/// <summary>
/// Creates a new object representation of a variation source in an ANOVA experiment.
/// </summary>
///
/// <param name="anova">The associated ANOVA analysis.</param>
/// <param name="source">The name of the variation source.</param>
/// <param name="degreesOfFreedom">The degrees of freedom for the source.</param>
/// <param name="sumOfSquares">The sum of squares of the source.</param>
/// <param name="test">The F-Test containing the F-Statistic for the source.</param>
///
public AnovaVariationSource(IAnova anova, string source, double sumOfSquares,
int degreesOfFreedom, FTest test)
{
this.anova = anova;
this.Source = source;
this.SumOfSquares = sumOfSquares;
this.DegreesOfFreedom = degreesOfFreedom;
this.Significance = test;
}
/// <summary>
/// Creates a new object representation of a variation source in an ANOVA experiment.
/// </summary>
///
/// <param name="anova">The associated ANOVA analysis.</param>
/// <param name="source">The name of the variation source.</param>
/// <param name="degreesOfFreedom">The degrees of freedom for the source.</param>
/// <param name="sumOfSquares">The sum of squares of the source.</param>
/// <param name="test">The F-Test containing the F-Statistic for the source.</param>
///
public AnovaVariationSource(IAnova anova, string source, double sumOfSquares,
int degreesOfFreedom, FTest test)
{
this.anova = anova;
this.Source = source;
this.SumOfSquares = sumOfSquares;
this.DegreesOfFreedom = degreesOfFreedom;
this.Significance = test;
}
private void initialize(double[][] samples)
{
DFb = groupCount - 1;
DFw = totalSize - groupCount;
DFt = totalSize - 1;
// Step 1. Calculate the mean within each group
means = Statistics.Tools.Mean(samples, 1);
// Step 2. Calculate the overall mean
totalMean = Statistics.Tools.GrandMean(means, sizes);
// Step 3. Calculate the "between-group" sum of squares
for (int i = 0; i < samples.Length; i++)
{
// between-group sum of squares
double u = (means[i] - totalMean);
SSb += sizes[i] * u * u;
}
// Step 4. Calculate the "within-group" sum of squares
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
double u = samples[i][j] - means[i];
SSw += u * u;
}
}
SSt = SSb + SSw; // total sum of squares
// Step 5. Calculate the F statistic
MSb = SSb / DFb; // between-group mean square
MSw = SSw / DFw; // within-group mean square
FTest = new FTest(MSb / MSw, DFb, DFw);
// Step 6. Create the ANOVA table
List <AnovaVariationSource> table = new List <AnovaVariationSource>();
table.Add(new AnovaVariationSource(this, "Between-Groups", SSb, DFb, FTest));
table.Add(new AnovaVariationSource(this, "Within-Groups", SSw, DFw, null));
table.Add(new AnovaVariationSource(this, "Total", SSt, DFt, null));
this.Table = new AnovaSourceCollection(table);
}
public void FTestConstructorTest2()
{
// The following example has been based on the page "F-Test for Equality
// of Two Variances", from NIST/SEMATECH e-Handbook of Statistical Methods:
//
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm
//
// Consider a data set containing 480 ceramic strength
// measurements for two batches of material. The summary
// statistics for each batch are shown below:
// BATCH 1:
int numberOfObservations1 = 240;
// double mean1 = 688.9987;
double stdDev1 = 65.54909;
double var1 = stdDev1 * stdDev1;
// BATCH 2:
int numberOfObservations2 = 240;
// double mean2 = 611.1559;
double stdDev2 = 61.85425;
double var2 = stdDev2 * stdDev2;
// Here, we will be testing the null hypothesis that
// the variances for the two batches are equal.
int degreesOfFreedom1 = numberOfObservations1 - 1;
int degreesOfFreedom2 = numberOfObservations2 - 1;
// Now we can create a F-Test to test the difference between variances
var ftest = new FTest(var1, var2, degreesOfFreedom1, degreesOfFreedom2);
double statistic = ftest.Statistic; // 1.123037
double pvalue = ftest.PValue; // 0.185191
bool significant = ftest.Significant; // false
// The F test indicates that there is not enough evidence
// to reject the null hypothesis that the two batch variances
// are equal at the 0.05 significance level.
Assert.AreEqual(1.1230374607443194, statistic);
Assert.AreEqual(0.18519157993853722, pvalue);
Assert.IsFalse(significant);
}
public void FTestConstructorTest()
{
double var1 = 1.05766555271071;
double var2 = 1.16570834301777;
int d1 = 49;
int d2 = 49;
FTest oneGreater = new FTest(var1, var2, d1, d2, TwoSampleHypothesis.FirstValueIsGreaterThanSecond);
FTest oneSmaller = new FTest(var1, var2, d1, d2, TwoSampleHypothesis.FirstValueIsSmallerThanSecond);
FTest twoTail = new FTest(var1, var2, d1, d2, TwoSampleHypothesis.ValuesAreDifferent);
Assert.AreEqual(0.632, oneGreater.PValue, 1e-3);
Assert.AreEqual(0.367, oneSmaller.PValue, 1e-3);
Assert.AreEqual(0.734, twoTail.PValue, 1e-3);
Assert.IsFalse(Double.IsNaN(oneGreater.PValue));
Assert.IsFalse(Double.IsNaN(oneSmaller.PValue));
Assert.IsFalse(Double.IsNaN(twoTail.PValue));
}
private void initialize(double[][] samples)
{
DFb = groupCount - 1;
DFw = totalSize - groupCount;
DFt = totalSize - 1;
// Step 1. Calculate the mean within each group
means = Statistics.Tools.Mean(samples, 1);
// Step 2. Calculate the overall mean
totalMean = Statistics.Tools.GrandMean(means, sizes);
// Step 3. Calculate the "between-group" sum of squares
for (int i = 0; i < samples.Length; i++)
{
// between-group sum of squares
double u = (means[i] - totalMean);
SSb += sizes[i] * u * u;
}
// Step 4. Calculate the "within-group" sum of squares
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
double u = samples[i][j] - means[i];
SSw += u * u;
}
}
SSt = SSb + SSw; // total sum of squares
// Step 5. Calculate the F statistic
MSb = SSb / DFb; // between-group mean square
MSw = SSw / DFw; // within-group mean square
FTest = new FTest(MSb / MSw, DFb, DFw);
// Step 6. Create the ANOVA table
List<AnovaVariationSource> table = new List<AnovaVariationSource>();
table.Add(new AnovaVariationSource(this, "Between-Groups", SSb, DFb, FTest));
table.Add(new AnovaVariationSource(this, "Within-Groups", SSw, DFw, null));
table.Add(new AnovaVariationSource(this, "Total", SSt, DFt, null));
this.Table = new AnovaSourceCollection(table);
}
private void initialize(double[][][] samples, TwoWayAnovaModel type)
{
// References:
// - http://www.smi.hst.aau.dk/~cdahl/BiostatPhD/ANOVA.pdf
ModelType = type;
Observations = FirstFactorSamples * SecondFactorSamples * Replications;
// Step 1. Initialize all degrees of freedom
int cellDegreesOfFreedom = FirstFactorSamples * SecondFactorSamples - 1;
int aDegreesOfFreedom = FirstFactorSamples - 1;
int bDegreesOfFreedom = SecondFactorSamples - 1;
int abDegreesOfFreedom = cellDegreesOfFreedom - aDegreesOfFreedom - bDegreesOfFreedom;
int errorDegreesOfFreedom = FirstFactorSamples * SecondFactorSamples * (Replications - 1);
int totalDegreesOfFreedom = Observations - 1;
// Step 1. Calculate cell means
cellMeans = new double[FirstFactorSamples, SecondFactorSamples];
double sum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
sum += cellMeans[i, j] = Measures.Mean(samples[i][j]);
}
}
// Step 2. Calculate the total mean (grand mean)
totalMean = sum / (FirstFactorSamples * SecondFactorSamples);
// Step 3. Calculate factor means
aMean = new double[FirstFactorSamples];
for (int i = 0; i < samples.Length; i++)
{
sum = 0;
for (int j = 0; j < samples[i].Length; j++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
sum += samples[i][j][k];
}
}
aMean[i] = sum / (SecondFactorSamples * Replications);
}
bMean = new double[SecondFactorSamples];
for (int j = 0; j < samples[0].Length; j++)
{
sum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
sum += samples[i][j][k];
}
}
bMean[j] = sum / (FirstFactorSamples * Replications);
}
// Step 4. Calculate total sum of squares
double ssum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
double u = samples[i][j][k] - totalMean;
ssum += u * u;
}
}
}
double totalSumOfSquares = ssum;
// Step 5. Calculate the cell sum of squares
ssum = 0;
for (int i = 0; i < FirstFactorSamples; i++)
{
for (int j = 0; j < SecondFactorSamples; j++)
{
double u = cellMeans[i, j] - totalMean;
ssum += u * u;
}
}
double cellSumOfSquares = ssum * Replications;
// Step 6. Compute within-cells error sum of squares
ssum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
double u = samples[i][j][k] - cellMeans[i, j];
ssum += u * u;
}
}
}
double errorSumOfSquares = ssum;
// Step 7. Compute factors sum of squares
ssum = 0;
for (int i = 0; i < aMean.Length; i++)
{
double u = aMean[i] - totalMean;
ssum += u * u;
}
double aSumOfSquares = ssum * SecondFactorSamples * Replications;
ssum = 0;
for (int i = 0; i < bMean.Length; i++)
{
double u = bMean[i] - totalMean;
ssum += u * u;
}
double bSumOfSquares = ssum * FirstFactorSamples * Replications;
// Step 9. Compute interaction sum of squares
double abSumOfSquares = cellSumOfSquares - aSumOfSquares - bSumOfSquares;
// Step 10. Compute mean squares
double aMeanSquares = aSumOfSquares / aDegreesOfFreedom;
double bMeanSquares = bSumOfSquares / bDegreesOfFreedom;
double abMeanSquares = abSumOfSquares / abDegreesOfFreedom;
double errorMeanSquares = errorSumOfSquares / errorDegreesOfFreedom;
// Step 10. Create the F-Statistics
FTest aSignificance, bSignificance, abSignificance;
if (type == TwoWayAnovaModel.Fixed)
{
// Model 1: Factors A and B fixed
aSignificance = new FTest(aMeanSquares / abMeanSquares, aDegreesOfFreedom, abDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / abMeanSquares, bDegreesOfFreedom, abDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else if (type == TwoWayAnovaModel.Mixed)
{
// Model 2: Factors A and B random
aSignificance = new FTest(aMeanSquares / errorMeanSquares, aDegreesOfFreedom, errorDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / errorMeanSquares, bDegreesOfFreedom, errorDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else if (type == TwoWayAnovaModel.Random)
{
// Model 3: Factor A fixed, factor B random
aSignificance = new FTest(aMeanSquares / abMeanSquares, aDegreesOfFreedom, abDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / errorMeanSquares, bDegreesOfFreedom, errorDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else
{
throw new ArgumentException("Unhandled analysis type.", "type");
}
// Step 11. Create the ANOVA table and sources
AnovaVariationSource cell = new AnovaVariationSource(this, "Cells", cellSumOfSquares, cellDegreesOfFreedom);
AnovaVariationSource a = new AnovaVariationSource(this, "Factor A", aSumOfSquares, aDegreesOfFreedom, aMeanSquares, aSignificance);
AnovaVariationSource b = new AnovaVariationSource(this, "Factor B", bSumOfSquares, bDegreesOfFreedom, bMeanSquares, bSignificance);
AnovaVariationSource ab = new AnovaVariationSource(this, "Interaction AxB", abSumOfSquares, abDegreesOfFreedom, abMeanSquares, abSignificance);
AnovaVariationSource error = new AnovaVariationSource(this, "Within-cells (error)", errorSumOfSquares, errorDegreesOfFreedom, errorMeanSquares);
AnovaVariationSource total = new AnovaVariationSource(this, "Total", totalSumOfSquares, totalDegreesOfFreedom);
this.Sources = new TwoWayAnovaVariationSources()
{
Cells = cell,
FactorA = a,
FactorB = b,
Interaction = ab,
Error = error,
Total = total
};
this.Table = new AnovaSourceCollection(cell, a, b, ab, error, total);
}
private void initialize(double[][][] samples, TwoWayAnovaModel type)
{
// References:
// - http://www.smi.hst.aau.dk/~cdahl/BiostatPhD/ANOVA.pdf
ModelType = type;
Observations = FirstFactorSamples * SecondFactorSamples * Replications;
// Step 1. Initialize all degrees of freedom
int cellDegreesOfFreedom = FirstFactorSamples * SecondFactorSamples - 1;
int aDegreesOfFreedom = FirstFactorSamples - 1;
int bDegreesOfFreedom = SecondFactorSamples - 1;
int abDegreesOfFreedom = cellDegreesOfFreedom - aDegreesOfFreedom - bDegreesOfFreedom;
int errorDegreesOfFreedom = FirstFactorSamples * SecondFactorSamples * (Replications - 1);
int totalDegreesOfFreedom = Observations - 1;
// Step 1. Calculate cell means
cellMeans = new double[FirstFactorSamples, SecondFactorSamples];
double sum = 0;
for (int i = 0; i < samples.Length; i++)
for (int j = 0; j < samples[i].Length; j++)
sum += cellMeans[i, j] = Measures.Mean(samples[i][j]);
// Step 2. Calculate the total mean (grand mean)
totalMean = sum / (FirstFactorSamples * SecondFactorSamples);
// Step 3. Calculate factor means
aMean = new double[FirstFactorSamples];
for (int i = 0; i < samples.Length; i++)
{
sum = 0;
for (int j = 0; j < samples[i].Length; j++)
for (int k = 0; k < samples[i][j].Length; k++)
sum += samples[i][j][k];
aMean[i] = sum / (SecondFactorSamples * Replications);
}
bMean = new double[SecondFactorSamples];
for (int j = 0; j < samples[0].Length; j++)
{
sum = 0;
for (int i = 0; i < samples.Length; i++)
for (int k = 0; k < samples[i][j].Length; k++)
sum += samples[i][j][k];
bMean[j] = sum / (FirstFactorSamples * Replications);
}
// Step 4. Calculate total sum of squares
double ssum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
double u = samples[i][j][k] - totalMean;
ssum += u * u;
}
}
}
double totalSumOfSquares = ssum;
// Step 5. Calculate the cell sum of squares
ssum = 0;
for (int i = 0; i < FirstFactorSamples; i++)
{
for (int j = 0; j < SecondFactorSamples; j++)
{
double u = cellMeans[i, j] - totalMean;
ssum += u * u;
}
}
double cellSumOfSquares = ssum * Replications;
// Step 6. Compute within-cells error sum of squares
ssum = 0;
for (int i = 0; i < samples.Length; i++)
{
for (int j = 0; j < samples[i].Length; j++)
{
for (int k = 0; k < samples[i][j].Length; k++)
{
double u = samples[i][j][k] - cellMeans[i, j];
ssum += u * u;
}
}
}
double errorSumOfSquares = ssum;
// Step 7. Compute factors sum of squares
ssum = 0;
for (int i = 0; i < aMean.Length; i++)
{
double u = aMean[i] - totalMean;
ssum += u * u;
}
double aSumOfSquares = ssum * SecondFactorSamples * Replications;
ssum = 0;
for (int i = 0; i < bMean.Length; i++)
{
double u = bMean[i] - totalMean;
ssum += u * u;
}
double bSumOfSquares = ssum * FirstFactorSamples * Replications;
// Step 9. Compute interaction sum of squares
double abSumOfSquares = cellSumOfSquares - aSumOfSquares - bSumOfSquares;
// Step 10. Compute mean squares
double aMeanSquares = aSumOfSquares / aDegreesOfFreedom;
double bMeanSquares = bSumOfSquares / bDegreesOfFreedom;
double abMeanSquares = abSumOfSquares / abDegreesOfFreedom;
double errorMeanSquares = errorSumOfSquares / errorDegreesOfFreedom;
// Step 10. Create the F-Statistics
FTest aSignificance, bSignificance, abSignificance;
if (type == TwoWayAnovaModel.Fixed)
{
// Model 1: Factors A and B fixed
aSignificance = new FTest(aMeanSquares / abMeanSquares, aDegreesOfFreedom, abDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / abMeanSquares, bDegreesOfFreedom, abDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else if (type == TwoWayAnovaModel.Mixed)
{
// Model 2: Factors A and B random
aSignificance = new FTest(aMeanSquares / errorMeanSquares, aDegreesOfFreedom, errorDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / errorMeanSquares, bDegreesOfFreedom, errorDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else if (type == TwoWayAnovaModel.Random)
{
// Model 3: Factor A fixed, factor B random
aSignificance = new FTest(aMeanSquares / abMeanSquares, aDegreesOfFreedom, abDegreesOfFreedom);
bSignificance = new FTest(bMeanSquares / errorMeanSquares, bDegreesOfFreedom, errorDegreesOfFreedom);
abSignificance = new FTest(abMeanSquares / errorMeanSquares, abDegreesOfFreedom, errorDegreesOfFreedom);
}
else throw new ArgumentException("Unhandled analysis type.","type");
// Step 11. Create the ANOVA table and sources
AnovaVariationSource cell = new AnovaVariationSource(this, "Cells", cellSumOfSquares, cellDegreesOfFreedom);
AnovaVariationSource a = new AnovaVariationSource(this, "Factor A", aSumOfSquares, aDegreesOfFreedom, aMeanSquares, aSignificance);
AnovaVariationSource b = new AnovaVariationSource(this, "Factor B", bSumOfSquares, bDegreesOfFreedom, bMeanSquares, bSignificance);
AnovaVariationSource ab = new AnovaVariationSource(this, "Interaction AxB", abSumOfSquares, abDegreesOfFreedom, abMeanSquares, abSignificance);
AnovaVariationSource error = new AnovaVariationSource(this, "Within-cells (error)", errorSumOfSquares, errorDegreesOfFreedom, errorMeanSquares);
AnovaVariationSource total = new AnovaVariationSource(this, "Total", totalSumOfSquares, totalDegreesOfFreedom);
this.Sources = new TwoWayAnovaVariationSources()
{
Cells = cell,
FactorA = a,
FactorB = b,
Interaction = ab,
Error = error,
Total = total
};
this.Table = new AnovaSourceCollection(cell, a, b, ab, error, total);
}
/// <summary>
/// Creates a new object representation of a variation source in an ANOVA experiment.
/// </summary>
///
/// <param name="anova">The associated ANOVA analysis.</param>
/// <param name="source">The name of the variation source.</param>
/// <param name="degreesOfFreedom">The degrees of freedom for the source.</param>
/// <param name="sumOfSquares">The sum of squares of the source.</param>
/// <param name="test">The F-Test containing the F-Statistic for the source.</param>
///
public AnovaVariationSource(IAnova anova, string source, double sumOfSquares,
int degreesOfFreedom, FTest test)
: this(anova, source, sumOfSquares, degreesOfFreedom, sumOfSquares / degreesOfFreedom, test) { }
/// <summary>
/// Creates a new object representation of a variation source in an ANOVA experiment.
/// </summary>
///
/// <param name="anova">The associated ANOVA analysis.</param>
/// <param name="source">The name of the variation source.</param>
/// <param name="degreesOfFreedom">The degrees of freedom for the source.</param>
/// <param name="sumOfSquares">The sum of squares of the source.</param>
/// <param name="test">The F-Test containing the F-Statistic for the source.</param>
///
public AnovaVariationSource(IAnova anova, string source, double sumOfSquares,
int degreesOfFreedom, FTest test)
: this(anova, source, sumOfSquares, degreesOfFreedom, sumOfSquares / degreesOfFreedom, test)
{
}
