On the solution of the phase problem. IV. Distributions fitted using the Kolmogorov test

The proposed method of determination of a correct set of phases is based on a comparison between the trial and theoretical distributions of seminvariants using the Kolmogorov test. If the Kolmogorov test is restricted to a single region of magnitudes where only a small variance around the mean seminvariant value is expected, then the test is reduced to a simple rule. The smaller the number of seminvariants differing significantly from the expected mean value, the more probable the set of phases. In this simple form the Kolmogorov test has been used since the very beginnings of direct methods. In spite of the fact that the method seems to be less efficient than the distribution fitting using the x² test [Hasek (1984). Acta Cryst. A40, its simplicity and low claim on computing time enables one to survey a large number of trial sets and so to increase the power of the method based on a combination of the Kolmogorov test with the x² test, or with the low-order distribution moment test.