public void TwoWayAnovaConstructorTest2()
{
// Example by Aalborg Universitet
// http://www.smi.hst.aau.dk/~cdahl/BiostatPhD/ANOVA.pdf
double[] samples =
{
16.3, 20.4, 12.4, 15.8, 9.5, // female, no hormone
15.3, 17.4, 10.9, 10.3, 6.7, // male, no hormone
38.1, 26.2, 32.3, 35.8, 30.2, // female, hormone
34.0, 22.8, 27.8, 25.0, 29.3, // male, hormone
};
int[] hormone =
{
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1
};
int[] sex =
{
0, 0, 0, 0, 0, 1, 1, 1, 1, 1,
0, 0, 0, 0, 0, 1, 1, 1, 1, 1
};
TwoWayAnova target = new TwoWayAnova(samples, hormone, sex, TwoWayAnovaModel.Mixed);
testSources(target);
}
public void TwoWayAnovaConstructorTest()
{
// Example by Aalborg Universitet
// http://www.smi.hst.aau.dk/~cdahl/BiostatPhD/ANOVA.pdf
double[][][] samples =
{
new double[][] // No hormone treatment
{
// Female
new double[] { 16.3, 20.4, 12.4, 15.8, 9.5 },
// Male
new double[] { 15.3, 17.4, 10.9, 10.3, 6.7 }
},
new double[][] // Hormone treatment
{
// Female
new double[] { 38.1, 26.2, 32.3, 35.8, 30.2 },
// Male
new double[] { 34.0, 22.8, 27.8, 25.0, 29.3 }
}
};
TwoWayAnova target = new TwoWayAnova(samples, TwoWayAnovaModel.Mixed);
testSources(target);
}
private static void testSources(TwoWayAnova target)
{
AnovaVariationSource cells = target.Sources.Cells;
Assert.AreEqual("Cells", cells.Source);
Assert.AreEqual(1461.3254999999995, cells.SumOfSquares);
Assert.AreEqual(3, cells.DegreesOfFreedom);
Assert.IsTrue(target.Table.Contains(cells));
AnovaVariationSource error = target.Sources.Error;
Assert.AreEqual("Within-cells (error)", error.Source);
Assert.AreEqual(301.39200000000005, error.SumOfSquares);
Assert.AreEqual(16, error.DegreesOfFreedom);
Assert.IsTrue(target.Table.Contains(error));
AnovaVariationSource factorA = target.Sources.FactorA;
Assert.AreEqual("Factor A", factorA.Source);
Assert.AreEqual(1386.1125, factorA.SumOfSquares, 1e-4);
Assert.AreEqual(1, factorA.DegreesOfFreedom);
Assert.AreEqual(1386.1125, factorA.MeanSquares, 1e-4);
Assert.AreEqual(73.58, factorA.Significance.Statistic, 1e-2);
Assert.AreEqual(1, factorA.Significance.DegreesOfFreedom1);
Assert.AreEqual(16, factorA.Significance.DegreesOfFreedom2);
Assert.IsTrue(factorA.Significance.Significant);
AnovaVariationSource factorB = target.Sources.FactorB;
Assert.AreEqual("Factor B", factorB.Source);
Assert.AreEqual(70.3125, factorB.SumOfSquares, 1e-4);
Assert.AreEqual(1, factorB.DegreesOfFreedom);
Assert.AreEqual(70.3125, factorB.MeanSquares, 1e-4);
Assert.AreEqual(3.73, factorB.Significance.Statistic, 1e-2);
Assert.AreEqual(1, factorB.Significance.DegreesOfFreedom1);
Assert.AreEqual(16, factorB.Significance.DegreesOfFreedom2);
Assert.IsFalse(factorB.Significance.Significant);
AnovaVariationSource interaction = target.Sources.Interaction;
Assert.AreEqual("Interaction AxB", interaction.Source);
Assert.AreEqual(4.9005, interaction.SumOfSquares, 1e-4);
Assert.AreEqual(1, interaction.DegreesOfFreedom);
Assert.AreEqual(4.9005, interaction.MeanSquares, 1e-4);
Assert.AreEqual(0.260, interaction.Significance.Statistic, 1e-3);
Assert.AreEqual(1, interaction.Significance.DegreesOfFreedom1);
Assert.AreEqual(16, interaction.Significance.DegreesOfFreedom2);
Assert.IsFalse(interaction.Significance.Significant);
}
public void TwoWayAnovaConstructorTest()
{
// Example by Aalborg Universitet, slide 22:
// http://www.smi.hst.aau.dk/~cdahl/BiostatPhD/ANOVA.pdf
// There are three set of hypothesis in atwo-way ANOVA. In the example above, they are:
// - H0: There is no effect of hormone treatment on the mean plasma concentration
// - H0: There is no difference in mean plasma concentration between sexes
// - H0: There is no interaction of sex and hormone treatment on the mean plasma concentration
double[][][] samples =
{
new double[][] // No hormone treatment
{
// Female
new double[] { 16.3, 20.4, 12.4, 15.8, 9.5 },
// Male
new double[] { 15.3, 17.4, 10.9, 10.3, 6.7 }
},
new double[][] // Hormone treatment
{
// Female
new double[] { 38.1, 26.2, 32.3, 35.8, 30.2 },
// Male
new double[] { 34.0, 22.8, 27.8, 25.0, 29.3 }
}
};
// Let's create a mixed-effect effects ANOVA model (ANOVA model 3)
var twoWayAnova = new TwoWayAnova(samples, TwoWayAnovaModel.Mixed);
testSources(twoWayAnova);
}
public void doc_test()
{
#region doc_test
// Example by J. Jones, Professor of Mathematics in Richland Community
// College: https://people.richland.edu/james/lecture/m170/ch13-2wy.html
// In this example, we collected the number of successfully grown corn plants
// given the use of 4 types of fertilizer, and 3 different types of seed.
double[,,] samples =
{
// Fert I Fert II Fert III Fert IV Fert V
/* Seed A-402 */ { { 106, 110 }, { 95, 100 }, { 94, 107 }, { 103, 104 }, { 100, 102 } },
/* Seed B-894 */ { { 110, 112 }, { 98, 99 }, { 100, 101 }, { 108, 112 }, { 105, 107 } },
/* Seed C-952 */ { { 94, 97 }, { 86, 87 }, { 98, 99 }, { 99, 101 }, { 94, 98 } },
};
// There are always three hypothesis in a 2-way ANOVA:
// - There is no difference between population means for the first factor;
// - There is no difference between population means for the second factor;
// - There is no interaction between the two different factors
// Let's create a mixed-effect effects ANOVA model (ANOVA model 3)
var twoWayAnova = new TwoWayAnova(samples, TwoWayAnovaModel.Mixed);
// Now, we can obtain the test summary table by using:
TwoWayAnovaVariationSources sources = twoWayAnova.Sources;
// Seed source of variation
double seedSS = sources.FactorA.SumOfSquares; // 512.86666666666713
double seedDF = sources.FactorA.DegreesOfFreedom; // 2
double seedMS = sources.FactorA.MeanSquares; // 256.43333333333356
double seedF = sources.FactorA.Statistic.Value; // 28.283088235294144
double seedPValue = sources.FactorA.Significance.PValue; // 8.1353422904297046E-06
double seedCrit = sources.FactorA.Significance.CriticalValue; // 3.6823203436732341
bool seedSignificant = sources.FactorA.Significance.Significant; // true
// Fertilizer source of variation
double fertilizerSS = sources.FactorB.SumOfSquares; // 449.46666666666607
double fertilizerDF = sources.FactorB.DegreesOfFreedom; // 4
double fertilizerMS = sources.FactorB.MeanSquares; // 112.36666666666652
double fertilizerF = sources.FactorB.Statistic.Value; // 12.39338235294116
double fertilizerPValue = sources.FactorB.Significance.PValue; // 0.00011887234971294213
double fertilizerCrit = sources.FactorB.Significance.CriticalValue; // 3.0555682759065936
bool fertilizerSignificant = sources.FactorB.Significance.Significant; // true
// Interaction source of variation
double interactionSS = sources.Interaction.SumOfSquares; // 143.1333333333335
double interactionDF = sources.Interaction.DegreesOfFreedom; // 8
double interactionMS = sources.Interaction.MeanSquares; // 17.891666666666687
double interactionF = sources.Interaction.Statistic.Value; // 1.9733455882352964
double interactionPValue = sources.Interaction.Significance.PValue; // 0.12208995001760085
double interactionCrit = sources.Interaction.Significance.CriticalValue; // 2.6407968829069017
bool interactionSignificant = sources.Interaction.Significance.Significant; // false
// Within-variance source of variation
double withinSS = sources.Error.SumOfSquares; // 136
double withinDF = sources.Error.DegreesOfFreedom; // 15
double withinMS = sources.Error.MeanSquares; // 9.0666666666666664
#endregion
Assert.AreEqual(512.86666666666713, seedSS, 1e-8);
Assert.AreEqual(2, seedDF, 1e-8);
Assert.AreEqual(256.43333333333356, seedMS, 1e-8);
Assert.AreEqual(28.283088235294144, seedF, 1e-8);
Assert.AreEqual(8.1353422904297046E-06, seedPValue, 1e-8);
Assert.AreEqual(3.6823203436732341, seedCrit, 1e-8);
Assert.AreEqual(true, seedSignificant);
Assert.AreEqual(449.46666666666607, fertilizerSS, 1e-8);
Assert.AreEqual(4, fertilizerDF, 1e-8);
Assert.AreEqual(112.36666666666652, fertilizerMS, 1e-8);
Assert.AreEqual(12.39338235294116, fertilizerF, 1e-8);
Assert.AreEqual(0.00011887234971294213, fertilizerPValue, 1e-8);
Assert.AreEqual(3.0555682759065936, fertilizerCrit, 1e-8);
Assert.AreEqual(true, fertilizerSignificant);
Assert.AreEqual(143.1333333333335, interactionSS, 1e-8);
Assert.AreEqual(8, interactionDF, 1e-8);
Assert.AreEqual(17.891666666666687, interactionMS, 1e-8);
Assert.AreEqual(1.9733455882352964, interactionF, 1e-8);
Assert.AreEqual(0.12208995001760085, interactionPValue, 1e-8);
Assert.AreEqual(2.6407968829069017, interactionCrit, 1e-8);
Assert.AreEqual(false, interactionSignificant);
Assert.AreEqual(136, withinSS, 1e-8);
Assert.AreEqual(15, withinDF, 1e-8);
Assert.AreEqual(9.0666666666666664, withinMS, 1e-8);
}
