mirror of
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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.
247 lines
9.2 KiB
C#
247 lines
9.2 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 System.Diagnostics;
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using Accord.Compat;
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/// <summary>
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/// Snedecor's F-Test.
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/// </summary>
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///
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/// <remarks>
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/// <para>
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/// A F-test is any statistical test in which the test statistic has an
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/// <see cref="FDistribution">F-distribution</see> under the null hypothesis.
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/// It is most often used when comparing statistical models that have been fit
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/// to a data set, in order to identify the model that best fits the population
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/// from which the data were sampled.</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/F-test">
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/// Wikipedia, The Free Encyclopedia. F-Test. Available on:
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/// http://en.wikipedia.org/wiki/F-test </a></description></item>
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/// </list></para>
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/// </remarks>
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///
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/// <seealso cref="OneWayAnova"/>
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/// <seealso cref="TwoWayAnova"/>
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///
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/// <example>
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/// <code>
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/// // The following example has been based on the page "F-Test for Equality
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/// // of Two Variances", from NIST/SEMATECH e-Handbook of Statistical Methods:
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/// //
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/// // http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
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/// //
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///
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/// // Consider a data set containing 480 ceramic strength
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/// // measurements for two batches of material. The summary
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/// // statistics for each batch are shown below:
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///
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/// // Batch 1:
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/// int numberOfObservations1 = 240;
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/// // double mean1 = 688.9987;
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/// double stdDev1 = 65.54909;
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/// double var1 = stdDev1 * stdDev1;
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///
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/// // Batch 2:
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/// int numberOfObservations2 = 240;
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/// // double mean2 = 611.1559;
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/// double stdDev2 = 61.85425;
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/// double var2 = stdDev2 * stdDev2;
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///
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/// // Here, we will be testing the null hypothesis that
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/// // the variances for the two batches are equal.
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///
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/// int degreesOfFreedom1 = numberOfObservations1 - 1;
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/// int degreesOfFreedom2 = numberOfObservations2 - 1;
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///
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/// // Now we can create a F-Test to test the difference between variances
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/// var ftest = new FTest(var1, var2, degreesOfFreedom1, degreesOfFreedom2);
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///
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/// double statistic = ftest.Statistic; // 1.123037
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/// double pvalue = ftest.PValue; // 0.185191
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/// bool significant = ftest.Significant; // false
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///
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/// // The F test indicates that there is not enough evidence
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/// // to reject the null hypothesis that the two batch variances
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/// // are equal at the 0.05 significance level.
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/// </code>
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/// </example>
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///
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/// <seealso cref="Accord.Statistics.Distributions.Univariate.FDistribution"/>
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///
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[Serializable]
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public class FTest : HypothesisTest<FDistribution>
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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 degrees of freedom for the
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/// numerator in the test distribution.
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/// </summary>
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///
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public int DegreesOfFreedom1 { get { return StatisticDistribution.DegreesOfFreedom1; } }
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/// <summary>
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/// Gets the degrees of freedom for the
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/// denominator in the test distribution.
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/// </summary>
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///
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public int DegreesOfFreedom2 { get { return StatisticDistribution.DegreesOfFreedom2; } }
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/// <summary>
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/// Creates a new F-Test for a given statistic with given degrees of freedom.
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/// </summary>
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///
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/// <param name="var1">The variance of the first sample.</param>
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/// <param name="var2">The variance of the second sample.</param>
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/// <param name="d1">The degrees of freedom for the first sample.</param>
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/// <param name="d2">The degrees of freedom for 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 FTest(double var1, double var2, int d1, int d2,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.FirstValueIsGreaterThanSecond)
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{
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Compute(var1 / var2, d1, d2, alternate);
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}
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/// <summary>
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/// Creates a new F-Test for a given statistic with given degrees of freedom.
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/// </summary>
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///
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/// <param name="statistic">The test statistic.</param>
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/// <param name="d1">The degrees of freedom for the numerator.</param>
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/// <param name="d2">The degrees of freedom for the denominator.</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 FTest(double statistic, int d1, int d2,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.FirstValueIsGreaterThanSecond)
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{
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Compute(statistic, d1, d2, alternate);
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}
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/// <summary>
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/// Computes the F-test.
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/// </summary>
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///
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protected void Compute(double statistic, int d1, int d2, TwoSampleHypothesis alternate)
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{
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this.Statistic = statistic;
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this.StatisticDistribution = new FDistribution(d1, d2);
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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>
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/// Creates a new F-Test.
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/// </summary>
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///
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protected FTest()
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{
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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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if (Double.IsNaN(this.Statistic))
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{
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Trace.TraceWarning("The test statistic is NaN, probably because its standard error is zero. This test is not applicable in this case as the samples do " +
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"not come from a normal distribution. One way to overcome this problem may be to increase the number of samples in your experiment.");
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return Double.NaN;
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}
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double p;
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switch (Tail)
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{
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case DistributionTail.TwoTail:
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p = 2.0 * StatisticDistribution.DistributionFunction(Math.Abs(x));
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break;
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case DistributionTail.OneUpper:
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p = StatisticDistribution.ComplementaryDistributionFunction(x);
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break;
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case DistributionTail.OneLower:
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p = StatisticDistribution.DistributionFunction(x);
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break;
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default:
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throw new InvalidOperationException();
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}
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return p;
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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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double f;
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switch (Tail)
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{
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case DistributionTail.OneLower:
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f = StatisticDistribution.InverseDistributionFunction(p);
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break;
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case DistributionTail.OneUpper:
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f = StatisticDistribution.InverseDistributionFunction(1.0 - p);
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break;
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case DistributionTail.TwoTail:
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f = StatisticDistribution.InverseDistributionFunction(1.0 - p / 2.0);
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break;
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default:
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throw new InvalidOperationException();
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}
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return f;
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}
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}
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}
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