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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.
319 lines
12 KiB
C#
319 lines
12 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.Statistics.Testing.Power;
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using Accord.Compat;
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/// <summary>
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/// Two-sample Student's T test.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// The two-sample t-test assesses whether the means of two groups are statistically
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/// different from each other.</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's_t-test">
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/// Wikipedia, The Free Encyclopedia. Student's T-Test. </a></description></item>
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/// <item><description><a href="http://www.le.ac.uk/bl/gat/virtualfc/Stats/ttest.html">
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/// William M.K. Trochim. The T-Test. Research methods Knowledge Base, 2009.
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/// Available on: http://www.le.ac.uk/bl/gat/virtualfc/Stats/ttest.html </a></description></item>
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/// <item><description><a href="http://en.wikipedia.org/wiki/One-way_ANOVA">
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/// Graeme D. Ruxton. The unequal variance t-test is an underused alternative to Student's
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/// t-test and the Mann–Whitney U test. Oxford Journals, Behavioral Ecology Volume 17, Issue 4, pp.
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/// 688-690. 2006. Available on: http://beheco.oxfordjournals.org/content/17/4/688.full </a></description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <seealso cref="TTest"/>
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/// <seealso cref="TDistribution"/>
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///
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[Serializable]
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public class TwoSampleTTest : HypothesisTest<TDistribution>
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{
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private TwoSampleTTestPowerAnalysis powerAnalysis;
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/// <summary>
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/// Gets the power analysis for the test, if available.
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/// </summary>
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///
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public ITwoSamplePowerAnalysis Analysis { get { return powerAnalysis; } }
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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 whether the test assumes equal sample variance.
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/// </summary>
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///
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public bool AssumeEqualVariance { get; private set; }
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/// <summary>
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/// Gets the standard error for the difference.
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/// </summary>
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///
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public double StandardError { get; protected set; }
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/// <summary>
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/// Gets the combined sample variance.
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/// </summary>
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///
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public double Variance { get; protected set; }
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/// <summary>
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/// Gets the estimated value for the first sample.
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/// </summary>
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///
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public double EstimatedValue1 { get; protected set; }
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/// <summary>
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/// Gets the estimated value for the second sample.
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/// </summary>
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///
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public double EstimatedValue2 { get; protected set; }
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/// <summary>
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/// Gets the hypothesized difference between the two estimated values.
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/// </summary>
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///
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public double HypothesizedDifference { get; protected set; }
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/// <summary>
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/// Gets the actual difference between the two estimated values.
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/// </summary>
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public double ObservedDifference { get; protected set; }
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/// <summary>
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/// Gets the degrees of freedom for the test statistic.
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/// </summary>
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///
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public double DegreesOfFreedom { get { return StatisticDistribution.DegreesOfFreedom; } }
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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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/// Tests whether the means of two samples are different.
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/// </summary>
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///
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/// <param name="sample1">The first sample.</param>
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/// <param name="sample2">The second sample.</param>
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/// <param name="hypothesizedDifference">The hypothesized sample difference.</param>
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/// <param name="assumeEqualVariances">True to assume equal variances, false otherwise. Default is true.</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 TwoSampleTTest(double[] sample1, double[] sample2,
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bool assumeEqualVariances = true, double hypothesizedDifference = 0,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.ValuesAreDifferent)
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{
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// References: http://en.wikipedia.org/wiki/Student's_t-test#Worked_examples
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double x1 = sample1.Mean();
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double x2 = sample2.Mean();
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double s1 = sample1.Variance();
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double s2 = sample2.Variance();
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int n1 = sample1.Length;
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int n2 = sample2.Length;
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Compute(x1, s1, n1, x2, s2, n2,
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hypothesizedDifference, assumeEqualVariances, alternate);
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power(s1, s2, sample1.Length, sample2.Length);
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}
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/// <summary>
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/// Tests whether the means of two samples are different.
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/// </summary>
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///
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/// <param name="mean1">The first sample's mean.</param>
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/// <param name="mean2">The second sample's mean.</param>
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/// <param name="var1">The first sample's variance.</param>
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/// <param name="var2">The second sample's variance.</param>
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/// <param name="samples1">The number of observations in the first sample.</param>
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/// <param name="samples2">The number of observations in the second sample.</param>
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/// <param name="assumeEqualVariances">True assume equal variances, false otherwise. Default is true.</param>
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/// <param name="hypothesizedDifference">The hypothesized sample difference.</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 TwoSampleTTest(double mean1, double var1, int samples1, double mean2, double var2, int samples2,
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bool assumeEqualVariances = true, double hypothesizedDifference = 0,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.ValuesAreDifferent)
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{
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Compute(mean1, var1, samples1, mean2, var2, samples2,
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hypothesizedDifference, assumeEqualVariances, alternate);
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power(var1, var2, samples1, samples2);
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}
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/// <summary>
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/// Creates a new two-sample T-Test.
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/// </summary>
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protected TwoSampleTTest()
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{
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}
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/// <summary>
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/// Computes the T Test.
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/// </summary>
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///
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protected void Compute(
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double x1, double s1, int n1,
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double x2, double s2, int n2,
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double hypothesizedDifference, bool equalVar,
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TwoSampleHypothesis alternate)
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{
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double df;
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this.AssumeEqualVariance = equalVar;
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this.EstimatedValue1 = x1;
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this.EstimatedValue2 = x2;
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if (AssumeEqualVariance)
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{
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// Assume the two samples share the same underlying population variance.
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Variance = ((n1 - 1) * s1 + (n2 - 1) * s2) / (n1 + n2 - 2);
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StandardError = Math.Sqrt(Variance) * Math.Sqrt(1.0 / n1 + 1.0 / n2);
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df = n1 + n2 - 2;
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}
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else
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{
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// Assume samples have unequal variances.
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StandardError = Math.Sqrt(s1 / n1 + s2 / n2);
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Variance = (s1 + s2) / 2.0;
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double r1 = s1 / n1;
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double r2 = s2 / n2;
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df = ((r1 + r2) * (r1 + r2)) / ((r1 * r1) / (n1 - 1) + (r2 * r2) / (n2 - 1));
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}
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this.ObservedDifference = (x1 - x2);
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this.HypothesizedDifference = hypothesizedDifference;
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this.Statistic = (ObservedDifference - HypothesizedDifference) / StandardError;
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this.StatisticDistribution = new TDistribution(df);
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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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private void power(double var1, double var2, int n1, int n2)
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{
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double stdDev = Math.Sqrt((var1 + var2) / 2.0);
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powerAnalysis = new TwoSampleTTestPowerAnalysis(Hypothesis)
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{
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Samples1 = n1,
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Samples2 = n2,
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Effect = (ObservedDifference - HypothesizedDifference) / stdDev,
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Size = Size,
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};
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powerAnalysis.ComputePower();
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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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if (Analysis != null)
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{
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powerAnalysis.Size = Size;
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powerAnalysis.ComputePower();
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}
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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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} |