A natural approach to the experimental study of dependence between statistical tests

To test the hypothesis on the independence of tests included in the NIST Statistical Test Suite for each of 10000 binary segments we compute the number $\nu$ of tests which reject this segment as not corresponding to the equiprobable Bernoulli sequence hypothesis. If the tests were independent and have the same error probability, then $\nu$ should have the binomial distribution. It appears that collections of 14 and 162 NIST's tests do not satisfy this condition, but 11 tests from 14 may be considered as satisfying it. It is shown also that some sequences obtained by merging seqments of linear recurrent sequences are not rejected by NIST's package.