/*
* 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 Chi-Square tests.
* <p>This interface handles only known distributions. If the distribution is
* unknown and should be provided by a sample, then the {@link UnknownDistributionChiSquareTest
* UnknownDistributionChiSquareTest} extended interface should be used instead.</p>
* @version $Id: ChiSquareTest.java 1131229 2011-06-03 20:49:25Z luc $
*/
public interface ChiSquareTest {
/**
* Computes the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm">
* Chi-Square statistic</a> comparing <code>observed</code> and <code>expected</code>
* 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</strong>: <ul>
* <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></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @param observed array of observed frequency counts
* @param expected array of expected frequency counts
* @return chiSquare statistic
* @throws IllegalArgumentException if preconditions are not met
*/
double chiSquare(double[] expected, long[] observed)
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://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm">
* Chi-square goodness of fit test</a> comparing the <code>observed</code>
* frequency counts to those in the <code>expected</code> 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</strong>: <ul>
* <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></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @param observed array of observed frequency counts
* @param expected array of expected frequency counts
* @return p-value
* @throws IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs computing the p-value
*/
double chiSquareTest(double[] expected, long[] observed)
throws IllegalArgumentException, MathException;
/**
* 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</code>. Returns true iff the null hypothesis can be rejected
* with 100 * (1 - alpha) percent confidence.
* <p>
* <strong>Example:</strong><br>
* To test the hypothesis that <code>observed</code> follows
* <code>expected</code> at the 99% level, use </p><p>
* <code>chiSquareTest(expected, observed, 0.01) </code></p>
* <p>
* <strong>Preconditions</strong>: <ul>
* <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> <code> 0 < alpha < 0.5 </code>
* </li></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</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 IllegalArgumentException if preconditions are not met
* @throws MathException if an error occurs performing the test
*/
boolean chiSquareTest(double[] expected, long[] observed, double alpha)
throws IllegalArgumentException, MathException;
/**
* 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 <code>counts</code>
* array, viewed as a two-way table.
* <p>
* The rows of the 2-way table are
* <code>count[0], ... , count[count.length - 1] </code></p>
* <p>
* <strong>Preconditions</strong>: <ul>
* <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 <code>counts</code> must have at
* least 2 columns and at least 2 rows.
* </li>
* </li></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @param counts array representation of 2-way table
* @return chiSquare statistic
* @throws IllegalArgumentException if preconditions are not met
*/
double chiSquare(long[][] counts)
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://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm">
* chi-square test of independence</a> based on the input <code>counts</code>
* array, viewed as a two-way table.
* <p>
* The rows of the 2-way table are
* <code>count[0], ... , count[count.length - 1] </code></p>
* <p>
* <strong>Preconditions</strong>: <ul>
* <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 <code>counts</code> must have at least 2 columns and
* at least 2 rows.
* </li>
* </li></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @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
*/
double chiSquareTest(long[][] counts)
throws IllegalArgumentException, MathException;
/**
* 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</code>. 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] </code></p>
* <p>
* <strong>Example:</strong><br>
* To test the null hypothesis that the counts in
* <code>count[0], ... , count[count.length - 1] </code>
* all correspond to the same underlying probability distribution at the 99% level, use </p><p>
* <code>chiSquareTest(counts, 0.01) </code></p>
* <p>
* <strong>Preconditions</strong>: <ul>
* <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 <code>counts</code> must have at least 2 columns and
* at least 2 rows.
* </li>
* </li></ul></p><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @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
*/
boolean chiSquareTest(long[][] counts, double alpha)
throws IllegalArgumentException, MathException;
}