public override double Test(IList <IList <double> > samples)
{
double total_count = ToolsCollection.CountElements(samples);
double pooled_mean = ToolsMathStatistics.MeanAll(samples);
double nominator_part = 0.0;
double denominator_part = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
double sample_mean = ToolsMathStatistics.Mean(samples[sample_index]);
double sample_median = ToolsMathStatistics.Quantile(samples[sample_index], 0.5f);
nominator_part += (sample_mean - pooled_mean) * (sample_mean - pooled_mean) * samples[sample_index].Count;
for (int measurement_index = 0; measurement_index < samples[sample_index].Count; measurement_index++)
{
double diff = Math.Abs(sample_median - samples[sample_index][measurement_index]) - sample_mean; //This is the difference with brown forsythe test
denominator_part += diff * diff;
}
}
double degrees_of_freedom_0 = samples.Count - 1;
double degrees_of_freedom_1 = total_count - samples.Count;
double f_statistic = (degrees_of_freedom_1 * nominator_part) / (degrees_of_freedom_0 * denominator_part);
FisherSnedecor distribution = new FisherSnedecor(degrees_of_freedom_0, degrees_of_freedom_1, new Random());
return(distribution.CumulativeDistribution(f_statistic));
}
public static Tuple <double, double> TestStatic(IList <IList <double> > samples)
{
int sample_size = samples[0].Count;
foreach (IList <double> sample in samples)
{
if (sample.Count != sample_size)
{
throw new Exception("samples must be of equal size");
}
}
// Larsen Marx 4Th editiopn P779
double sample_count = samples.Count;
double total_count = ToolsCollection.CountElements(samples);
double total_mean = ToolsMathStatistics.MeanAll(samples);
double sum_squared_all = ToolsMathStatistics.SumSquaredAll(samples);
IList <double> sample_sums = ToolsMathCollection.Sums0(samples);
IList <double> measurement_sums = ToolsMathCollection.Sums1(samples);
// compute C
double c = ToolsMath.Sqr(total_mean * total_count) / (sample_size * sample_count);
double sstot = sum_squared_all - c;
double ssb = 0;
for (int measurement_index = 0; measurement_index < sample_size; measurement_index++)
{
ssb += ToolsMath.Sqr(measurement_sums[measurement_index]) / sample_count;
}
ssb -= c;
double sstr = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
sstr += ToolsMath.Sqr(sample_sums[sample_index]) / sample_size;
}
sstr -= c;
double sse = sstot - ssb - sstr;
double degrees_of_freedom_0_samples = (sample_count - 1.0);
double degrees_of_freedom_0_measurements = (sample_size - 1.0);
double degrees_of_freedom_1 = degrees_of_freedom_0_samples * degrees_of_freedom_0_measurements;
//F-Transform samples
double f_statistic_samples = (sstr / degrees_of_freedom_0_samples) / (sse / degrees_of_freedom_1);
//F-Transform measurements
double f_statistic_measurements = (ssb / degrees_of_freedom_0_measurements) / (sse / degrees_of_freedom_1);
return(new Tuple <double, double>(
FisherSnedecor.CDF(degrees_of_freedom_0_samples, degrees_of_freedom_1, f_statistic_samples),
FisherSnedecor.CDF(degrees_of_freedom_0_measurements, degrees_of_freedom_1, f_statistic_measurements)));
}
public static double TestStatic(IList <IList <double> > samples)
{
double sample_count = samples.Count;
double total_count = ToolsCollection.CountElements(samples);
double total_mean = ToolsMathStatistics.MeanAll(samples);
IList <double> sample_means = ToolsMathStatistics.Means0(samples);
double sstr = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
sstr += samples[sample_index].Count * ToolsMath.Sqr(sample_means[sample_index] - total_mean);
}
double sse = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
for (int measurement_index = 0; measurement_index < samples[sample_index].Count; measurement_index++)
{
sse += ToolsMath.Sqr(samples[sample_index][measurement_index] - sample_means[sample_index]);
}
}
//FTransform
double degrees_of_freedom_0 = (sample_count - 1.0);
double degrees_of_freedom_1 = (total_count - sample_count);
double summed_variance = sstr / degrees_of_freedom_0;
double total_varaiance = sse / degrees_of_freedom_1;
double f_statistic = summed_variance / total_varaiance;
return(FisherSnedecor.CDF(degrees_of_freedom_0, degrees_of_freedom_1, f_statistic));
}
//TODO implement 3 mean variants
//http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
public static double TestStatic(IList <IList <double> > samples)
{
double total_count = ToolsCollection.CountElements(samples);
double total_mean = ToolsMathStatistics.MeanAll(samples);
//double[] sample_means = ToolsMathStatistics.Means0(samples);
//double total_mean = ToolsMathStatistics.MedianAll(samples);
double[] sample_means = ToolsMathStatistics.Medians0(samples);
double summed_varriance = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
summed_varriance += samples[sample_index].Count * ToolsMath.Sqr(sample_means[sample_index] - total_mean);
}
double total_variance = 0.0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
for (int measurement_index = 0; measurement_index < samples[sample_index].Count; measurement_index++)
{
total_variance += ToolsMath.Sqr(samples[sample_index][measurement_index] - sample_means[sample_index]);
}
}
double degrees_of_freedom_0 = samples.Count - 1;
double degrees_of_freedom_1 = total_count - samples.Count;
double f_statistic = (degrees_of_freedom_1 * summed_varriance) / (degrees_of_freedom_0 * total_variance);
return(FisherSnedecor.CDF(degrees_of_freedom_0, degrees_of_freedom_1, f_statistic));
}
public static double TestStatic(IList <IList <double> > samples)
{
double pooled_varriance = ToolsMathStatistics.VariancePooled(samples);
double total_count = ToolsCollection.CountElements(samples);
double nom_part = 0;
double denom_part = 0;
for (int sample_index = 0; sample_index < samples.Count; sample_index++)
{
nom_part += (samples[sample_index].Count - 1.0) * Math.Log(ToolsMathStatistics.Variance(samples[sample_index]));
denom_part += (1.0 / (samples[sample_index].Count - 1));
}
double nominator = (total_count - samples.Count) * Math.Log(pooled_varriance) - nom_part;
double denominator = 1 + ((1.0 / (3 * (samples.Count - 1))) * (denom_part - (1 / (total_count - samples.Count))));
double chi_square_statisic = nominator / denominator;
double degrees_of_freedom = samples.Count - 1;
return(ChiSquared.CDF(degrees_of_freedom, chi_square_statisic));;
}
