• :

    Abstract:  The Point Estimate (PE) and the Confidence Interval (CI) of the error rate are of great interest for their applications in auditing.  This paper will focus on comparing two types of Confidence Intervals (CI), namely the Likelihood Ratio CI (LRCI), and Wendell CI for the error rate in an audited population.  We will examine the confidence intervals for the error rate when the sample is selected without replacement form the population. The LRCI method is based on finding the range values for hypergeometric parameter M, which will satisfy the likelihood ratio equation for the observed Maximum Likelihood Estimate (MLE) for M. The Wendell method is also based on the hypergeometric distribution, and the confidence interval is calculated by inverting the hypothesis test for the parameter M.  We simulated 1,000 random samples using R and examined the coverage probabilities and expected lengths of the interval for the two types of intervals. We determined that the LRCI produced better coverage probabilities and shorter length confidence intervals, especially when the error rate is near the boundaries values for its support. 

     KEY WORDS:  Audit sampling; Hypergeometric distribution; Coverage probability; Likelihood Ratio Confidence Interval, Wendell Method.

     The views expressed are attributable to the authors and do not necessarily reflect the views of the Department of Defense.

  • : V. Venu, K. Selvavel
  • : Department of Defense
  • : V. Venu
  • : statistics
  • : advanced/theoretical
  • : anant.venu@dodig.mil
  • : 703-699-6092 (W), 703-651-2530 (Cell)
Comparing Confidence Intervals for error rates based on the Hypergeometric Parameter M