  Testing the quality of pseudorandom number generators is an important issue.
Security requirements become more and more demanding, weaknesses in this matter
are simply not acceptable. There is a need for an in-depth analysis of
statistical tests -- one has to be sure that rejecting/accepting a generator as
good is not a result of errors in computations or approximations. In this paper
we propose a second level statistical test based on the arcsine law for random
walks. We provide a Berry-Essen type inequality for approximating the arcsine
distribution, what allows us to perform a detailed error analysis of the
proposed test.
