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Diffstat (limited to 'src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java')
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diff --git a/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java b/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java new file mode 100644 index 0000000..662e4d6 --- /dev/null +++ b/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java @@ -0,0 +1,144 @@ +/* + * 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; + +} |