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/*
* 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 for unknown distributions.
* <p>Two samples tests are used when the distribution is unknown <i>a priori</i>
* but provided by one sample. We compare the second sample against the first.</p>
*
* @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
* @since 1.2
*/
public interface UnknownDistributionChiSquareTest extends ChiSquareTest {
/**
* <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</code> and <code>observed2</code>. 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</sup> / (observed1[i] + observed2[i])]
* </code> where
* <br/><code>K = &sqrt;[&sum(observed2 / ∑(observed1)]</code>
* </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</strong>: <ul>
* <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 <code>observed1</code> and <code>observed2</code> 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 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 statistic
* @throws IllegalArgumentException if preconditions are not met
*/
double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
throws IllegalArgumentException;
/**
* <p>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 Chi-Square two sample test comparing
* bin frequency counts in <code>observed1</code> and
* <code>observed2</code>.
* </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</strong>: <ul>
* <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 <code>observed1</code> and <code>observed2</code> must
* have the same length and
* their common length must be at least 2.
* </li></ul><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @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
*/
double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
throws IllegalArgumentException, MathException;
/**
* <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</code>. 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</strong>: <ul>
* <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 <code>observed1</code> and <code>observed2</code> must
* have the same length and their common length must be at least 2.
* </li>
* <li> <code> 0 < alpha < 0.5 </code>
* </li></ul><p>
* If any of the preconditions are not met, an
* <code>IllegalArgumentException</code> is thrown.</p>
*
* @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
*/
boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
throws IllegalArgumentException, MathException;
}
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