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Commons Math example source code file (TTest.java)

This example Commons Math source code file (TTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Java - Commons Math tags/keywords

illegalargumentexception, illegalargumentexception, mathexception, mathexception, statisticalsummary, statisticalsummary, ttest, ttest

The Commons Math TTest.java source code

/*
 * 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
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math.stat.inference;

import org.apache.commons.math.MathException;
import org.apache.commons.math.stat.descriptive.StatisticalSummary;

/**
 * An interface for Student's t-tests.
 * <p>
 * Tests can be:<ul>
 * <li>One-sample or two-sample
 * <li>One-sided or two-sided
 * <li>Paired or unpaired (for two-sample tests)
 * <li>Homoscedastic (equal variance assumption) or heteroscedastic
 * (for two sample tests)</li>
 * <li>Fixed significance level (boolean-valued) or returning p-values.
 * </li>

* <p> * Test statistics are available for all tests. Methods including "Test" in * in their names perform tests, all other methods return t-statistics. Among * the "Test" methods, <code>double-valued methods return p-values; * <code>boolean-valued methods perform fixed significance level tests. * Significance levels are always specified as numbers between 0 and 0.5 * (e.g. tests at the 95% level use <code>alpha=0.05).

* <p> * Input to tests can be either <code>double[] arrays or * {@link StatisticalSummary} instances.</p> * * * @version $Revision: 811786 $ $Date: 2009-09-06 05:36:08 -0400 (Sun, 06 Sep 2009) $ */ public interface TTest { /** * Computes a paired, 2-sample t-statistic based on the data in the input * arrays. The t-statistic returned is equivalent to what would be returned by * computing the one-sample t-statistic {@link #t(double, double[])}, with * <code>mu = 0 and the sample array consisting of the (signed) * differences between corresponding entries in <code>sample1 and * <code>sample2. * <p> * <strong>Preconditions:
    * <li>The input arrays must have the same length and their common length * must be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return t statistic * @throws IllegalArgumentException if the precondition is not met * @throws MathException if the statistic can not be computed do to a * convergence or other numerical error. */ double pairedT(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i> p-value, associated with a paired, two-sample, two-tailed t-test * based on the data in the input arrays. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the mean of the paired * differences is 0 in favor of the two-sided alternative that the mean paired * difference is not equal to 0. For a one-sided test, divide the returned * value by 2.</p> * <p> * This test is equivalent to a one-sample t-test computed using * {@link #tTest(double, double[])} with <code>mu = 0 and the sample * array consisting of the signed differences between corresponding elements of * <code>sample1 and sample2.

* <p> * <strong>Usage Note:
* The validity of the p-value depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The input array lengths must be the same and their common length must * be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return p-value for t-test * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double pairedTTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Performs a paired t-test evaluating the null hypothesis that the * mean of the paired differences between <code>sample1 and * <code>sample2 is 0 in favor of the two-sided alternative that the * mean paired difference is not equal to 0, with significance level * <code>alpha. * <p> * Returns <code>true iff the null hypothesis can be rejected with * confidence <code>1 - alpha. To perform a 1-sided test, use * <code>alpha * 2

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The input array lengths must be the same and their common length * must be at least 2. * </li> * <li> 0 < alpha < 0.5 * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @param alpha significance level of the test * @return true if the null hypothesis can be rejected with * confidence 1 - alpha * @throws IllegalArgumentException if the preconditions are not met * @throws MathException if an error occurs performing the test */ boolean pairedTTest( double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException; /** * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula"> * t statistic </a> given observed values and a comparison constant. * <p> * This statistic can be used to perform a one sample t-test for the mean. * </p>

* <strong>Preconditions:

    * <li>The observed array length must be at least 2. * </li>

* * @param mu comparison constant * @param observed array of values * @return t statistic * @throws IllegalArgumentException if input array length is less than 2 */ double t(double mu, double[] observed) throws IllegalArgumentException; /** * Computes a <a href="http://www.itl.nist.gov/div898/handbook/prc/section2/prc22.htm#formula"> * t statistic </a> to use in comparing the mean of the dataset described by * <code>sampleStats to mu. * <p> * This statistic can be used to perform a one sample t-test for the mean. * </p>

* <strong>Preconditions:

    * <li>observed.getN() > = 2. * </li>

* * @param mu comparison constant * @param sampleStats DescriptiveStatistics holding sample summary statitstics * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ double t(double mu, StatisticalSummary sampleStats) throws IllegalArgumentException; /** * Computes a 2-sample t statistic, under the hypothesis of equal * subpopulation variances. To compute a t-statistic without the * equal variances hypothesis, use {@link #t(double[], double[])}. * <p> * This statistic can be used to perform a (homoscedastic) two-sample * t-test to compare sample means.</p> * <p> * The t-statisitc is</p> * <p> *   <code> t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var)) * </p>

* where <strong>n1 is the size of first sample; * <strong> n2 is the size of second sample; * <strong> m1 is the mean of first sample; * <strong> m2 is the mean of second sample * </ul> * and <strong>var is the pooled variance estimate: * </p>

* <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1))) * </p>

* with <strong>var1 the variance of the first sample and * <strong>var2 the variance of the second sample. * </p>

* <strong>Preconditions:

    * <li>The observed array lengths must both be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ double homoscedasticT(double[] sample1, double[] sample2) throws IllegalArgumentException; /** * Computes a 2-sample t statistic, without the hypothesis of equal * subpopulation variances. To compute a t-statistic assuming equal * variances, use {@link #homoscedasticT(double[], double[])}. * <p> * This statistic can be used to perform a two-sample t-test to compare * sample means.</p> * <p> * The t-statisitc is</p> * <p> *    <code> t = (m1 - m2) / sqrt(var1/n1 + var2/n2) * </p>

* where <strong>n1 is the size of the first sample * <strong> n2 is the size of the second sample; * <strong> m1 is the mean of the first sample; * <strong> m2 is the mean of the second sample; * <strong> var1 is the variance of the first sample; * <strong> var2 is the variance of the second sample; * </p>

* <strong>Preconditions:

    * <li>The observed array lengths must both be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ double t(double[] sample1, double[] sample2) throws IllegalArgumentException; /** * Computes a 2-sample t statistic </a>, comparing the means of the datasets * described by two {@link StatisticalSummary} instances, without the * assumption of equal subpopulation variances. Use * {@link #homoscedasticT(StatisticalSummary, StatisticalSummary)} to * compute a t-statistic under the equal variances assumption. * <p> * This statistic can be used to perform a two-sample t-test to compare * sample means.</p> * <p> * The returned t-statisitc is</p> * <p> *    <code> t = (m1 - m2) / sqrt(var1/n1 + var2/n2)
* </p>

* where <strong>n1 is the size of the first sample; * <strong> n2 is the size of the second sample; * <strong> m1 is the mean of the first sample; * <strong> m2 is the mean of the second sample * <strong> var1 is the variance of the first sample; * <strong> var2 is the variance of the second sample * </p>

* <strong>Preconditions:

    * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li>

* * @param sampleStats1 StatisticalSummary describing data from the first sample * @param sampleStats2 StatisticalSummary describing data from the second sample * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ double t( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException; /** * Computes a 2-sample t statistic, comparing the means of the datasets * described by two {@link StatisticalSummary} instances, under the * assumption of equal subpopulation variances. To compute a t-statistic * without the equal variances assumption, use * {@link #t(StatisticalSummary, StatisticalSummary)}. * <p> * This statistic can be used to perform a (homoscedastic) two-sample * t-test to compare sample means.</p> * <p> * The t-statisitc returned is</p> * <p> *   <code> t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var)) * </p>

* where <strong>n1 is the size of first sample; * <strong> n2 is the size of second sample; * <strong> m1 is the mean of first sample; * <strong> m2 is the mean of second sample * and <strong>var is the pooled variance estimate: * </p>

* <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1))) * </p>

* with <strong>var1 the variance of the first sample and * <strong>var2 the variance of the second sample. * </p>

* <strong>Preconditions:

    * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li>

* * @param sampleStats1 StatisticalSummary describing data from the first sample * @param sampleStats2 StatisticalSummary describing data from the second sample * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ double homoscedasticT( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a one-sample, two-tailed t-test * comparing the mean of the input array with the constant <code>mu. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the mean equals * <code>mu in favor of the two-sided alternative that the mean * is different from <code>mu. For a one-sided test, divide the * returned value by 2.</p> * <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here * </p>

* <strong>Preconditions:

    * <li>The observed array length must be at least 2. * </li>

* * @param mu constant value to compare sample mean against * @param sample array of sample data values * @return p-value * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double tTest(double mu, double[] sample) throws IllegalArgumentException, MathException; /** * Performs a <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm"> * two-sided t-test</a> evaluating the null hypothesis that the mean of the population from * which <code>sample is drawn equals mu. * <p> * Returns <code>true iff the null hypothesis can be * rejected with confidence <code>1 - alpha. To * perform a 1-sided test, use <code>alpha * 2

* <p> * <strong>Examples:
    * <li>To test the (2-sided) hypothesis sample mean = mu at * the 95% level, use <br>tTest(mu, sample, 0.05) * </li> * <li>To test the (one-sided) hypothesis sample mean < mu * at the 99% level, first verify that the measured sample mean is less * than <code>mu and then use * <br>tTest(mu, sample, 0.02) * </li>

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the one-sample * parametric t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here * </p>

* <strong>Preconditions:

    * <li>The observed array length must be at least 2. * </li>

* * @param mu constant value to compare sample mean against * @param sample array of sample data values * @param alpha significance level of the test * @return p-value * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error computing the p-value */ boolean tTest(double mu, double[] sample, double alpha) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a one-sample, two-tailed t-test * comparing the mean of the dataset described by <code>sampleStats * with the constant <code>mu. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the mean equals * <code>mu in favor of the two-sided alternative that the mean * is different from <code>mu. For a one-sided test, divide the * returned value by 2.</p> * <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The sample must contain at least 2 observations. * </li>

* * @param mu constant value to compare sample mean against * @param sampleStats StatisticalSummary describing sample data * @return p-value * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double tTest(double mu, StatisticalSummary sampleStats) throws IllegalArgumentException, MathException; /** * Performs a <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm"> * two-sided t-test</a> evaluating the null hypothesis that the mean of the * population from which the dataset described by <code>stats is * drawn equals <code>mu. * <p> * Returns <code>true iff the null hypothesis can be rejected with * confidence <code>1 - alpha. To perform a 1-sided test, use * <code>alpha * 2.

* <p> * <strong>Examples:
    * <li>To test the (2-sided) hypothesis sample mean = mu at * the 95% level, use <br>tTest(mu, sampleStats, 0.05) * </li> * <li>To test the (one-sided) hypothesis sample mean < mu * at the 99% level, first verify that the measured sample mean is less * than <code>mu and then use * <br>tTest(mu, sampleStats, 0.02) * </li>

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the one-sample * parametric t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/sg_glos.html#one-sample">here * </p>

* <strong>Preconditions:

    * <li>The sample must include at least 2 observations. * </li>

* * @param mu constant value to compare sample mean against * @param sampleStats StatisticalSummary describing sample data values * @param alpha significance level of the test * @return p-value * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ boolean tTest( double mu, StatisticalSummary sampleStats, double alpha) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a two-sample, two-tailed t-test * comparing the means of the input arrays. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the two means are * equal in favor of the two-sided alternative that they are different. * For a one-sided test, divide the returned value by 2.</p> * <p> * The test does not assume that the underlying popuation variances are * equal and it uses approximated degrees of freedom computed from the * sample data to compute the p-value. The t-statistic used is as defined in * {@link #t(double[], double[])} and the Welch-Satterthwaite approximation * to the degrees of freedom is used, * as described * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm"> * here.</a> To perform the test under the assumption of equal subpopulation * variances, use {@link #homoscedasticTTest(double[], double[])}.</p> * <p> * <strong>Usage Note:
* The validity of the p-value depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The observed array lengths must both be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return p-value for t-test * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double tTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a two-sample, two-tailed t-test * comparing the means of the input arrays, under the assumption that * the two samples are drawn from subpopulations with equal variances. * To perform the test without the equal variances assumption, use * {@link #tTest(double[], double[])}.</p> * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the two means are * equal in favor of the two-sided alternative that they are different. * For a one-sided test, divide the returned value by 2.</p> * <p> * A pooled variance estimate is used to compute the t-statistic. See * {@link #homoscedasticT(double[], double[])}. The sum of the sample sizes * minus 2 is used as the degrees of freedom.</p> * <p> * <strong>Usage Note:
* The validity of the p-value depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The observed array lengths must both be at least 2. * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @return p-value for t-test * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double homoscedasticTTest( double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Performs a * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm"> * two-sided t-test</a> evaluating the null hypothesis that sample1 * and <code>sample2 are drawn from populations with the same mean, * with significance level <code>alpha. This test does not assume * that the subpopulation variances are equal. To perform the test assuming * equal variances, use * {@link #homoscedasticTTest(double[], double[], double)}. * <p> * Returns <code>true iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha. To * perform a 1-sided test, use <code>alpha * 2

* <p> * See {@link #t(double[], double[])} for the formula used to compute the * t-statistic. Degrees of freedom are approximated using the * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm"> * Welch-Satterthwaite approximation.</a>

* <p> * <strong>Examples:
    * <li>To test the (2-sided) hypothesis mean 1 = mean 2 at * the 95% level, use * <br>tTest(sample1, sample2, 0.05). * </li> * <li>To test the (one-sided) hypothesis mean 1 < mean 2 , * at the 99% level, first verify that the measured mean of <code>sample 1 * is less than the mean of <code>sample 2 and then use * <br>tTest(sample1, sample2, 0.02) * </li>

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The observed array lengths must both be at least 2. * </li> * <li> 0 < alpha < 0.5 * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @param alpha significance level of the test * @return true if the null hypothesis can be rejected with * confidence 1 - alpha * @throws IllegalArgumentException if the preconditions are not met * @throws MathException if an error occurs performing the test */ boolean tTest( double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException; /** * Performs a * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm"> * two-sided t-test</a> evaluating the null hypothesis that sample1 * and <code>sample2 are drawn from populations with the same mean, * with significance level <code>alpha, assuming that the * subpopulation variances are equal. Use * {@link #tTest(double[], double[], double)} to perform the test without * the assumption of equal variances. * <p> * Returns <code>true iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha. To * perform a 1-sided test, use <code>alpha * 2. To perform the test * without the assumption of equal subpopulation variances, use * {@link #tTest(double[], double[], double)}.</p> * <p> * A pooled variance estimate is used to compute the t-statistic. See * {@link #t(double[], double[])} for the formula. The sum of the sample * sizes minus 2 is used as the degrees of freedom.</p> * <p> * <strong>Examples:
    * <li>To test the (2-sided) hypothesis mean 1 = mean 2 at * the 95% level, use <br>tTest(sample1, sample2, 0.05). * </li> * <li>To test the (one-sided) hypothesis mean 1 < mean 2, * at the 99% level, first verify that the measured mean of * <code>sample 1 is less than the mean of sample 2 * and then use * <br>tTest(sample1, sample2, 0.02) * </li>

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The observed array lengths must both be at least 2. * </li> * <li> 0 < alpha < 0.5 * </li>

* * @param sample1 array of sample data values * @param sample2 array of sample data values * @param alpha significance level of the test * @return true if the null hypothesis can be rejected with * confidence 1 - alpha * @throws IllegalArgumentException if the preconditions are not met * @throws MathException if an error occurs performing the test */ boolean homoscedasticTTest( double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a two-sample, two-tailed t-test * comparing the means of the datasets described by two StatisticalSummary * instances. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the two means are * equal in favor of the two-sided alternative that they are different. * For a one-sided test, divide the returned value by 2.</p> * <p> * The test does not assume that the underlying popuation variances are * equal and it uses approximated degrees of freedom computed from the * sample data to compute the p-value. To perform the test assuming * equal variances, use * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}.</p> * <p> * <strong>Usage Note:
* The validity of the p-value depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li>

* * @param sampleStats1 StatisticalSummary describing data from the first sample * @param sampleStats2 StatisticalSummary describing data from the second sample * @return p-value for t-test * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double tTest( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException, MathException; /** * Returns the <i>observed significance level, or * <i>p-value, associated with a two-sample, two-tailed t-test * comparing the means of the datasets described by two StatisticalSummary * instances, under the hypothesis of equal subpopulation variances. To * perform a test without the equal variances assumption, use * {@link #tTest(StatisticalSummary, StatisticalSummary)}. * <p> * The number returned is the smallest significance level * at which one can reject the null hypothesis that the two means are * equal in favor of the two-sided alternative that they are different. * For a one-sided test, divide the returned value by 2.</p> * <p> * See {@link #homoscedasticT(double[], double[])} for the formula used to * compute the t-statistic. The sum of the sample sizes minus 2 is used as * the degrees of freedom.</p> * <p> * <strong>Usage Note:
* The validity of the p-value depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html">here * </p>

* <strong>Preconditions:

    * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li>

* * @param sampleStats1 StatisticalSummary describing data from the first sample * @param sampleStats2 StatisticalSummary describing data from the second sample * @return p-value for t-test * @throws IllegalArgumentException if the precondition is not met * @throws MathException if an error occurs computing the p-value */ double homoscedasticTTest( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException, MathException; /** * Performs a * <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm"> * two-sided t-test</a> evaluating the null hypothesis that * <code>sampleStats1 and sampleStats2 describe * datasets drawn from populations with the same mean, with significance * level <code>alpha. This test does not assume that the * subpopulation variances are equal. To perform the test under the equal * variances assumption, use * {@link #homoscedasticTTest(StatisticalSummary, StatisticalSummary)}. * <p> * Returns <code>true iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha. To * perform a 1-sided test, use <code>alpha * 2

* <p> * See {@link #t(double[], double[])} for the formula used to compute the * t-statistic. Degrees of freedom are approximated using the * <a href="http://www.itl.nist.gov/div898/handbook/prc/section3/prc31.htm"> * Welch-Satterthwaite approximation.</a>

* <p> * <strong>Examples:
    * <li>To test the (2-sided) hypothesis mean 1 = mean 2 at * the 95%, use * <br>tTest(sampleStats1, sampleStats2, 0.05) * </li> * <li>To test the (one-sided) hypothesis mean 1 < mean 2 * at the 99% level, first verify that the measured mean of * <code>sample 1 is less than the mean of sample 2 * and then use * <br>tTest(sampleStats1, sampleStats2, 0.02) * </li>

* <p> * <strong>Usage Note:
* The validity of the test depends on the assumptions of the parametric * t-test procedure, as discussed * <a href="http://www.basic.nwu.edu/statguidefiles/ttest_unpaired_ass_viol.html"> * here</a>

* <p> * <strong>Preconditions:
    * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li> * <li> 0 < alpha < 0.5 * </li>

* * @param sampleStats1 StatisticalSummary describing sample data values * @param sampleStats2 StatisticalSummary describing sample data values * @param alpha significance level of the test * @return true if the null hypothesis can be rejected with * confidence 1 - alpha * @throws IllegalArgumentException if the preconditions are not met * @throws MathException if an error occurs performing the test */ boolean tTest( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha) throws IllegalArgumentException, MathException; }

Other Commons Math examples (source code examples)

Here is a short list of links related to this Commons Math TTest.java source code file:

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