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.
303 lines
10 KiB
C#
303 lines
10 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 System.Diagnostics;
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using Accord.Compat;
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/// <summary>
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/// Two sample Z-Test.
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/// </summary>
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///
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/// <remarks>
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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/Z-test">
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/// Wikipedia, The Free Encyclopedia. Z-Test. Available on:
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/// http://en.wikipedia.org/wiki/Z-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="ZTest"/>
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/// <seealso cref="TwoSampleTTest"/>
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/// <seealso cref="NormalDistribution"/>
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///
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[Serializable]
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public class TwoSampleZTest : HypothesisTest<NormalDistribution>
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{
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private TwoSampleZTestPowerAnalysis 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 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 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 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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/// Constructs a Z test.
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/// </summary>
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///
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/// <param name="sample1">The first data sample.</param>
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/// <param name="sample2">The second data sample.</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 TwoSampleZTest(double[] sample1, double[] sample2, double hypothesizedDifference = 0,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.ValuesAreDifferent)
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{
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int samples1 = sample1.Length;
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int samples2 = sample2.Length;
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if (samples1 < 30 || samples2 < 30)
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{
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Trace.TraceWarning("Warning: running a Z test for less than 30 samples. Consider running a Student's T Test instead.");
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}
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double mean1 = sample1.Mean();
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double mean2 = sample2.Mean();
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double var1 = sample1.Variance(mean: mean1);
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double var2 = sample2.Variance(mean: mean2);
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double sqStdError1 = var1 / sample1.Length;
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double sqStdError2 = var2 / sample2.Length;
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this.Compute(mean1, mean2, sqStdError1, sqStdError2, hypothesizedDifference, alternate);
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this.power(var1, var2, sample1.Length, sample2.Length);
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}
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/// <summary>
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/// Constructs a Z test.
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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="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 TwoSampleZTest(
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double mean1, double var1, int samples1,
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double mean2, double var2, int samples2,
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double hypothesizedDifference = 0,
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TwoSampleHypothesis alternate = TwoSampleHypothesis.ValuesAreDifferent)
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{
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if (samples1 < 30 || samples2 < 30)
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{
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Trace.TraceWarning("Warning: running a Z test for less than 30 samples. Consider running a Student's T Test instead.");
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}
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double sqStdError1 = var1 / samples1;
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double sqStdError2 = var2 / samples2;
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this.Compute(mean1, mean2, sqStdError1, sqStdError2, hypothesizedDifference, alternate);
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this.power(var1, var2, samples1, samples2);
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}
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/// <summary>
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/// Constructs a Z test.
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/// </summary>
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///
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protected TwoSampleZTest()
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{
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}
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/// <summary>
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/// Computes the Z test.
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/// </summary>
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///
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protected void Compute(double value1, double value2,
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double squareStdError1, double squareStdError2,
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double hypothesizedDifference, TwoSampleHypothesis alternate)
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{
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this.EstimatedValue1 = value1;
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this.EstimatedValue2 = value2;
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double diff = value1 - value2;
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double stdError = Math.Sqrt(squareStdError1 + squareStdError2);
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Compute(diff, hypothesizedDifference, stdError, alternate);
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}
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/// <summary>
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/// Computes the Z test.
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/// </summary>
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///
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protected void Compute(double observedDifference, double hypothesizedDifference,
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double standardError, TwoSampleHypothesis alternate)
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{
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this.ObservedDifference = observedDifference;
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this.HypothesizedDifference = hypothesizedDifference;
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this.StandardError = standardError;
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// Compute Z statistic
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double z = (ObservedDifference - HypothesizedDifference) / StandardError;
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Compute(z, alternate);
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}
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/// <summary>
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/// Computes the Z test.
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/// </summary>
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///
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protected void Compute(double statistic, TwoSampleHypothesis alternate)
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{
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this.Statistic = statistic;
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this.StatisticDistribution = NormalDistribution.Standard;
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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);
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powerAnalysis = new TwoSampleZTestPowerAnalysis(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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}
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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 ZTest.PValueToStatistic(p, 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 ZTest.StatisticToPValue(x, Tail);
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}
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}
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}
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