0
$\begingroup$

When applying several tests to a given generator, p-values smaller than 0.01 or larger than 0.99 are often obtained by chance even if the RNG behaves correctly with respect to these tests (such values should normally appear approximately 2% of the time). In this case, suspicious values would not reappear systematically (unless we are extremely unlucky). (Source, page 6.)

Here's result where the test MaxOft AD produces a p-value close to 1 and so the RNG fails that test.

========= Summary results of SmallCrush =========
[...]
The following tests gave p-values outside [0.001, 0.9990]:
[...]
Test p-value
----------------------------------------------
[...]
6 MaxOft AD 1 - 3.6e-06
[...]
----------------------------------------------
All other tests were passed
[...]

NIST SP 800-22 calls such values "perfect randomness" (page 1-4, that is, PDF-page 16).

If a P-value for a test is determined to be equal to 1, then the sequence appears to have perfect randomness. A P-value of zero indicates that the sequence appears to be completely non-random.

So, what's wrong with a p-value close to 1?

$\endgroup$
1
  • $\begingroup$ what is the test Max Oft AD? and NIST only says “appears to have perfect randomness”. $\endgroup$ – kodlu Sep 14 '20 at 22:21
2
$\begingroup$

So, what's wrong with a p-value close to 1?

Because random sequences don't look 'perfectly random' (or, rather, they have a low probability of doing so). We're checking if this sequence quacks [1] like a perfectly random sequence; acting 'too uniform' is evidence that it is not.


[1]: from the proverb "if it acts like a duck, and it quacks like a duck, then it is a duck". Fairly common where I am; however you never know how regional sayings like this are..

$\endgroup$
1
  • $\begingroup$ Thanks for checking the culture factor. $\endgroup$ – user12406990 Sep 14 '20 at 20:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.