  Statistical tests of pseudorandom number generators (PRNGs) are applicable to
any type of random number generators and are indispensable for evaluation.
While several practical packages for statistical tests of randomness exist,
they may suffer from a lack of reliability: for some tests, the amount of
approximation error can be deemed significant. Reducing this error by finding a
better approximation is necessary, but it generally requires an enormous amount
of effort. In this paper, we introduce an experimental method for revealing
defects in statistical tests by using a three-level test proposed by Okutomi
and Nakamura. In particular, we investigate the NIST test suite and the test
batteries in TestU01, which are widely used statistical packages. Furthermore,
we show the efficiency of several modifications for some tests.
