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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.
* Two samples tests are used when the distribution is unknown a priori
* but provided by one sample. We compare the second sample against the first.
*
* @version $Revision: 670469 $ $Date: 2008-06-23 04:01:38 -0400 (Mon, 23 Jun 2008) $
* @since 1.2
*/
public interface UnknownDistributionChiSquareTest extends ChiSquareTest {
/**
* Computes a
*
* Chi-Square two sample test statistic comparing bin frequency counts
* in observed1 and observed2. 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
*
* ∑[(K * observed1[i] - observed2[i]/K)2 / (observed1[i] + observed2[i])]
* where
*
K = &sqrt;[&sum(observed2 / ∑(observed1)]
*
* This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that
* both observed counts follow the same distribution.
*
* Preconditions:
* - Observed counts must be non-negative.
*
* - Observed counts for a specific bin must not both be zero.
*
* - Observed counts for a specific sample must not all be 0.
*
* - The arrays
observed1 and observed2 must have the same length and
* their common length must be at least 2.
*
* If any of the preconditions are not met, an
* IllegalArgumentException is thrown.
*
* @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;
/**
* Returns the observed significance level, or
* p-value, associated with a Chi-Square two sample test comparing
* bin frequency counts in observed1 and
* observed2.
*
* 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.
*
* 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.
*
* Preconditions:
* - Observed counts must be non-negative.
*
* - Observed counts for a specific bin must not both be zero.
*
* - Observed counts for a specific sample must not all be 0.
*
* - The arrays
observed1 and observed2 must
* have the same length and
* their common length must be at least 2.
*
* If any of the preconditions are not met, an
* IllegalArgumentException is thrown.
*
* @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;
/**
* 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 alpha. Returns true iff the null
* hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
*
* 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.
*
* Preconditions:
* - Observed counts must be non-negative.
*
* - Observed counts for a specific bin must not both be zero.
*
* - Observed counts for a specific sample must not all be 0.
*
* - The arrays
observed1 and observed2 must
* have the same length and their common length must be at least 2.
*
* -
0 < alpha < 0.5
*
* If any of the preconditions are not met, an
* IllegalArgumentException is thrown.
*
* @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;
}