/*
* 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.math4.stat.inference;
import org.apache.commons.math4.exception.NullArgumentException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.math4.exception.OutOfRangeException;
import org.apache.commons.math4.stat.descriptive.SummaryStatistics;
import org.apache.commons.math4.stat.inference.TTest;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
/**
* Test cases for the TTestImpl class.
*
*/
public class TTestTest {
protected TTest testStatistic = new TTest();
private double[] tooShortObs = { 1.0 };
private double[] emptyObs = {};
private SummaryStatistics emptyStats = new SummaryStatistics();
SummaryStatistics tooShortStats = null;
@Before
public void setUp() {
tooShortStats = new SummaryStatistics();
tooShortStats.addValue(0d);
}
@Test
public void testOneSampleT() {
double[] observed =
{93.0, 103.0, 95.0, 101.0, 91.0, 105.0, 96.0, 94.0, 101.0, 88.0, 98.0, 94.0, 101.0, 92.0, 95.0 };
double mu = 100.0;
SummaryStatistics sampleStats = null;
sampleStats = new SummaryStatistics();
for (int i = 0; i < observed.length; i++) {
sampleStats.addValue(observed[i]);
}
// Target comparison values computed using R version 1.8.1 (Linux version)
Assert.assertEquals("t statistic", -2.81976445346,
testStatistic.t(mu, observed), 10E-10);
Assert.assertEquals("t statistic", -2.81976445346,
testStatistic.t(mu, sampleStats), 10E-10);
Assert.assertEquals("p value", 0.0136390585873,
testStatistic.tTest(mu, observed), 10E-10);
Assert.assertEquals("p value", 0.0136390585873,
testStatistic.tTest(mu, sampleStats), 10E-10);
try {
testStatistic.t(mu, (double[]) null);
Assert.fail("arguments too short, NullArgumentException expected");
} catch (NullArgumentException ex) {
// expected
}
try {
testStatistic.t(mu, (SummaryStatistics) null);
Assert.fail("arguments too short, NullArgumentException expected");
} catch (NullArgumentException ex) {
// expected
}
try {
testStatistic.t(mu, emptyObs);
Assert.fail("arguments too short, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.t(mu, emptyStats);
Assert.fail("arguments too short, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.t(mu, tooShortObs);
Assert.fail("insufficient data to compute t statistic, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.tTest(mu, tooShortObs);
Assert.fail("insufficient data to perform t test, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.t(mu, tooShortStats);
Assert.fail("insufficient data to compute t statistic, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.tTest(mu, tooShortStats);
Assert.fail("insufficient data to perform t test, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
}
@Test
public void testOneSampleTTest() {
double[] oneSidedP =
{2d, 0d, 6d, 6d, 3d, 3d, 2d, 3d, -6d, 6d, 6d, 6d, 3d, 0d, 1d, 1d, 0d, 2d, 3d, 3d };
SummaryStatistics oneSidedPStats = new SummaryStatistics();
for (int i = 0; i < oneSidedP.length; i++) {
oneSidedPStats.addValue(oneSidedP[i]);
}
// Target comparison values computed using R version 1.8.1 (Linux version)
Assert.assertEquals("one sample t stat", 3.86485535541,
testStatistic.t(0d, oneSidedP), 10E-10);
Assert.assertEquals("one sample t stat", 3.86485535541,
testStatistic.t(0d, oneSidedPStats),1E-10);
Assert.assertEquals("one sample p value", 0.000521637019637,
testStatistic.tTest(0d, oneSidedP) / 2d, 10E-10);
Assert.assertEquals("one sample p value", 0.000521637019637,
testStatistic.tTest(0d, oneSidedPStats) / 2d, 10E-5);
Assert.assertTrue("one sample t-test reject", testStatistic.tTest(0d, oneSidedP, 0.01));
Assert.assertTrue("one sample t-test reject", testStatistic.tTest(0d, oneSidedPStats, 0.01));
Assert.assertTrue("one sample t-test accept", !testStatistic.tTest(0d, oneSidedP, 0.0001));
Assert.assertTrue("one sample t-test accept", !testStatistic.tTest(0d, oneSidedPStats, 0.0001));
try {
testStatistic.tTest(0d, oneSidedP, 95);
Assert.fail("alpha out of range, OutOfRangeException expected");
} catch (OutOfRangeException ex) {
// expected
}
try {
testStatistic.tTest(0d, oneSidedPStats, 95);
Assert.fail("alpha out of range, OutOfRangeException expected");
} catch (OutOfRangeException ex) {
// expected
}
}
@Test
public void testTwoSampleTHeterscedastic() {
double[] sample1 = { 7d, -4d, 18d, 17d, -3d, -5d, 1d, 10d, 11d, -2d };
double[] sample2 = { -1d, 12d, -1d, -3d, 3d, -5d, 5d, 2d, -11d, -1d, -3d };
SummaryStatistics sampleStats1 = new SummaryStatistics();
for (int i = 0; i < sample1.length; i++) {
sampleStats1.addValue(sample1[i]);
}
SummaryStatistics sampleStats2 = new SummaryStatistics();
for (int i = 0; i < sample2.length; i++) {
sampleStats2.addValue(sample2[i]);
}
// Target comparison values computed using R version 1.8.1 (Linux version)
Assert.assertEquals("two sample heteroscedastic t stat", 1.60371728768,
testStatistic.t(sample1, sample2), 1E-10);
Assert.assertEquals("two sample heteroscedastic t stat", 1.60371728768,
testStatistic.t(sampleStats1, sampleStats2), 1E-10);
Assert.assertEquals("two sample heteroscedastic p value", 0.128839369622,
testStatistic.tTest(sample1, sample2), 1E-10);
Assert.assertEquals("two sample heteroscedastic p value", 0.128839369622,
testStatistic.tTest(sampleStats1, sampleStats2), 1E-10);
Assert.assertTrue("two sample heteroscedastic t-test reject",
testStatistic.tTest(sample1, sample2, 0.2));
Assert.assertTrue("two sample heteroscedastic t-test reject",
testStatistic.tTest(sampleStats1, sampleStats2, 0.2));
Assert.assertTrue("two sample heteroscedastic t-test accept",
!testStatistic.tTest(sample1, sample2, 0.1));
Assert.assertTrue("two sample heteroscedastic t-test accept",
!testStatistic.tTest(sampleStats1, sampleStats2, 0.1));
try {
testStatistic.tTest(sample1, sample2, .95);
Assert.fail("alpha out of range, OutOfRangeException expected");
} catch (OutOfRangeException ex) {
// expected
}
try {
testStatistic.tTest(sampleStats1, sampleStats2, .95);
Assert.fail("alpha out of range, OutOfRangeException expected");
} catch (OutOfRangeException ex) {
// expected
}
try {
testStatistic.tTest(sample1, tooShortObs, .01);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.tTest(sampleStats1, tooShortStats, .01);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.tTest(sample1, tooShortObs);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.tTest(sampleStats1, tooShortStats);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.t(sample1, tooShortObs);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
try {
testStatistic.t(sampleStats1, tooShortStats);
Assert.fail("insufficient data, NumberIsTooSmallException expected");
} catch (NumberIsTooSmallException ex) {
// expected
}
}
@Test
public void testTwoSampleTHomoscedastic() {
double[] sample1 ={2, 4, 6, 8, 10, 97};
double[] sample2 = {4, 6, 8, 10, 16};
SummaryStatistics sampleStats1 = new SummaryStatistics();
for (int i = 0; i < sample1.length; i++) {
sampleStats1.addValue(sample1[i]);
}
SummaryStatistics sampleStats2 = new SummaryStatistics();
for (int i = 0; i < sample2.length; i++) {
sampleStats2.addValue(sample2[i]);
}
// Target comparison values computed using R version 1.8.1 (Linux version)
Assert.assertEquals("two sample homoscedastic t stat", 0.73096310086,
testStatistic.homoscedasticT(sample1, sample2), 10E-11);
Assert.assertEquals("two sample homoscedastic p value", 0.4833963785,
testStatistic.homoscedasticTTest(sampleStats1, sampleStats2), 1E-10);
Assert.assertTrue("two sample homoscedastic t-test reject",
testStatistic.homoscedasticTTest(sample1, sample2, 0.49));
Assert.assertTrue("two sample homoscedastic t-test accept",
!testStatistic.homoscedasticTTest(sample1, sample2, 0.48));
}
@Test
public void testSmallSamples() {
double[] sample1 = {1d, 3d};
double[] sample2 = {4d, 5d};
// Target values computed using R, version 1.8.1 (linux version)
Assert.assertEquals(-2.2360679775, testStatistic.t(sample1, sample2),
1E-10);
Assert.assertEquals(0.198727388935, testStatistic.tTest(sample1, sample2),
1E-10);
}
@Test
public void testPaired() {
double[] sample1 = {1d, 3d, 5d, 7d};
double[] sample2 = {0d, 6d, 11d, 2d};
double[] sample3 = {5d, 7d, 8d, 10d};
// Target values computed using R, version 1.8.1 (linux version)
Assert.assertEquals(-0.3133, testStatistic.pairedT(sample1, sample2), 1E-4);
Assert.assertEquals(0.774544295819, testStatistic.pairedTTest(sample1, sample2), 1E-10);
Assert.assertEquals(0.001208, testStatistic.pairedTTest(sample1, sample3), 1E-6);
Assert.assertFalse(testStatistic.pairedTTest(sample1, sample3, .001));
Assert.assertTrue(testStatistic.pairedTTest(sample1, sample3, .002));
}
}