Runs test

A test whether a one-dimensional data sample is compatible with being a random sampling from a given distribution. It is also used to test whether two data samples are compatible with being random samplings of the same, unknown distribution.

One first forms the histogram of the difference between the two histograms to be compared, or of the difference between the histogram and the function to be compared, and then one counts the number of runs in the difference. This number is then compared with that expected under the null hypothesis, which is such that all orderings of sign are equally probable ( Runs).

The runs test is usually not as powerful as the Kolmogorov test or the test ( Chi-Square Test), but it can be combined with the test since it is (asymptotically) independent of it.