FACTS, FANTASIES, AND A NEW PROPOSAL CONCERNING THE STRINGER BOUND

The Stringer bound is a widely used nonparametric 100(1 - alpha)% uppe r confidence bound for the fraction of errors in an accounting populat ion. This bound has been found in practice to be rather conservative, but no rigorous mathematical proof of the correctness of the Stringer bound as an upper confidence bound is known, and until 1994 also no co unterexamples were available. In a pioneering paper Bickel [1] has giv en some fixed sample support to the bound's conservatism together with an asymptotic expansion in probability of the Stringer bound, which h as led to his claim of the asymptotic conservatism of the Stringer bou nd. In [2], expansions have been obtained of arbitrary order of the co efficients in the Stringer bound. As a consequence they showed that Bi ckel's asymptotic expansion also holds with probability 1 and proved t hat the asymptotic conservatism holds for confidence levels 1 - alpha, with alpha is an element of (0, (1/2)]. It means that in general also in a finite sampling situation the Stringer bound does not necessaril y have the right confidence level. Based on these expansions they prop osed st modified Stringer bound which has asymptotically precisely the right nominal confidence level. The main aim of the paper is to discu ss the meaning and implementation of these recent results in auditing practice and to give examples where the modified Stringer bound has be en applied.