Abstract
Auxiliary information estimators, such as the ratio and difference estimators, are widely used in statistical auditing because they produce more precise point estimates than other estimators (e.g., the mean per unit estimator) which do not utilize as much information. However, these auxiliary information estimators do not always yield reliable confidence intervals, that is, their true levels of confidence can differ drastically from the stated levels. Studies by Kaplan [1973], Neter and Loebbecke [1975; 1977], and Frost and Tamura [1982] have documented this problem, but have not explained why it occurs. The purpose of this paper is to show that the skewness of the distribution of these estimators largely accounts for their failure to yield reliable confidence intervals in statistical auditing. The skewness is induced by the low error rates in accounts. Other conjectures have been made about the underlying causes of this problem. These conjectures center on the statistic T, defined as:
Published Version
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