The Wikipedia article on the two-sample Kolmogorov-Smirnov test states that:
The Kolmogorov–Smirnov test may also be used to test whether two
underlying one-dimensional probability distributions differ. In this
case, the Kolmogorov–Smirnov statistic is$$D_{n,n'}=\sup_x |F_{1,n}(x)-F_{2,n'}(x)|$$
where $F_{1,n}$ and $F_{2,n'}$ are the empirical distribution
functions of the first and the second sample respectively. The null
hypothesis is rejected at level $\alpha$ if$$D_{n,n'}>c(\alpha)\sqrt{\frac{n + n'}{n n'}}.$$
It is not clear to me the meaning of the $\alpha$ level. Where does it come from and what does it mean statistically?
Best Answer
The level $\alpha$ is the "significance level" of the test, the rate of Type I error, the probability of detecting a difference under the assumptions of the null hypothesis (that the two samples are drawn from the same distribution).