Conformance Analysis of Population Means under Restricted Stratified Sampling



Risk based auditing has recently been promoted by national and international auditing standards, e. g., SAS 10 through SAS 111, ISA 315 and ISA 330, IDW PS 261. These schemes have created a broadening demand for stochastic methods of risk quantification and risk control in the auditing community. In particular, risk based auditing requires the specification and control of the detection risk, i. e., the probability that the auditor erroneously approves the conformance of the financial statements of the audited entity with the de facto financial status. Confronted with large volumes of accounting and inventory data, auditors are interested in sampling based methods of conformance testing. Customary sampling schemes are not completely in line with the requirements of conformance testing in auditing. The paper introduces restricted stratified sampling as a viable scheme for auditing purposes.


Conformance Analysis Restricted Sampling Enterprise Resource Planning Audit Standard Sales Transaction 


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  1. 1.
    AICPA (2006) AU Section 350 – Audit Sampling. American Institute of Certified Public Accountants, New York.Google Scholar
  2. 2.
    AICPA (2007) AU Section 312 – Audit Risk and Materiality in Conducting an Audit. American Institute of Certified Public Accountants, New York.Google Scholar
  3. 3.
    Anderson, T. W. (1958) An Introduction to Multivariate Statistical Analysis. John Wiley & Sons, Inc., New York, London, Sydney.MATHGoogle Scholar
  4. 4.
    Cochran, W. G. (1977) Sampling Techniques. Third edition. John Wiley & Sons, Inc., New York, London, Sydney.MATHGoogle Scholar
  5. 5.
    Dalenius, T., and Hodges, J. L. (1959) Minimum variance stratification. Journal of the American Statistical Association, Vol. 54, pp. 88-101.MATHCrossRefGoogle Scholar
  6. 6.
    Göb, R. (1996) An Elementary Model for Statistical Lot Inspection and Its Application to Sampling by Variables. Metrika, Vol. 44, pp. 135-163.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Guy, D. M., Carmichael, D. R., and Whittington, O. R. (2002) Audit Sampling: An Introduction. Fifth Edition. John Wiley & Sons, Inc., New York, London, Sydney.Google Scholar
  8. 8.
    Hayes, R., Dassen, R., Schilder, A., an Wallage, P. (2005) Principles of Auditing: An Introduction to International Standards on Auditing. Second Edition. Prentice Hall, Harlow, England.Google Scholar
  9. 9.
    Neyman, J. (1934) On two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. Journal of the Royal Statistical Society, Vol. 97, pp. 558-606.CrossRefGoogle Scholar
  10. 10.
    Satterthwaite, F. E. (1941) Synthesis of variance. Psychometrika, Vol. 6, pp. 309-316.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Satterthwaite, F. E. (1946) An approximate distribution of estimates of variance components. Biometrics Bulletin, Vol. 2., No. 6, pp. 110-114.CrossRefGoogle Scholar
  12. 12.
    Tschuprow, A. A. (1923) On the Mathematical Expectation of the Moments of Frequency Distributions in the Case of Correlated Observations. Metron 2, pp. 461-493, 646-683.Google Scholar
  13. 13.
    Welch, B. L. (1947) The generalization of ”student’s” problem when several different population variances are involved. Biometrika, Vol. 34, pp. 28-35.MATHMathSciNetGoogle Scholar

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© Physica-Verlag Heidelberg 2010

Authors and Affiliations

  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgGermany

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