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    1   /*
    2    * Copyright 2004 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16  package org.apache.commons.math.stat.inference;
    17
    18  import org.apache.commons.math.MathException;
    19  import org.apache.commons.math.distribution.DistributionFactory;
    20  import org.apache.commons.math.distribution.ChiSquaredDistribution;
    21
    22  /***
    23   * Implements Chi-Square test statistics defined in the {@link ChiSquareTest} interface.
    24   *
    25   * @version $Revision: 155427 $ $Date: 2005-02-26 06:11:52 -0700 (Sat, 26 Feb 2005) $
    26   */
    27  public class ChiSquareTestImpl implements ChiSquareTest {
    28
    29      /*** Cached DistributionFactory used to create ChiSquaredDistribution instances */
    30      private DistributionFactory distributionFactory = null;
    31
    32      /***
    33       * Construct a ChiSquareTestImpl
    34       */
    35      public ChiSquareTestImpl() {
    36          super();
    37      }
    38
    39       /***
    40       * @param observed array of observed frequency counts
    41       * @param expected array of expected frequency counts
    42       * @return chi-square test statistic
    43       * @throws IllegalArgumentException if preconditions are not met
    44       * or length is less than 2
    45       */
    46      public double chiSquare(double[] expected, long[] observed)
    47          throws IllegalArgumentException {
    48          double sumSq = 0.0d;
    49          double dev = 0.0d;
    50          if ((expected.length < 2) || (expected.length != observed.length)) {
    51              throw new IllegalArgumentException(
    52                      "observed, expected array lengths incorrect");
    53          }
    54          if (!isPositive(expected) || !isNonNegative(observed)) {
    55              throw new IllegalArgumentException(
    56                  "observed counts must be non-negative and expected counts must be postive");
    57          }
    58          for (int i = 0; i < observed.length; i++) {
    59              dev = ((double) observed[i] - expected[i]);
    60              sumSq += dev * dev / expected[i];
    61          }
    62          return sumSq;
    63      }
    64
    65      /***
    66       * @param observed array of observed frequency counts
    67       * @param expected array of exptected frequency counts
    68       * @return p-value
    69       * @throws IllegalArgumentException if preconditions are not met
    70       * @throws MathException if an error occurs computing the p-value
    71       */
    72      public double chiSquareTest(double[] expected, long[] observed)
    73          throws IllegalArgumentException, MathException {
    74          ChiSquaredDistribution chiSquaredDistribution =
    75              getDistributionFactory().createChiSquareDistribution(
    76                      (double) expected.length - 1);
    77          return 1 - chiSquaredDistribution.cumulativeProbability(
    78                  chiSquare(expected, observed));
    79      }
    80
    81      /***
    82       * @param observed array of observed frequency counts
    83       * @param expected array of exptected frequency counts
    84       * @param alpha significance level of the test
    85       * @return true iff null hypothesis can be rejected with confidence
    86       * 1 - alpha
    87       * @throws IllegalArgumentException if preconditions are not met
    88       * @throws MathException if an error occurs performing the test
    89       */
    90      public boolean chiSquareTest(double[] expected, long[] observed,
    91              double alpha) throws IllegalArgumentException, MathException {
    92          if ((alpha <= 0) || (alpha > 0.5)) {
    93              throw new IllegalArgumentException(
    94                      "bad significance level: " + alpha);
    95          }
    96          return (chiSquareTest(expected, observed) < alpha);
    97      }
    98
    99      /***
    100      * @param counts array representation of 2-way table
    101      * @return chi-square test statistic
    102      * @throws IllegalArgumentException if preconditions are not met
    103      */
    104     public double chiSquare(long[][] counts) throws IllegalArgumentException {
    105
    106         checkArray(counts);
    107         int nRows = counts.length;
    108         int nCols = counts[0].length;
    109
    110         // compute row, column and total sums
    111         double[] rowSum = new double[nRows];
    112         double[] colSum = new double[nCols];
    113         double total = 0.0d;
    114         for (int row = 0; row < nRows; row++) {
    115             for (int col = 0; col < nCols; col++) {
    116                 rowSum[row] += (double) counts[row][col];
    117                 colSum[col] += (double) counts[row][col];
    118                 total += (double) counts[row][col];
    119             }
    120         }
    121
    122         // compute expected counts and chi-square
    123         double sumSq = 0.0d;
    124         double expected = 0.0d;
    125         for (int row = 0; row < nRows; row++) {
    126             for (int col = 0; col < nCols; col++) {
    127                 expected = (rowSum[row] * colSum[col]) / total;
    128                 sumSq += (((double) counts[row][col] - expected) *
    129                         ((double) counts[row][col] - expected)) / expected;
    130             }
    131         }
    132         return sumSq;
    133     }
    134
    135     /***
    136      * @param counts array representation of 2-way table
    137      * @return p-value
    138      * @throws IllegalArgumentException if preconditions are not met
    139      * @throws MathException if an error occurs computing the p-value
    140      */
    141     public double chiSquareTest(long[][] counts)
    142     throws IllegalArgumentException, MathException {
    143         checkArray(counts);
    144         double df = ((double) counts.length -1) * ((double) counts[0].length - 1);
    145         ChiSquaredDistribution chiSquaredDistribution =
    146             getDistributionFactory().createChiSquareDistribution(df);
    147         return 1 - chiSquaredDistribution.cumulativeProbability(chiSquare(counts));
    148     }
    149
    150     /***
    151      * @param counts array representation of 2-way table
    152      * @param alpha significance level of the test
    153      * @return true iff null hypothesis can be rejected with confidence
    154      * 1 - alpha
    155      * @throws IllegalArgumentException if preconditions are not met
    156      * @throws MathException if an error occurs performing the test
    157      */
    158     public boolean chiSquareTest(long[][] counts, double alpha)
    159     throws IllegalArgumentException, MathException {
    160         if ((alpha <= 0) || (alpha > 0.5)) {
    161             throw new IllegalArgumentException("bad significance level: " + alpha);
    162         }
    163         return (chiSquareTest(counts) < alpha);
    164     }
    165
    166     /***
    167      * Checks to make sure that the input long[][] array is rectangular,
    168      * has at least 2 rows and 2 columns, and has all non-negative entries,
    169      * throwing IllegalArgumentException if any of these checks fail.
    170      *
    171      * @param in input 2-way table to check
    172      * @throws IllegalArgumentException if the array is not valid
    173      */
    174     private void checkArray(long[][] in) throws IllegalArgumentException {
    175
    176         if (in.length < 2) {
    177             throw new IllegalArgumentException("Input table must have at least two rows");
    178         }
    179
    180         if (in[0].length < 2) {
    181             throw new IllegalArgumentException("Input table must have at least two columns");
    182         }
    183
    184         if (!isRectangular(in)) {
    185             throw new IllegalArgumentException("Input table must be rectangular");
    186         }
    187
    188         if (!isNonNegative(in)) {
    189             throw new IllegalArgumentException("All entries in input 2-way table must be non-negative");
    190         }
    191
    192     }
    193
    194     //---------------------  Protected methods ---------------------------------
    195     /***
    196      * Gets a DistributionFactory to use in creating ChiSquaredDistribution instances.
    197      *
    198      * @return a DistributionFactory
    199      */
    200     protected DistributionFactory getDistributionFactory() {
    201         if (distributionFactory == null) {
    202             distributionFactory = DistributionFactory.newInstance();
    203         }
    204         return distributionFactory;
    205     }
    206
    207     //---------------------  Private array methods -- should find a utility home for these
    208
    209     /***
    210      * Returns true iff input array is rectangular.
    211      *
    212      * @param in array to be tested
    213      * @return true if the array is rectangular
    214      * @throws NullPointerException if input array is null
    215      * @throws ArrayIndexOutOfBoundsException if input array is empty
    216      */
    217     private boolean isRectangular(long[][] in) {
    218         for (int i = 1; i < in.length; i++) {
    219             if (in[i].length != in[0].length) {
    220                 return false;
    221             }
    222         }
    223         return true;
    224     }
    225
    226     /***
    227      * Returns true iff all entries of the input array are > 0.
    228      * Returns true if the array is non-null, but empty
    229      *
    230      * @param in array to be tested
    231      * @return true if all entries of the array are positive
    232      * @throws NullPointerException if input array is null
    233      */
    234     private boolean isPositive(double[] in) {
    235         for (int i = 0; i < in.length; i ++) {
    236             if (in[i] <= 0) {
    237                 return false;
    238             }
    239         }
    240         return true;
    241     }
    242
    243     /***
    244      * Returns true iff all entries of the input array are >= 0.
    245      * Returns true if the array is non-null, but empty
    246      *
    247      * @param in array to be tested
    248      * @return true if all entries of the array are non-negative
    249      * @throws NullPointerException if input array is null
    250      */
    251     private boolean isNonNegative(long[] in) {
    252         for (int i = 0; i < in.length; i ++) {
    253             if (in[i] < 0) {
    254                 return false;
    255             }
    256         }
    257         return true;
    258     }
    259
    260     /***
    261      * Returns true iff all entries of (all subarrays of) the input array are >= 0.
    262      * Returns true if the array is non-null, but empty
    263      *
    264      * @param in array to be tested
    265      * @return true if all entries of the array are non-negative
    266      * @throws NullPointerException if input array is null
    267      */
    268     private boolean isNonNegative(long[][] in) {
    269         for (int i = 0; i < in.length; i ++) {
    270             for (int j = 0; j < in[i].length; j++) {
    271                 if (in[i][j] < 0) {
    272                     return false;
    273                 }
    274             }
    275         }
    276         return true;
    277     }
    278
    279 }