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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.
259 lines
10 KiB
C#
259 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.Power
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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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/// Power analysis for one-sample Z-Tests.
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/// </summary>
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///
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/// <example>
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/// // When creating a power analysis, we have three things we can
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/// // change. We can always freely configure two of those things
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/// // and then ask the analysis to give us the third.
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///
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/// var analysis = new ZTestPowerAnalysis(OneSampleHypothesis.ValueIsDifferentFromHypothesis);
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///
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/// // Those are:
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/// double e = analysis.Effect; // the test's minimum detectable effect size
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/// double n = analysis.Samples; // the number of samples in the test
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/// double p = analysis.Power; // the probability of committing a type-2 error
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///
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/// // Let's set the desired effect size and the
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/// // number of samples so we can get the power
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///
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/// analysis.Effect = 0.2; // we would like to detect at least 0.2 std. dev. apart
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/// analysis.Samples = 60; // we would like to use at most 60 samples
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/// analysis.ComputePower(); // what will be the power of this test?
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///
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/// double power = analysis.Power; // The power is going to be 0.34 (or 34%)
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///
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/// // Let's set the desired power and the number
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/// // of samples so we can get the effect size
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///
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/// analysis.Power = 0.8; // we would like to create a test with 80% power
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/// analysis.Samples = 60; // we would like to use at most 60 samples
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/// analysis.ComputeEffect(); // what would be the minimum effect size we can detect?
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///
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/// double effect = analysis.Effect; // The effect will be 0.36 standard deviations.
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///
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/// // Let's set the desired power and the effect
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/// // size so we can get the number of samples
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///
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/// analysis.Power = 0.8; // we would like to create a test with 80% power
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/// analysis.Effect = 0.2; // we would like to detect at least 0.2 std. dev. apart
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/// analysis.ComputeSamples();
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///
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/// double samples = analysis.Samples; // We would need around 197 samples.
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/// </example>
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///
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/// <seealso cref="ZTest"/>
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/// <seealso cref="TwoSampleZTestPowerAnalysis"/>
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/// <seealso cref="TTestPowerAnalysis"/>
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///
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[Serializable]
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public class ZTestPowerAnalysis : BaseOneSamplePowerAnalysis
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{
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/// <summary>
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/// Creates a new <see cref="ZTestPowerAnalysis"/>.
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/// </summary>
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///
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/// <param name="hypothesis">The hypothesis tested.</param>
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///
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public ZTestPowerAnalysis(OneSampleHypothesis hypothesis)
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: base((DistributionTail)hypothesis)
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{
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}
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/// <summary>
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/// Creates a new <see cref="ZTestPowerAnalysis"/>.
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/// </summary>
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///
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/// <param name="test">The test to create the analysis for.</param>
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///
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public ZTestPowerAnalysis(TwoSampleZTest test)
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: base(test.Tail)
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{
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this.Power = test.Analysis.Power;
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this.Size = test.Analysis.Size;
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this.Effect = test.Analysis.Effect;
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this.Samples = test.Analysis.Samples;
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}
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/// <summary>
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/// Computes the power for a test with givens values of
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/// <see cref="IPowerAnalysis.Effect">effect size</see> and <see cref="IPowerAnalysis.Samples">
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/// number of samples</see> under <see cref="IPowerAnalysis.Size"/>.
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/// </summary>
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///
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/// <returns>
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/// The power for the test under the given conditions.
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/// </returns>
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///
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public override void ComputePower()
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{
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switch (Tail)
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{
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case DistributionTail.TwoTail:
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{
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double Za = NormalDistribution.Standard.InverseDistributionFunction(1.0 - Size / 2.0);
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double Zb = Za - Math.Sqrt(Samples) * Effect;
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Power = NormalDistribution.Standard.ComplementaryDistributionFunction(Zb);
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break;
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}
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case DistributionTail.OneLower:
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{
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double Za = NormalDistribution.Standard.InverseDistributionFunction(Size);
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double Zb = Za - Math.Sqrt(Samples) * Effect;
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double beta = NormalDistribution.Standard.ComplementaryDistributionFunction(Zb);
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Power = 1.0 - beta;
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break;
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}
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case DistributionTail.OneUpper:
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{
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double Za = NormalDistribution.Standard.InverseDistributionFunction(1.0 - Size);
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double Zb = Za - Math.Sqrt(Samples) * Effect;
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Power = NormalDistribution.Standard.ComplementaryDistributionFunction(Zb);
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break;
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}
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default:
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throw new InvalidOperationException();
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}
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}
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/// <summary>
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/// Gets the recommended sample size for the test to attain
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/// the power indicating in <see cref="IPowerAnalysis.Power"/> considering
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/// values of <see cref="IPowerAnalysis.Effect"/> and <see cref="IPowerAnalysis.Size"/>.
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/// </summary>
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///
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/// <returns>
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/// Recommended sample size for attaining the given
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/// <see cref="IPowerAnalysis.Power"/> for size effect <see cref="IPowerAnalysis.Effect"/>
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/// under the given <see cref="IPowerAnalysis.Size"/>.
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/// </returns>
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///
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public override void ComputeSamples()
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{
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double Za = ZTest.PValueToStatistic(Size, Tail);
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double Zb = NormalDistribution.Standard
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.InverseDistributionFunction(Power);
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double n = (Za + Zb) / Effect;
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Samples = n * n;
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}
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/// <summary>
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/// Computes the minimum detectable effect size for the test
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/// considering the power given in <see cref="IPowerAnalysis.Power"/>, the
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/// number of samples in <see cref="IPowerAnalysis.Samples"/> and the significance
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/// level <see cref="IPowerAnalysis.Size"/>.
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/// </summary>
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///
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/// <returns>
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/// The minimum detectable <see cref="IPowerAnalysis.Effect">effect
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/// size</see> for the test under the given conditions.
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/// </returns>
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///
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public override void ComputeEffect()
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{
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double Za = ZTest.PValueToStatistic(Size, Tail);
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double Zb = NormalDistribution.Standard
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.InverseDistributionFunction(Power);
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double n = Math.Sqrt(Samples);
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double d = (Za + Zb) / n;
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Effect = d;
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}
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/// <summary>
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/// Estimates the number of samples necessary to attain the
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/// required power level for the given effect size.
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/// </summary>
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///
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/// <param name="delta">The minimum detectable difference.</param>
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/// <param name="standardDeviation">The difference standard deviation.</param>
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/// <param name="power">The desired power level. Default is 0.8.</param>
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/// <param name="alpha">The desired significance level. Default is 0.05.</param>
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/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
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///
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/// <returns>The required number of samples.</returns>
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///
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public static ZTestPowerAnalysis GetSampleSize(double delta,
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double standardDeviation = 1, double power = 0.8, double alpha = 0.05,
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OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
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{
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ZTestPowerAnalysis analysis = new ZTestPowerAnalysis(hypothesis)
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{
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Effect = (delta) / standardDeviation,
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Size = alpha,
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Power = power,
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};
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analysis.ComputeSamples();
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return analysis;
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}
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/// <summary>
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/// Estimates the number of samples necessary to attain the
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/// required power level for the given effect size.
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/// </summary>
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///
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/// <param name="sampleSize">The number of observations in the sample.</param>
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/// <param name="power">The desired power level. Default is 0.8.</param>
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/// <param name="alpha">The desired significance level. Default is 0.05.</param>
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/// <param name="hypothesis">The alternative hypothesis (research hypothesis) to be tested.</param>
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///
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/// <returns>The required number of samples.</returns>
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///
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public static ZTestPowerAnalysis GetEffectSize(int sampleSize, double power = 0.8, double alpha = 0.05,
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OneSampleHypothesis hypothesis = OneSampleHypothesis.ValueIsDifferentFromHypothesis)
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{
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var analysis = new ZTestPowerAnalysis(hypothesis)
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{
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Samples = sampleSize,
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Size = alpha,
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Power = power,
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};
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analysis.ComputeEffect();
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return analysis;
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}
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}
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}
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