TTest.java

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		org.apache.commons.math.stat.inference
		Commons Math

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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; import org.apache.commons.math.stat.descriptive.StatisticalSummary; /** * An interface for Student's t-tests. * * Tests can be:<ul> * <li>One-sample or two-sample</li> * <li>One-sided or two-sided</li> * <li>Paired or unpaired (for two-sample tests)</li> * <li>Homoscedastic (equal variance assumption) or heteroscedastic * (for two sample tests)</li> * <li>Fixed significance level (boolean-valued) or returning p-values. * </li></ul> * * 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-</code>valued methods return p-values; * <code>boolean-</code>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</code>). * * Input to tests can be either <code>double[]</code> arrays or * {@link StatisticalSummary} instances. * * * @version $Revision: 617953 $ $Date: 2008-02-03 00:54:00 -0500 (Sun, 03 Feb 2008) $ */ 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</code> and the sample array consisting of the (signed) * differences between corresponding entries in <code>sample1</code> and * <code>sample2.</code> * * Preconditions: <ul> * <li>The input arrays must have the same length and their common length * must be at least 2. * </li></ul> * * @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. */ public abstract double pairedT(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * p-value, associated with a paired, two-sample, two-tailed t-test * based on the data in the input arrays. * * 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. * * This test is equivalent to a one-sample t-test computed using * {@link #tTest(double, double[])} with <code>mu = 0</code> and the sample * array consisting of the signed differences between corresponding elements of * <code>sample1</code> and <code>sample2.</code> * * 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> * * Preconditions: <ul> * <li>The input array lengths must be the same and their common length must * be at least 2. * </li></ul> * * @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 */ public abstract 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</code> and * <code>sample2</code> is 0 in favor of the two-sided alternative that the * mean paired difference is not equal to 0, with significance level * <code>alpha</code>. * * Returns <code>true</code> iff the null hypothesis can be rejected with * confidence <code>1 - alpha</code>. To perform a 1-sided test, use * <code>alpha * 2</code> * * 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> * * Preconditions: <ul> * <li>The input array lengths must be the same and their common length * must be at least 2. * </li> * <li> <code> 0 < alpha < 0.5 </code> * </li></ul> * * @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 */ public abstract 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. * * This statistic can be used to perform a one sample t-test for the mean. * * Preconditions: <ul> * <li>The observed array length must be at least 2. * </li></ul> * * @param mu comparison constant * @param observed array of values * @return t statistic * @throws IllegalArgumentException if input array length is less than 2 */ public abstract 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</code> to <code>mu</code>. * * This statistic can be used to perform a one sample t-test for the mean. * * Preconditions: <ul> * <li><code>observed.getN() > = 2</code>. * </li></ul> * * @param mu comparison constant * @param sampleStats DescriptiveStatistics holding sample summary statitstics * @return t statistic * @throws IllegalArgumentException if the precondition is not met */ public abstract 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[])}. * * This statistic can be used to perform a (homoscedastic) two-sample * t-test to compare sample means. * * The t-statisitc is * *   <code> t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code> * * where <code>n1</code> is the size of first sample; * <code> n2</code> is the size of second sample; * <code> m1</code> is the mean of first sample; * <code> m2</code> is the mean of second sample</li> * </ul> * and <code>var</code> is the pooled variance estimate: * * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code> * * with <code>var1<code> the variance of the first sample and * <code>var2</code> the variance of the second sample. * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li></ul> * * @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 */ public abstract 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[])}. * * This statistic can be used to perform a two-sample t-test to compare * sample means. * * The t-statisitc is * *    <code> t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code> * * where <code>n1</code> is the size of the first sample * <code> n2</code> is the size of the second sample; * <code> m1</code> is the mean of the first sample; * <code> m2</code> is the mean of the second sample; * <code> var1</code> is the variance of the first sample; * <code> var2</code> is the variance of the second sample; * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li></ul> * * @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 */ public abstract 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. * * This statistic can be used to perform a two-sample t-test to compare * sample means. * * The returned t-statisitc is * *    <code> t = (m1 - m2) / sqrt(var1/n1 + var2/n2)</code> * * where <code>n1</code> is the size of the first sample; * <code> n2</code> is the size of the second sample; * <code> m1</code> is the mean of the first sample; * <code> m2</code> is the mean of the second sample * <code> var1</code> is the variance of the first sample; * <code> var2</code> is the variance of the second sample * * Preconditions: <ul> * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li></ul> * * @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 */ public abstract 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)}. * * This statistic can be used to perform a (homoscedastic) two-sample * t-test to compare sample means. * * The t-statisitc returned is * *   <code> t = (m1 - m2) / (sqrt(1/n1 +1/n2) sqrt(var))</code> * * where <code>n1</code> is the size of first sample; * <code> n2</code> is the size of second sample; * <code> m1</code> is the mean of first sample; * <code> m2</code> is the mean of second sample * and <code>var</code> is the pooled variance estimate: * * <code>var = sqrt(((n1 - 1)var1 + (n2 - 1)var2) / ((n1-1) + (n2-1)))</code> * * with <code>var1<code> the variance of the first sample and * <code>var2</code> the variance of the second sample. * * Preconditions: <ul> * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li></ul> * * @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 */ public abstract double homoscedasticT( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException; /** * Returns the observed significance level, or * p-value, associated with a one-sample, two-tailed t-test * comparing the mean of the input array with the constant <code>mu</code>. * * The number returned is the smallest significance level * at which one can reject the null hypothesis that the mean equals * <code>mu</code> in favor of the two-sided alternative that the mean * is different from <code>mu</code>. For a one-sided test, divide the * returned value by 2. * * 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> * * Preconditions: <ul> * <li>The observed array length must be at least 2. * </li></ul> * * @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 */ public abstract 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</code> is drawn equals <code>mu</code>. * * Returns <code>true</code> iff the null hypothesis can be * rejected with confidence <code>1 - alpha</code>. To * perform a 1-sided test, use <code>alpha * 2</code> * * Examples: <ol> * <li>To test the (2-sided) hypothesis <code>sample mean = mu </code> at * the 95% level, use <code>tTest(mu, sample, 0.05) </code> * </li> * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code> * at the 99% level, first verify that the measured sample mean is less * than <code>mu</code> and then use * <code>tTest(mu, sample, 0.02) </code> * </li></ol> * * 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</a> * * Preconditions: <ul> * <li>The observed array length must be at least 2. * </li></ul> * * @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 */ public abstract boolean tTest(double mu, double[] sample, double alpha) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * p-value, associated with a one-sample, two-tailed t-test * comparing the mean of the dataset described by <code>sampleStats</code> * with the constant <code>mu</code>. * * The number returned is the smallest significance level * at which one can reject the null hypothesis that the mean equals * <code>mu</code> in favor of the two-sided alternative that the mean * is different from <code>mu</code>. For a one-sided test, divide the * returned value by 2. * * 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> * * Preconditions: <ul> * <li>The sample must contain at least 2 observations. * </li></ul> * * @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 */ public abstract 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</code> is * drawn equals <code>mu</code>. * * Returns <code>true</code> iff the null hypothesis can be rejected with * confidence <code>1 - alpha</code>. To perform a 1-sided test, use * <code>alpha * 2.</code> * * Examples: <ol> * <li>To test the (2-sided) hypothesis <code>sample mean = mu </code> at * the 95% level, use <code>tTest(mu, sampleStats, 0.05) </code> * </li> * <li>To test the (one-sided) hypothesis <code> sample mean < mu </code> * at the 99% level, first verify that the measured sample mean is less * than <code>mu</code> and then use * <code>tTest(mu, sampleStats, 0.02) </code> * </li></ol> * * 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</a> * * Preconditions: <ul> * <li>The sample must include at least 2 observations. * </li></ul> * * @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 */ public abstract boolean tTest( double mu, StatisticalSummary sampleStats, double alpha) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * p-value, associated with a two-sample, two-tailed t-test * comparing the means of the input arrays. * * 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. * * 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[])}. * * 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> * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li></ul> * * @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 */ public abstract double tTest(double[] sample1, double[] sample2) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * 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[])}. * * 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. * * 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. * * 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> * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li></ul> * * @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 */ public abstract 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 <code>sample1</code> * and <code>sample2</code> are drawn from populations with the same mean, * with significance level <code>alpha</code>. This test does not assume * that the subpopulation variances are equal. To perform the test assuming * equal variances, use * {@link #homoscedasticTTest(double[], double[], double)}. * * Returns <code>true</code> iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha</code>. To * perform a 1-sided test, use <code>alpha * 2</code> * * 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> * * Examples: <ol> * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at * the 95% level, use * <code>tTest(sample1, sample2, 0.05). </code> * </li> * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code>, * at the 99% level, first verify that the measured mean of <code>sample 1</code> * is less than the mean of <code>sample 2</code> and then use * <code>tTest(sample1, sample2, 0.02) </code> * </li></ol> * * 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> * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li> * <li> <code> 0 < alpha < 0.5 </code> * </li></ul> * * @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 */ public abstract 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 <code>sample1</code> * and <code>sample2</code> are drawn from populations with the same mean, * with significance level <code>alpha</code>, assuming that the * subpopulation variances are equal. Use * {@link #tTest(double[], double[], double)} to perform the test without * the assumption of equal variances. * * Returns <code>true</code> iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha</code>. To * perform a 1-sided test, use <code>alpha * 2.</code> To perform the test * without the assumption of equal subpopulation variances, use * {@link #tTest(double[], double[], double)}. * * 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. * * Examples: <ol> * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at * the 95% level, use <code>tTest(sample1, sample2, 0.05). </code> * </li> * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2, </code> * at the 99% level, first verify that the measured mean of * <code>sample 1</code> is less than the mean of <code>sample 2</code> * and then use * <code>tTest(sample1, sample2, 0.02) </code> * </li></ol> * * 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> * * Preconditions: <ul> * <li>The observed array lengths must both be at least 2. * </li> * <li> <code> 0 < alpha < 0.5 </code> * </li></ul> * * @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 */ public abstract boolean homoscedasticTTest( double[] sample1, double[] sample2, double alpha) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * p-value, associated with a two-sample, two-tailed t-test * comparing the means of the datasets described by two StatisticalSummary * instances. * * 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. * * 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)}. * * 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> * * Preconditions: <ul> * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li></ul> * * @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 */ public abstract double tTest( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2) throws IllegalArgumentException, MathException; /** * Returns the observed significance level, or * 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)}. * * 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. * * 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. * * 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> * * Preconditions: <ul> * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li></ul> * * @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 */ public abstract 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</code> and <code>sampleStats2</code> describe * datasets drawn from populations with the same mean, with significance * level <code>alpha</code>. 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)}. * * Returns <code>true</code> iff the null hypothesis that the means are * equal can be rejected with confidence <code>1 - alpha</code>. To * perform a 1-sided test, use <code>alpha * 2</code> * * 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> * * Examples: <ol> * <li>To test the (2-sided) hypothesis <code>mean 1 = mean 2 </code> at * the 95%, use * <code>tTest(sampleStats1, sampleStats2, 0.05) </code> * </li> * <li>To test the (one-sided) hypothesis <code> mean 1 < mean 2 </code> * at the 99% level, first verify that the measured mean of * <code>sample 1</code> is less than the mean of <code>sample 2</code> * and then use * <code>tTest(sampleStats1, sampleStats2, 0.02) </code> * </li></ol> * * 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> * * Preconditions: <ul> * <li>The datasets described by the two Univariates must each contain * at least 2 observations. * </li> * <li> <code> 0 < alpha < 0.5 </code> * </li></ul> * * @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 */ public abstract boolean tTest( StatisticalSummary sampleStats1, StatisticalSummary sampleStats2, double alpha) throws IllegalArgumentException, MathException; }

The table below shows all metrics for TTest.java.

Metric	Value	Description
BLOCKS	0.00	Number of blocks
BLOCK_COMMENT	16.00	Number of block comment lines
COMMENTS	699.00	Comment lines
COMMENT_DENSITY	9.99	Comment density
COMPARISONS	0.00	Number of comparison operators
CYCLOMATIC	0.00	Cyclomatic complexity
DECL_COMMENTS	22.00	Comments in declarations
DOC_COMMENT	683.00	Number of javadoc comment lines
ELOC	70.00	Effective lines of code
EXEC_COMMENTS	0.00	Comments in executable code
EXITS	0.00	Procedure exits
FUNCTIONS	20.00	Number of function declarations
HALSTEAD_DIFFICULTY	14.57	Halstead difficulty
HALSTEAD_EFFORT	0.00	Halstead effort
INTERFACE_COMPLEXITY	46.00	Interface complexity
JAVA0001	0.00	JAVA0001 Package name does not contain only lower case letters
JAVA0002	0.00	JAVA0002 Package name does not begin with a top level domain name or country code
JAVA0003	0.00	JAVA0003 Minimize use of on-demand (.*) imports
JAVA0004	0.00	JAVA0004 Unnecessary import from java.lang
JAVA0005	0.00	JAVA0005 Imports not in specified order
JAVA0006	0.00	JAVA0006 Empty finally block
JAVA0007	0.00	JAVA0007 Should not declare public field
JAVA0008	0.00	JAVA0008 Empty catch block
JAVA0009	0.00	JAVA0009 Protected member in final class
JAVA0010	0.00	JAVA0010 Non-instantiable class does not contain a non-private static member
JAVA0011	0.00	JAVA0011 Abstract class does not contain an abstract method
JAVA0012	0.00	JAVA0012 Non-constructor method with same name as declaring class
JAVA0013	0.00	JAVA0013 Non-blank final field is not static
JAVA0014	0.00	JAVA0014 Class with only static members has non-private constructor
JAVA0015	0.00	JAVA0015 Package class contains public nested type
JAVA0016	0.00	JAVA0016 Abstract class contains public constructor
JAVA0017	0.00	JAVA0017 Class name does not have required form
JAVA0018	0.00	JAVA0018 Method name does not have required form
JAVA0019	0.00	JAVA0019 Interface name does not have required form
JAVA0020	0.00	JAVA0020 Field name does not have required form
JAVA0021	0.00	JAVA0021 Interface method name does not have required form
JAVA0022	0.00	JAVA0022 Static final field name does not have required form
JAVA0023	0.00	JAVA0023 Empty finalize method
JAVA0024	0.00	JAVA0024 Empty class
JAVA0025	0.00	JAVA0025 Method override is empty
JAVA0026	0.00	JAVA0026 Finalize method with parameters
JAVA0029	0.00	JAVA0029 Private method not used
JAVA0030	0.00	JAVA0030 Private field not used
JAVA0031	0.00	JAVA0031 Case statement not properly closed
JAVA0032	0.00	JAVA0032 Switch statement missing default
JAVA0033	0.00	JAVA0033 default: not last case in switch statement
JAVA0034	0.00	JAVA0034 Missing braces in if statement
JAVA0035	0.00	JAVA0035 Missing braces in for statement
JAVA0036	0.00	JAVA0036 Missing braces in while statement
JAVA0038	0.00	JAVA0038 Non-case label in switch statement
JAVA0039	0.00	JAVA0039 Break statement with label
JAVA0040	0.00	JAVA0040 Switch statement contains N cases (maximum: M)
JAVA0041	0.00	JAVA0041 Nested synchronized block
JAVA0042	0.00	JAVA0042 Empty synchronized statement
JAVA0043	0.00	JAVA0043 Inner class does not use outer class
JAVA0044	0.00	JAVA0044 Serializable class with no instance variables
JAVA0045	0.00	JAVA0045 Serializable class with only transient fields
JAVA0046	0.00	JAVA0046 Name of class not derived from Exception ends with 'Exception'
JAVA0047	0.00	JAVA0047 Serializable class derives from invalid base class
JAVA0048	0.00	JAVA0048 Name of class derived from Exception does not end with 'Exception'
JAVA0049	0.00	JAVA0049 Nested block at depth N (maximum: M)
JAVA0050	0.00	JAVA0050 Class derives from java.lang.Error
JAVA0051	0.00	JAVA0051 Class derives from java.lang.RuntimeException
JAVA0052	0.00	JAVA0052 Class derives from java.lang.Throwable
JAVA0053	0.00	JAVA0053 Unused label
JAVA0054	0.00	JAVA0054 Inheritance depth N exceeds maximum M
JAVA0055	0.00	JAVA0055 Class should be interface
JAVA0056	0.00	JAVA0056 Unnecessary abstract modifier for interface or annotation
JAVA0057	0.00	JAVA0057 Unnecessary default constructor
JAVA0058	0.00	JAVA0058 Constructor calls super()
JAVA0059	0.00	JAVA0059 Method override only calls super()
JAVA0061	0.00	JAVA0061 Inaccessible member in anonymous class
JAVA0062	0.00	JAVA0062 Public class missing public member or protected constructor
JAVA0063	0.00	JAVA0063 Identifier name should not contain '$'
JAVA0064	0.00	JAVA0064 N variations of identifier name (maximum: M)
JAVA0065	0.00	JAVA0065 Unnecessary final modifier for method in final class
JAVA0066	0.00	JAVA0066 Unnecessary modifier for interface nested type
JAVA0067	0.00	JAVA0067 Array descriptor on identifier name
JAVA0068	0.00	JAVA0068 Modifiers not declared in recommended order
JAVA0071	0.00	JAVA0071 Strings compared with ==
JAVA0073	0.00	JAVA0073 Integer division in floating-point context
JAVA0074	0.00	JAVA0074 Use of Object.notify()
JAVA0075	0.00	JAVA0075 Method parameter hides field
JAVA0076	0.00	JAVA0076 Use of magic number
JAVA0077	0.00	JAVA0077 Private field not used in declaring class
JAVA0078	0.00	JAVA0078 Floating point values compared with ==
JAVA0079	0.00	JAVA0079 Use of instance to reference static member
JAVA0080	0.00	JAVA0080 Import declaration not used
JAVA0081	0.00	JAVA0081 Boolean literal in comparison
JAVA0082	0.00	JAVA0082 Unnecessary widening cast
JAVA0083	0.00	JAVA0083 Unnecessary instanceof test
JAVA0084	0.00	JAVA0084 Should use compound assignment operator
JAVA0085	0.00	JAVA0085 Use of sun.* class
JAVA0087	0.00	JAVA0087 Use of Thread.sleep()
JAVA0089	0.00	JAVA0089 Use of restricted package
JAVA0092	0.00	JAVA0092 Use of restricted type
JAVA0093	0.00	JAVA0093 Redundant assignment
JAVA0094	0.00	JAVA0094 Field hides a superclass field
JAVA0095	0.00	JAVA0095 Uninitialized private field
JAVA0096	0.00	JAVA0096 Field in nested class hides outer field
JAVA0098	0.00	JAVA0098 Minimize use of implicit field initializers
JAVA0100	0.00	JAVA0100 Class contains N non-final fields (maximum: M)
JAVA0101	0.00	JAVA0101 Unnecessary modifier for field in interface
JAVA0102	0.00	JAVA0102 Last statement in finalize() not super.finalize()
JAVA0103	0.00	JAVA0103 Explicit call to finalize()
JAVA0104	0.00	JAVA0104 finalize() only calls super.finalize()
JAVA0105	0.00	JAVA0105 Duplicate import declaration
JAVA0106	0.00	JAVA0106 Unnecessary import from current package
JAVA0108	0.00	JAVA0108 Incorrect javadoc: no @param tag for 'parameter'
JAVA0109	0.00	JAVA0109 Incorrect javadoc: no parameter 'parameter'
JAVA0110	0.00	JAVA0110 Incorrect javadoc: no @return tag
JAVA0111	0.00	JAVA0111 Incorrect javadoc: @return tag for void method
JAVA0112	0.00	JAVA0112 Incorrect javadoc: no exception 'exception' in throws
JAVA0113	1.00	JAVA0113 Incorrect javadoc: no @author tag
JAVA0114	0.00	JAVA0114 Incorrect javadoc: no @version tag
JAVA0115	0.00	JAVA0115 Incorrect javadoc: no @throws or @exception tag for 'exception'
JAVA0116	0.00	JAVA0116 Missing javadoc: field 'field'
JAVA0117	0.00	JAVA0117 Missing javadoc: method 'method'
JAVA0118	0.00	JAVA0118 Missing javadoc: type 'type'
JAVA0119	0.00	JAVA0119 Control variable changed within body of for loop
JAVA0123	0.00	JAVA0123 Use all three components of for loop
JAVA0125	0.00	JAVA0125 Continue statement with label
JAVA0126	20.00	JAVA0126 Method declares unchecked exception in throws
JAVA0128	0.00	JAVA0128 Public constructor in non-public class
JAVA0130	0.00	JAVA0130 Non-static method does not use instance fields
JAVA0131	0.00	JAVA0131 Compatible method does not override base
JAVA0132	0.00	JAVA0132 Method overload with compatible signature
JAVA0133	0.00	JAVA0133 Non-synchronized method overrides synchronized method
JAVA0135	0.00	JAVA0135 Only one of Object.equals and Object.hashCode defined: missing 'method'
JAVA0136	0.00	JAVA0136 N methods defined in class (maximum: M)
JAVA0137	0.00	JAVA0137 Non-abstract class missing constructor
JAVA0138	0.00	JAVA0138 N parameters defined for method (maximum: M)
JAVA0139	0.00	JAVA0139 Definition of main other than public static void main(java.lang.String[])
JAVA0141	40.00	JAVA0141 Unnecessary modifier for method in interface
JAVA0143	0.00	JAVA0143 Synchronized method
JAVA0144	0.00	JAVA0144 Line exceeds maximum M characters
JAVA0145	0.00	JAVA0145 Tab character used in source file
JAVA0150	0.00	JAVA0150 java.lang.Error (or subclass) thrown
JAVA0153	0.00	JAVA0153 Inefficient conversion of integer to string
JAVA0159	0.00	JAVA0159 Inefficient conversion of string to integer
JAVA0160	0.00	JAVA0160 Method does not throw specified exception
JAVA0161	0.00	JAVA0161 Conditional wait() not in loop
JAVA0163	0.00	JAVA0163 Empty statement
JAVA0165	0.00	JAVA0165 Conflicting return statement in finally block
JAVA0166	0.00	JAVA0166 Generic exception caught
JAVA0167	0.00	JAVA0167 ThreadDeath not rethrown
JAVA0169	0.00	JAVA0169 Unnecessary catch block: exception 'exception'
JAVA0170	0.00	JAVA0170 Caught exception not derived from java.lang.Exception
JAVA0171	0.00	JAVA0171 Unused local variable
JAVA0173	0.00	JAVA0173 Unused method parameter
JAVA0174	0.00	JAVA0174 Assigned local variable never used
JAVA0175	0.00	JAVA0175 Successive assignment to variable
JAVA0176	0.00	JAVA0176 Local variable name does not have required form
JAVA0177	0.00	JAVA0177 Variable declaration missing initializer
JAVA0179	0.00	JAVA0179 Local variable hides visible field
JAVA0233	0.00	JAVA0233 Definition of serialVersionUID other than 'private static final long serialVersionUID'
JAVA0234	0.00	JAVA0234 Class is Serializable but does not define serialVersionUID
JAVA0235	0.00	JAVA0235 Class defines serialVersionUID but does not implement Serializable
JAVA0236	0.00	JAVA0236 Attempt to clone an object which does not implement Cloneable
JAVA0237	0.00	JAVA0237 Class implements Cloneable but does not have public clone method
JAVA0238	0.00	JAVA0238 Clone method does not call super.clone()
JAVA0239	0.00	JAVA0239 Class declares 'readObject' or 'writeObject' but does not implement Serializable
JAVA0240	0.00	JAVA0240 Serializable class which declares readObject or writeObject but not both
JAVA0241	0.00	JAVA0241 'readObject' or 'writeObject' should be declared private in Serializable class
JAVA0242	0.00	JAVA0242 Transient field in non-Serializable class
JAVA0243	0.00	JAVA0243 'readResolve' or 'writeReplace' should be declared private or protected
JAVA0244	0.00	JAVA0244 Field or method name in subclass differs only by case from inherited field or method
JAVA0245	0.00	JAVA0245 JUnit TestCase with non-trivial constructor
JAVA0246	0.00	JAVA0246 JUnit assertXXX statement missing message parameter
JAVA0247	0.00	JAVA0247 JUnit 'setUp()' and 'tearDown()' should call super method
JAVA0248	0.00	JAVA0248 JUnit method 'setUp' or 'tearDown' with incorrect signature
JAVA0249	0.00	JAVA0249 JUnit TestCase 'suite()' should be declared static
JAVA0250	0.00	JAVA0250 JUnit TestCase declares testXXX method with incorrect signature
JAVA0251	0.00	JAVA0251 Use '%n' for line breaks in printf/format for platform independence
JAVA0252	0.00	JAVA0252 'enum' is a Java 1.5 reserved word
JAVA0253	0.00	JAVA0253 Not all enum constants consumed in switch statement
JAVA0254	0.00	JAVA0254 Use enhanced for loop construct instead of Iterator
JAVA0255	0.00	JAVA0255 Result of method invocation not used
JAVA0256	0.00	JAVA0256 Assignment of external collection/array to field
JAVA0257	0.00	JAVA0257 Use of 'Constant Interface' anti-pattern
JAVA0258	0.00	JAVA0258 Implement Iterable for foreach compatibility
JAVA0259	0.00	JAVA0259 Return of collection/array field
JAVA0260	0.00	JAVA0260 Use 'enum' instead of Enumerated Type pattern
JAVA0261	0.00	JAVA0261 Use specialized Enum collection types
JAVA0262	0.00	JAVA0262 Use of char in integer context
JAVA0263	0.00	JAVA0263 Long literal ends with 'l' instead of 'L'
JAVA0264	0.00	JAVA0264 Integer math in long context - check for overflow
JAVA0265	0.00	JAVA0265 Use of Throwable.printStackTrace()
JAVA0266	0.00	JAVA0266 Use of System.out
JAVA0267	0.00	JAVA0267 Use of System.err
JAVA0269	0.00	JAVA0269 Contents of StringBuffer never used
JAVA0270	0.00	JAVA0270 Use Java 5.0 enhanced for loop construct to iterate over all elements in an array
JAVA0271	0.00	JAVA0271 Minimize use of on-demand (.*) static imports
JAVA0272	0.00	JAVA0272 Thread.run() called
JAVA0273	0.00	JAVA0273 Non-final derivative of Thread calls start() in constructor
JAVA0274	0.00	JAVA0274 Serializable class has a synchronized readObject()
JAVA0275	0.00	JAVA0275 Serializable class has a synchronized writeObject() and no other synchronized methods
JAVA0276	0.00	JAVA0276 Unnecessary use of String constructor
JAVA0277	0.00	JAVA0277 Iterator.next() implementation does not throw NoSuchElementException
JAVA0278	0.00	JAVA0278 Unnecessary use of Boolean constructor
JAVA0279	0.00	JAVA0279 Serialization method readObject or readObjectNoData calls an overridable method
JAVA0280	0.00	JAVA0280 IllegalMonitorStateException caught
JAVA0281	0.00	JAVA0281 Iterator.next() not called in loop
JAVA0282	0.00	JAVA0282 Call to Iterator.next() in loop which does not test Iterator.hasNext()
JAVA0283	0.00	JAVA0283 Control variable not updated in loop body
JAVA0284	0.00	JAVA0284 Explicit garbage collection
JAVA0285	0.00	JAVA0285 Dereference of potentially null variable
JAVA0286	0.00	JAVA0286 Dereference of null variable
JAVA0287	0.00	JAVA0287 Unnecessary null check
JAVA0288	0.00	JAVA0288 Inconsistent null check
LINES	771.00	Number of lines in the source file
LINE_COMMENT	0.00	Number of line comments
LOC	70.00	Lines of code
LOGICAL_LINES	23.00	Number of statements
LOOPS	0.00	Number of loops
NEST_DEPTH	0.00	Maximum nesting depth
OPERANDS	132.00	Number of operands
OPERATORS	280.00	Number of operators
PARAMS	46.00	Number of formal parameter declarations
PROGRAM_LENGTH	412.00	Halstead program length
PROGRAM_VOCAB	94.00	Halstead program vocabulary
PROGRAM_VOLUME	0.00	Halstead program volume
RETURNS	0.00	Number of return points from functions
SIZE	36775.00	Size of the file in bytes
UNIQUE_OPERANDS	77.00	Number of unique operands
UNIQUE_OPERATORS	17.00	Number of unique operators
WHITESPACE	2.00	Number of whitespace lines

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TTest.java