Generalization of Homogeneity Tests for Weighted Samples and Their Implementation in ROOT

In High Energy Physics, tests of homogeneity are used primarily in two cases: for verification that data sample does not differ significantly from numerically produced Monte Carlo sample and for verifying separation of signal from background. Since Monte Carlo samples are usually weighted, it is necessary to modify classical homogeneity tests in order to apply them to weighted samples. In ROOT, the only homogeneity tests that allow testing weighted samples are implemented for binned data. However, after the data are binned the full information is lost. Therefore we compare these ordinary tests with modified versions of the Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises tests that use full sample information. The proposed tests are compared by estimating a probability of type-I error which is crucial for a test's reliability.