In general, we find that the sales behavior pattern has a significant effect on alpha risk for the negative approach and on the beta risk for both approaches for each expectation model and this influence is consistent across all expectation models.
It is apparent from the discussion earlier (table 6) that in most of the positive testing approach cases the ARIMA and Martingale models yield a significantly lower alpha risk of error detection than the structural model (table 6) and the other models (table B.1 in appendix B).
An auditor must balance the costs associated with the ease of use of these estimators against the potential costs of more audit effort due to the high alpha risk when using the negative approach.
From table 6, the negative approach should be used to achieve a low beta risk ([absolute value of E]=M) and the positive approach should be used to achieve a low alpha risk ([absolute value of E]=0).
With the lower alpha risk, these two procedures can enhance audit efficiency by reducing excessive audit effort when no material error is present, while still providing the needed assurance of detecting a material error.
(21) Wheeler and Pany (1990) also adjust this sum by making an allowance for double-counting a Type 1 (alpha risk) and Type II (beta risk) error for the positive approach for the same situation.