Abstract The main objective of this study is to investigate whether the modified moment bounds (MMB) can be effective in producing two-sided confidence bounds, and how the behavior of these two-sided bounds compares with that of the corresponding one-sided upper MMBs. For various reasons, auditors often need to be concerned with both overstatement and understatement errors. When an accounting population has errors in both directions, and when the auditors do not have sufficient confidence whether the population has a net overstatement or understatement error, the auditors should construct two-sided bounds which provide a complete consideration of both understatement and overstatement errors. This is the first study that tests and reports the reliability and precision of two-sided bounds of the MMB method. The second objective of this paper is to test the behavior of the MMB using a set of accounting populations not directly generated out of chi-squared distributions. Testing the MMBs using a set of accounting populations that conform closer to actual error distributions than those used in previous studies on MMB enables auditors and researchers to draw more definitive conclusions about the performance of the MMB method. The results of this study confirm that, overall, the MMBs are reliable for low error rate populations. However, the reliability of two-sided bounds is lower than that of one-sided upper bounds, particularly at medium to high error rates with low confidence levels. This can be explained by the combination of two main factors: (1) for high error rate populations, the number of errors found in the sample tends to be large, thus reducing the effect of the hypothetical tainting which has been tested for one-sided upper bounds in previous studies; and (2) approximating the gamma confidence limits for MMB using a symmetric normal distribution could understate the lower bound, particularly at low confidence levels.
Hung et al. (Sat,) studied this question.