void significance(GArgReader& args)
{
GMatrix* pData = loadData(args.pop_string());
Holder<GMatrix> hData(pData);
int attr1 = args.pop_uint();
int attr2 = args.pop_uint();
// Parse options
double tolerance = 0.001;
while(args.size() > 0)
{
if(args.if_pop("-tol"))
tolerance = args.pop_double();
else
ThrowError("Invalid option: ", args.peek());
}
// Print some basic stats
cout.precision(8);
{
cout << "### Some basic stats\n";
cout << "Medians = " << pData->median(attr1) << ", " << pData->median(attr2) << "\n";
double mean1 = pData->mean(attr1);
double mean2 = pData->mean(attr2);
cout << "Means = " << mean1 << ", " << mean2 << "\n";
double var1 = pData->variance(attr1, mean1);
double var2 = pData->variance(attr2, mean2);
cout << "Standard deviations = " << sqrt(var1) << ", " << sqrt(var2) << "\n";
int less = 0;
int eq = 0;
int more = 0;
for(size_t i = 0; i < pData->rows(); i++)
{
double* pRow = pData->row(i);
if(std::abs(pRow[attr1] - pRow[attr2]) < tolerance)
eq++;
else if(pRow[attr1] < pRow[attr2])
less++;
else
more++;
}
cout << less << " less, " << eq << " same, " << more << " greater\n";
}
// Perform the significance tests
{
cout << "\n### Paired T-test\n";
size_t v;
double t;
pData->pairedTTest(&v, &t, attr1, attr2, false);
double p = GMath::tTestAlphaValue(v, t);
cout << "v=" << v << ", t=" << t << ", p=" << p << "\n";
}
{
cout << "\n### Paired T-test with normalized values\n";
size_t v;
double t;
pData->pairedTTest(&v, &t, attr1, attr2, true);
double p = GMath::tTestAlphaValue(v, t);
cout << "v=" << v << ", t=" << t << ", p=" << p << "\n";
}
{
cout << "\n### Wilcoxon Signed Ranks Test";
int num;
double wMinus, wPlus;
pData->wilcoxonSignedRanksTest(attr1, attr2, tolerance, &num, &wMinus, &wPlus);
cout << "Number of signed ranks: " << num << "\n";
double w_min = std::min(wMinus, wPlus);
double w_sum = wPlus - wMinus;
cout << "W- = " << wMinus << ", W+ = " << wPlus << ", W_min = " << w_min << ", W_sum = " << w_sum << "\n";
double p_min = 0.5 * GMath::wilcoxonPValue(num, w_min);
if(num < 10)
cout << "Because the number of signed ranks is small, you should use a lookup table, rather than rely on the normal approximation for the P-value.\n";
cout << "One-tailed P-value (for directional comparisons) computed with a normal approximation using W_min = " << 0.5 * p_min << "\n";
cout << "Two-tailed P-value (for non-directional comparisons) computed with a normal approximation using W_min = " << p_min << "\n";
cout << "To show that something is \"better\" than something else, use the one-tailed P-value.\n";
cout << "Commonly, a P-value less that 0.05 is considered to be significant.\n";
/*
double p_sum = GMath::wilcoxonPValue(num, w_sum);
cout << "Directional (one-tailed) P-value computed with W_sum = " << p_sum << "\n";
*/
}
}
