Facts, phantasies, and a new proposal concerning the stringer bound

The Stringer bound is a widely used nonparametric 100(1 - α)% upper confidence bound for the fraction of errors in an accounting population. 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 counterexamples were available. In a pioneering paper Bickel [1] has given some fixed sample support to the boundʹs conservatism together with an asymptotic expansion in probability of the Stringer bound, which has led to his claim of the asymptotic conservatism of the Stringer bound. In [2], expansions have been obtained of arbitrary order of the coefficients in the Stringer bound. As a consequence they showed that Bickelʹs asymptotic expansion also holds with probability 1 and proved that the asymptotic conservatism holds for confidence levels 1 - α, with α ε (0, (1/2)]. It means that in general also in a finite sampling situation the Stringer bound does not necessarily have the right confidence level. Based on these expansions they proposed a modified Stringer bound which has asymptotically precisely the right nominal confidence level. The main aim of the paper is to discuss the meaning and implementation of these recent results in auditing practice and to give examples where the modified Stringer bound has been applied.