private void computeKappaVariance()
{
// References: Statistical Methods for Rates and Proportions
int[,] m = matrix;
double k = Kappa;
double[] colMarginal = ColumnTotals.Divide((double)samples);
double[] rowMarginal = RowTotals.Divide((double)samples);
double directionSum = 0;
for (int i = 0; i < classes; i++)
{
directionSum += rowMarginal[i] * colMarginal[i];
}
double pe = directionSum;
// Compute A (eq. 18.16)
double A = 0;
for (int i = 0; i < classes; i++)
{
double u = 1 - (rowMarginal[i] + colMarginal[i]) * (1 - k);
A += (m[i, i] / (double)samples) * u * u;
}
// Compute B (eq. 18.17)
double sum = 0;
for (int i = 0; i < rowMarginal.Length; i++)
{
for (int j = 0; j < colMarginal.Length; j++)
{
if (i != j)
{
sum += (m[i, j] / (double)samples) * (colMarginal[i] + rowMarginal[j]);
}
}
}
double B = (1 - k) * (1 - k) * sum;
// Compute C
double v = k - pe * (1 - k);
double C = v * v;
// Compute variance using A, B and C
kappaVariance = (A + B - C) / ((1 - pe) * (1 - pe) * samples);
// Compute standard error directly
kappaStdError = Math.Sqrt(A + B - C) / ((1 - pe) * Math.Sqrt(samples));
}
