Outgoing from known basic pseudo-random number generators as congruential, shift register or cellular automata, characterized as ``good'' in the literature, by addition modulo 1, new, so-called hybrid random numbers are generated. These new generators dispose of remarkably better statistical properties than the basic ones. The proof for this effect is done empirically. Five test statistics are used in connection with a random walk constructed from the random number sequence in a natural way. From each of it, a sample of size 30 of corresponding \(\chi^2\)-values is formed, and Kolmogorov-Smirnov test is carried out 100 times.