Testing a generator for all possible seeds and sampling sizes is hardly practicable. Therefore, only a few subsequences of various lengths are actually tested.
Testing a random number sequence u1, u2, ..., un gives a p-value that falls within the range from 0 to 1. Being a function of a random sampling, this p-value is a random number itself. For the sequence u1, u2, ..., un of truly random numbers, the resulting p-value is supposed to be uniformly distributed over the interval (0, 1). Significant p-value deviation from the theoretical uniform distribution may indicate a defect in the tested sequence. For example, the sequence u1, u2, ..., un may be considered suspicious if the resulting p-value falls outside the interval (0.01, 0.99). The chance to reject a "good" sequence in this case is 2%.
Multiple testing of different subsequences of a sequence substantiates the statistical conclusion about the sequence randomness.