/// <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="meanSquares">The mean 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, double meanSquares, FTest test)
{
this.anova = anova;
this.Source = source;
this.SumOfSquares = sumOfSquares;
this.DegreesOfFreedom = degreesOfFreedom;
this.Significance = test;
this.MeanSquares = meanSquares;
}
private void initialize(double[][] samples)
{
DFb = groupCount - 1;
DFw = totalSize - groupCount;
DFt = totalSize - 1;
// Step 1. Calculate the mean within each group
means = BestCS.Statistics.Tools.Mean(samples, 1);
// Step 2. Calculate the overall mean
totalMean = BestCS.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] = BestCS.Statistics.Tools.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)
{
}
