Overcoming the Multiple Testing Problem When Testing Randomness

In this paper we propose a new method for overcoming the problem of adjusting for the multiple testing problem in the context of testing random number generators. We suggest it is to be used in conjunction with an existing method. More generally, the method can be useful in other situations where the multiple testing issue is encountered and the tests involved are not independent of each other, and their exact joint distribution is not readily available. The method makes use of the Mahalanobis distance and simulation. An example of its implementation is given using data from a roulette wheel.