What is the state of the art in statistics tests for distinguishing good from bad random number generators? There are many packages out there.  In particular, PractRand gives out an opinion on a number of them, but it's only an opinion.  Is there conventional wisdom about which set of set of statistics tests should be used to to test out a random number generator?

Update1: 
Given @usεr11852's comment, answers may go towards tests for PRNG or CSPRNG.  I'll consider it answered if any current formal recommendations exist for either one.

Update2: 
Given @usεr11852's and @DW's comment, answers should assume tests for PRNG (and not for CSPRNG).  (If that's possible at this stage.)
 A: In addition to the Dieharder suite that Sephan Kolassa mentioned, other well known test suites include TestU01 and the NIST Statistical Test Suite (STS).
The PractRand library you mentioned rates Dieharder and STS as "bad" and TestU01 as "good". But, unlike the other test suites, PractRand is not as well known, and there do not seem to be any academic papers or external review. So, one would have to use their own judgement in trusting these comparisons (there's a little bit of information here on the PractRand webpage).
I'd recommend having a look at crypto.stackexchange.com. For example, some relevant threads here and here.
An important thing to note is that scientific and cryptographic applications have different requirements for pseudorandom number generators. Statistical randomness is necessary for both. But, it's not sufficient for cryptographic applications, which also need resistance to attacks that try to exploit the internal workings of the random number generator. This cannot be verified by statistical tests, and requires cryptanalysis.
References


*

*L'Ecuyer et al. (2007). TestU01: A C library for empirical testing of random number generators.

*Bassham et al. (2010). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications.
A: In 1995, the Diehard suite of tests was distributed. This is no longer state of the art - one limitation is that Diehard only uses about 10 million random numbers in each test, but modern uses of random numbers may consume many more, so tests should base their conclusions on larger samples.
A successor to the Diehard suite is the Dieharder suite. I believe this is state of the art, but (disclaimer) I am not an expert in random number testing, so an answer from anyone who actually is an expert and could actually back their reply up with literature would be much appreciated.
