| /* |
| * 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; |
| |
| } |
