Dear Sir or Madam, I am trying to apply the two-sample Kolmogorov-Smirnov test implemented in Matlab (ktest2), but the description of the test statistic (ks2stat) used (as shown in the current documentation) is not clear enough. How is the test statistic calculated? The documentation provides some references but does not clearly specify what the ktest2 formula is really using as test stat. Could provide some more clarity on that? Tks!
The two-sided test as implemented is essentially described here:
The two-sided test computes the empirical CDFs of the two data samples and computes the statistic
T = max|F1(x) - F2(x)| where F1(x) is the empirical CDF of one sample and F2(x) is the empirical CDF of the other.
The p-value is computed from the result described on the above link in the "Kolmogorov distribution" section.
You can see that in MATLAB code here:
j = (1:101)'; pValue = 2 * sum((-1).^(j-1).*exp(-2*lambda*lambda*j.^2)); pValue = min(max(pValue, 0), 1);
The one-sided cases are a bit different, are you interested in the one-sided or two-sided case?
Sorry, just saw the first part of your answer, with the link. I will go through the rest now.