how to calculate the test statistic for two sample kolmogorov smirnov test?

Question

goodness of fit test

Answer 1

The test statistic is based on the empirical distribution function or ECDF, which is defined as E_N = n(i)/N, where you have N data points Y_1, Y_2, Y_3, ..., Y_N, and n(i) is the number of points less than Y_i. The Y values are ordered from smallest to largest. The test statistic is defined as D = max(F(Y_i) - (i - 1) / N, i / N - F(Y_i)) for 1 ≤ i ≤ N, where F(Y_i) is the theoretical cumulative distribution of the continuous distribution being tested.