On Passing Statistical Tests  

To be brief, a CSRNG should be unbreakable by smart attackers with lots of resources. If a CSRNG does not pass statistical tests, then this means that it can be broken by a chimpanzee. But if it passes the tests, this does in no way prove that it is cryptographically strong; it just means that the chimpanzee will be stumped.

tpornin on NCC Research