[i] subarrays must have the * same length).</li> * <li>The 2-way table represented by counts must have at least 2 columns and * at least 2 rows.</li> * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @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 NullArgumentException if the array is null * @throws DimensionMismatchException if the array is not rectangular * @throws NotPositiveException if {@code counts} has any negative entries * @throws OutOfRangeException if <code>alpha is not in the range (0, 0.5] * @throws MaxCountExceededException if an error occurs computing the p-value */ public boolean chiSquareTest(final long[][] counts, final double alpha) throws NullArgumentException, DimensionMismatchException, NotPositiveException, OutOfRangeException, MaxCountExceededException { if ((alpha <= 0) || (alpha > 0.5)) { throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, alpha, 0, 0.5); } return chiSquareTest(counts) < alpha; } /** * <p>Computes a * <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"> * Chi-Square two sample test statistic</a> comparing bin frequency counts * in <code>observed1 and observed2. The * sums of frequency counts in the two samples are not required to be the * same. The formula used to compute the test statistic is</p> * <code> * ∑[(K * observed1[i] - observed2[i]/K)<sup>2 / (observed1[i] + observed2[i])] * </code> where * <br/>K = &sqrt;[&sum(observed2 / ∑(observed1)] * </p> * <p>This statistic can be used to perform a Chi-Square test evaluating the * null hypothesis that both observed counts follow the same distribution.</p> * <p> * <strong>Preconditions:
    * <li>Observed counts must be non-negative. * </li> * <li>Observed counts for a specific bin must not both be zero. * </li> * <li>Observed counts for a specific sample must not all be 0. * </li> * <li>The arrays observed1 and observed2 must have * the same length and their common length must be at least 2. * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @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 chiSquare test statistic * @throws DimensionMismatchException the the length of the arrays does not match * @throws NotPositiveException if any entries in <code>observed1 or * <code>observed2 are negative * @throws ZeroException if either all counts of <code>observed1 or * <code>observed2 are zero, or if the count at some index is zero * for both arrays * @since 1.2 */ public double chiSquareDataSetsComparison(long[] observed1, long[] observed2) throws DimensionMismatchException, NotPositiveException, ZeroException { // Make sure lengths are same if (observed1.length < 2) { throw new DimensionMismatchException(observed1.length, 2); } if (observed1.length != observed2.length) { throw new DimensionMismatchException(observed1.length, observed2.length); } // Ensure non-negative counts MathArrays.checkNonNegative(observed1); MathArrays.checkNonNegative(observed2); // 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 == 0 || countSum2 == 0) { throw new ZeroException(); } // Compare and compute weight only if different unequalCounts = countSum1 != countSum2; if (unequalCounts) { weight = FastMath.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 ZeroException(LocalizedFormats.OBSERVED_COUNTS_BOTTH_ZERO_FOR_ENTRY, i); } else { obs1 = observed1[i]; obs2 = observed2[i]; if (unequalCounts) { // apply weights dev = obs1/weight - obs2 * weight; } else { dev = obs1 - obs2; } sumSq += (dev * dev) / (obs1 + obs2); } } return sumSq; } /** * <p>Returns the observed significance level, or
and * <code>observed2. * </p> * <p>The number returned is the smallest significance level at which one * can reject the null hypothesis that the observed counts conform to the * same distribution. * </p> * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for details * on the formula used to compute the test statistic. The degrees of * of freedom used to perform the test is one less than the common length * of the input observed count arrays. * </p> * <strong>Preconditions:
    * <li>Observed counts must be non-negative. * </li> * <li>Observed counts for a specific bin must not both be zero. * </li> * <li>Observed counts for a specific sample must not all be 0. * </li> * <li>The arrays observed1 and observed2 must * have the same length and * their common length must be at least 2. * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @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 DimensionMismatchException the the length of the arrays does not match * @throws NotPositiveException if any entries in <code>observed1 or * <code>observed2 are negative * @throws ZeroException if either all counts of <code>observed1 or * <code>observed2 are zero, or if the count at the same index is zero * for both arrays * @throws MaxCountExceededException if an error occurs computing the p-value * @since 1.2 */ public double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2) throws DimensionMismatchException, NotPositiveException, ZeroException, MaxCountExceededException { // pass a null rng to avoid unneeded overhead as we will not sample from this distribution final ChiSquaredDistribution distribution = new ChiSquaredDistribution(null, (double) observed1.length - 1); return 1 - distribution.cumulativeProbability( chiSquareDataSetsComparison(observed1, observed2)); } /** * <p>Performs a Chi-Square two sample test comparing two binned data * sets. The test evaluates the null hypothesis that the two lists of * observed counts conform to the same frequency distribution, with * significance level <code>alpha. Returns true iff the null * hypothesis can be rejected with 100 * (1 - alpha) percent confidence. * </p> * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for * details on the formula used to compute the Chisquare statistic used * in the test. The degrees of of freedom used to perform the test is * one less than the common length of the input observed count arrays. * </p> * <strong>Preconditions:
    * <li>Observed counts must be non-negative. * </li> * <li>Observed counts for a specific bin must not both be zero. * </li> * <li>Observed counts for a specific sample must not all be 0. * </li> * <li>The arrays observed1 and observed2 must * have the same length and their common length must be at least 2. * </li> * <li> 0 < alpha < 0.5 * </li>

* If any of the preconditions are not met, an * <code>IllegalArgumentException is thrown.

* * @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 DimensionMismatchException the the length of the arrays does not match * @throws NotPositiveException if any entries in <code>observed1 or * <code>observed2 are negative * @throws ZeroException if either all counts of <code>observed1 or * <code>observed2 are zero, or if the count at the same index is zero * for both arrays * @throws OutOfRangeException if <code>alpha is not in the range (0, 0.5] * @throws MaxCountExceededException if an error occurs performing the test * @since 1.2 */ public boolean chiSquareTestDataSetsComparison(final long[] observed1, final long[] observed2, final double alpha) throws DimensionMismatchException, NotPositiveException, ZeroException, OutOfRangeException, MaxCountExceededException { if (alpha <= 0 || alpha > 0.5) { throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL, alpha, 0, 0.5); } 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. * * @param in input 2-way table to check * @throws NullArgumentException if the array is null * @throws DimensionMismatchException if the array is not valid * @throws NotPositiveException if the array contains any negative entries */ private void checkArray(final long[][] in) throws NullArgumentException, DimensionMismatchException, NotPositiveException { if (in.length < 2) { throw new DimensionMismatchException(in.length, 2); } if (in[0].length < 2) { throw new DimensionMismatchException(in[0].length, 2); } MathArrays.checkRectangular(in); MathArrays.checkNonNegative(in); } }


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