Double Checking for Two Error Types

Abstract

Auditing a large population of recorded values is usually done by means of sampling.Based on the number of incorrect records that is detected in the sample, a point estimate and a confidence limit for the population fraction of incorrect values can be determined.In general it is (implicitly) assumed that the auditor does not make mistakes while judging the correctness of the values. However, in practice this assumption does not necessarily hold: auditors are human and can make errors.To take this possibility into account, a subsample of the audited records is checked once more by a second auditor who is assumed never to make mistakes.The information obtained from these two samples should be combined to derive an estimate for the error rate in the population.The starting point for this type of double checking was Moors et al.(2000).Only one possible error type was considered: auditors could only miss (fail to detect) existing errors.For the case of random sampling, the maximum likelihood estimator as well as an upper confidence limit for the error rate were derived.The present paper gives extensions in two directions.Firstly, a second error type is introduced: the auditor may consider a correct value as an error.Again, the sample information of both auditor and infallible expert is combined to give point and interval estimates for the fraction of errors in the population.Secondly, a Bayesian analysis is presented for both the model with one error type and the extended model.auditing;Bayesian statistics;quality control;sampling;error analysis