# Non-parametric test

A statistical test of a hypothesis $H_0$: $\theta\in\Theta_0\subset\Theta$ against the alternative $H_1$: $\theta\in\Theta_1=\Theta\setminus\Theta_0$ when at least one of the two parameter sets $\Theta_0$ and $\Theta_1$ is not topologically equivalent to a subset of a Euclidean space. Apart from this definition there is also another, wider one, according to which a statistical test is called non-parametric if the statistical inferences obtained using it do not depend on the particular null-hypothesis probability distribution of the observable random variables on the basis of which one wants to test $H_0$ against $H_1$. In this case, instead of the term "non-parametric test" one speaks frequently of a "distribution-free statistical testdistribution-free test" . The Kolmogorov test is a classic example of a non-parametric test. See also Non-parametric methods in statistics; Kolmogorov–Smirnov test.