NUMBER MAGIC, AUDITING ACID AND MATERIALITY - A CHALLENGE FOR AUDITING RESEARCH

This paper critiques null hypothesis testing in auditing, and proposes a Bayesian alternative. Classical procedures for null hypothesis testing are fundamentally flawed because they calculate the probability that the data would be observed if the null hypothesis were true, while that question of interest to most users is: how likely is the null hypothesis to be true? Moreover, classical procedures are strongly biased against the null hypotheses being tested, so strongly that they routinely reject them on the basis of evidence in their favor. The bias is illustrated with an example. After a brief exposition of fundamental Bayesian ideas, this paper shows how natural it is to test hypotheses about whether an error is material or not using Bayesian procedures. These procedures can save auditors money by reducing sample sizes and by exploiting prior information A computational appendix reworks an example from a textbook of auditing to show that the classical bias against null hypotheses can lead auditors to reject a null hypothesis of no material error on the basis of evidence in its favor, and thus to require an adjustment or a qualified opinion where a Bayesian procedure would not.