The relevance of second error probability in modern statistical analysis

Statistical tests are used extensively in selecting and testing random and pseudorandom number generators. This is important because the output of such generators can be used in various cryptographic applications, such as private key material. National Institute of Standards and Technologies proposed a methodology for conducting such tests, entitled Statistical Test Suite Special Publication 800-22. We propose an improvement of this methodology by computing the second order error, the probability of accepting a false hypothesis, by applying new decision rules and deriving formulas for the minimum sample size in order to achieve a desired rejection rate. We present the general context of this methodology, we emphasize the placing of our enhancement and point out its importance of usage in conjunction with the existing one.