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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
235 lines
8.6 KiB
C#
235 lines
8.6 KiB
C#
// Accord Statistics Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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namespace Accord.Statistics.Testing
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{
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using System;
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using Accord.Statistics.Distributions.Univariate;
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using Accord.Compat;
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/// <summary>
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/// T-Test for two paired samples.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// The Paired T-test can be used when the samples are dependent; that is, when there
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/// is only one sample that has been tested twice (repeated measures) or when there are
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/// two samples that have been matched or "paired". This is an example of a paired difference
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/// test.</para>
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///
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/// <para>
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/// References:
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/// <list type="bullet">
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/// <item><description><a href="http://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples">
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/// Wikipedia, The Free Encyclopedia. Student's t-test.
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/// Available from: http://en.wikipedia.org/wiki/Student%27s_t-test#Dependent_t-test_for_paired_samples </a></description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <example>
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/// <para>
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/// Suppose we would like to know the effect of a treatment (such
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/// as a new drug) in improving the well-being of 9 patients. The
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/// well-being is measured in a discrete scale, going from 0 to 10.</para>
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/// <code>
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/// // To do so, we need to register the initial state of each patient
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/// // and then register their state after a given time under treatment.
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///
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/// double[,] patients =
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/// {
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/// // before after
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/// // treatment treatment
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/// /* Patient 1.*/ { 0, 1 },
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/// /* Patient 2.*/ { 6, 5 },
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/// /* Patient 3.*/ { 4, 9 },
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/// /* Patient 4.*/ { 8, 6 },
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/// /* Patient 5.*/ { 1, 6 },
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/// /* Patient 6.*/ { 6, 7 },
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/// /* Patient 7.*/ { 3, 4 },
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/// /* Patient 8.*/ { 8, 7 },
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/// /* Patient 9.*/ { 6, 5 },
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/// };
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///
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/// // Extract the before and after columns
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/// double[] before = patients.GetColumn(0);
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/// double[] after = patients.GetColumn(1);
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///
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/// // Create the paired-sample T-test. Our research hypothesis is
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/// // that the treatment does improve the patient's well-being. So
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/// // we will be testing the hypothesis that the well-being of the
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/// // "before" sample, the first sample, is "smaller" in comparison
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/// // to the "after" treatment group.
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///
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/// PairedTTest test = new PairedTTest(before, after,
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/// TwoSampleHypothesis.FirstValueIsSmallerThanSecond);
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///
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/// bool significant = test.Significant; // not significant
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/// double pvalue = test.PValue; // p-value = 0.1650
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/// double tstat = test.Statistic; // t-stat = -1.0371
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/// </code>
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/// </example>
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///
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/// <seealso cref="TDistribution"/>
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/// <seealso cref="TTest"/>
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///
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[Serializable]
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public class PairedTTest : HypothesisTest<TDistribution>
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{
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/// <summary>
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/// Gets the alternative hypothesis under test. If the test is
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/// <see cref="IHypothesisTest.Significant"/>, the null hypothesis can be rejected
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/// in favor of this alternative hypothesis.
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/// </summary>
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///
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public TwoSampleHypothesis Hypothesis { get; private set; }
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/// <summary>
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/// Gets the first sample's mean.
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/// </summary>
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///
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public double Mean1 { get; private set; }
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/// <summary>
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/// Gets the second sample's mean.
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/// </summary>
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///
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public double Mean2 { get; private set; }
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/// <summary>
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/// Gets the observed mean difference between the two samples.
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/// </summary>
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///
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public double ObservedDifference { get; private set; }
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/// <summary>
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/// Gets the standard error of the difference.
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/// </summary>
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///
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public double StandardError { get; private set; }
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/// <summary>
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/// Gets the size of a sample.
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/// Both samples have equal size.
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/// </summary>
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///
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public int SampleSize { get; private set; }
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/// <summary>
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/// Gets the 95% confidence interval for the
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/// <see cref="ObservedDifference"/> statistic.
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/// </summary>
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///
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public DoubleRange Confidence { get; protected set; }
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/// <summary>
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/// Gets a confidence interval for the <see cref="ObservedDifference"/>
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/// statistic within the given confidence level percentage.
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/// </summary>
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///
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/// <param name="percent">The confidence level. Default is 0.95.</param>
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///
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/// <returns>A confidence interval for the estimated value.</returns>
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///
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public DoubleRange GetConfidenceInterval(double percent = 0.95)
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{
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double u = PValueToStatistic(1.0 - percent);
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return new DoubleRange(
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ObservedDifference - u * StandardError,
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ObservedDifference + u * StandardError);
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}
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/// <summary>
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/// Creates a new paired t-test.
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/// </summary>
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///
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/// <param name="sample1">The observations in the first sample.</param>
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/// <param name="sample2">The observations in the second sample.</param>
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/// <param name="alternate">The alternative hypothesis (research hypothesis) to test.</param>
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///
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public PairedTTest(double[] sample1, double[] sample2,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.ValuesAreDifferent)
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{
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if (sample1.Length != sample2.Length)
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throw new DimensionMismatchException("sample2", "Paired samples must have the same size.");
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int n = sample1.Length;
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double[] delta = new double[sample1.Length];
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for (int i = 0; i < delta.Length; i++)
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delta[i] = sample1[i] - sample2[i];
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double mean = delta.Mean();
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double std = delta.StandardDeviation();
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StandardError = std / Math.Sqrt(n);
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ObservedDifference = mean;
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Mean1 = sample1.Mean();
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Mean2 = sample2.Mean();
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SampleSize = n;
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Statistic = ObservedDifference / StandardError;
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StatisticDistribution = new TDistribution(n - 1);
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this.Hypothesis = alternate;
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this.Tail = (DistributionTail)alternate;
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this.PValue = StatisticToPValue(Statistic);
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this.OnSizeChanged();
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}
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/// <summary>Update event.</summary>
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protected override void OnSizeChanged()
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{
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this.Confidence = GetConfidenceInterval(1.0 - Size);
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}
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/// <summary>
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/// Converts a given p-value to a test statistic.
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/// </summary>
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///
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/// <param name="p">The p-value.</param>
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///
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/// <returns>The test statistic which would generate the given p-value.</returns>
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///
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public override double PValueToStatistic(double p)
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{
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return TTest.PValueToStatistic(p, StatisticDistribution, Tail);
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}
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/// <summary>
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/// Converts a given test statistic to a p-value.
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/// </summary>
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///
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/// <param name="x">The value of the test statistic.</param>
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///
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/// <returns>The p-value for the given statistic.</returns>
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///
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public override double StatisticToPValue(double x)
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{
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return TTest.StatisticToPValue(x, StatisticDistribution, Tail);
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}
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}
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}
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