Skip to main content
SpringerLink
Log in

Comparing the Efficiency of Sample Plans for Symmetric and Non-symmetric Distributions in Auditing

  • Chapter
  • First Online:
Book cover Contributions to Sampling Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

  • 1595 Accesses

Abstract

The aim of the sampling in auditing fields is to produce an upper confidence limits for mean or totals of unobserved mistakes on the observed values accounts (called book values) that are highly positively skewed. In the main auditing scenarios, it is possible to meet populations with a relatively large number of small accounts combined with high rate of mistakes, that means diffused low errors, or populations with a relatively large number of accounts combined with a small rate of mistakes, that means rare high errors. It seems interesting to evaluate whether the sampling method in relation to the different distribution shape of the population is able to distinguish the pure random error from the systematic error. In this work we will compare, by simulation, the mostly used audit sampling methods for different distribution shapes for book values with different hypothesis on the presence of the errors on the book values population.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The selection procedure for both sampling methods was the systematic procedure (Modow 1949).

References

  • American Institute of Certified Public Accountants (AICPA): Audit Guide: Audit Sampling. AICPA, New York (2008)

    Google Scholar 

  • Anderson, R.J., Teitlebaum, A.D.: Dollar-unit Sampling. Canadian Chartered Accountant, pp. 30–39 (April, 1973)

    Google Scholar 

  • Arens, A.A., Loebbecke, J.K.: Applications of Statistical Sampling to Auditing. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  • Beck, P.J.: A critical analysis of the regression estimator in audit sampling. J. Account. Res. 18, 16–37 (1980)

    Article  Google Scholar 

  • Bickel, P.J.: Inference and auditing: The stringer bound. Int. Stat. Rev. 60(2), 197–209 (1992)

    Article  MATH  Google Scholar 

  • Dworin, L., Grimlund, R.A.: Dollar unit sampling for accounts receivables and inventory. Account. Rev. 59, 218–241 (1984)

    Google Scholar 

  • Dworin, L., Grimlund, R.A.: Dollar-unit sampling: A comparison of the quasi-Bayesian and moment bounds. Account. Rev. 61(1), 36–58 (1986)

    Google Scholar 

  • Felix, W.L., Jr., Leslie, D.A. Neter, J.: University of Georgia Center for Audit Research Monetary-Unit Sampling Conference, 24 March 1981. Auditing J. Pract. Theory 1(2), 92–103 (1981)

    Google Scholar 

  • Fienberg, S.E, Neter, J., Leitch, R.A.: Estimating the total overstatement error in accounting population. J. Am. Stat. Assoc. 72(358), 295–302 (1977)

    Article  Google Scholar 

  • Financial Accounting Standards Board (FASB): Statement of Financial Accounting Concepts No. 2 (SFAC2 - Qualitative Characteristics of Accounting Information). Stamford, Conn.: FASB (1980)

    Google Scholar 

  • Fishman, G.S.: Confidence intervals for the mean in the bounded case. Stat. Probab. Lett. 12, 223–227 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • Goodfellow, J.L., Loebbecke, J.K., Neter, J.: Some perspectives on CAV sampling plans. Part I CA Magazine, October, pp. 23–30; Part II CA Magazine, November, pp. 46–53 (1974)

    Google Scholar 

  • Grimlund, R.A., Felix, D.W., Jr.: Simulation evidence and analysis of alternative methods of evaluating dollar-unit samples. Account. Rev. 62(3), 455–480 (1987)

    Google Scholar 

  • Ham, J., Losell, D., Smieliauskas, W.: An empirical study of error characteristics in accounting populations. Account. Rev. 60(3), 387–406 (1985)

    Google Scholar 

  • Hansen, M.H., Hurwitz, W.N.: On the theory of sampling from finite populations. Ann. Math. Stat. 14, 332–362 (1943)

    Article  MathSciNet  Google Scholar 

  • Horgan, J.M.: The moment bound with unrestricted random, cell and sieve sampling of monetary units. J. Account. Bus. Res. 26(3), 215–223 (1996)

    Article  Google Scholar 

  • Horvitz, D.G., Thompson, D.J.: A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47, 663–685 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  • Howard, R.C.: A combined bound for errors in auditing based on Hoeffding’s inequality and bootstrap. J. Bus. Econ. Stat. Am. Stat. Assoc. 12(4), 437–448 (1994)

    Google Scholar 

  • Johnson, J.R., Leitch, R.A., Neter, J.: Characteristics of errors in accounts receivables and inventory audits. Account. Rev. 58, 270–293 (1981)

    Google Scholar 

  • Kaplan, R.S.: Statistical sampling in auditing with auxiliary information estimators. J. Account. Res. 11(2), 238–258 (1973)

    Article  Google Scholar 

  • Kaplan, R.S.: Sample size computations for dollar-unit sampling. J. Account. Res. 13(3), 126–133 (1975)

    Article  Google Scholar 

  • Kvanli, A.H., Shen, Y.K., Deng, L.Y.: Construction of confidence intervals for the mean of a population containing many zero values. J. Bus. Econ. Stat. Am. Stat. Assoc. 16(3), 362–368 (1998)

    Google Scholar 

  • Leitch, R.A., Neter, J., Plante, R., Sinha, P.: Modified multinomial bounds for larger number of errors in audits. Account. Rev. 57(2), 384–400 (1982)

    Google Scholar 

  • Leslie, D.A., Teitlebaum, A.D., Anderson, R.J.: Dollar-Unit Sampling - A Practical Guide for Auditors. Pitman, London (1979)

    Google Scholar 

  • Modow, W.G.: On the theory of systematic sampling. Ann. Math. Stat. 20, 333–354 (1949)

    Article  Google Scholar 

  • Neter, J., Loebbecke, J.K.: Behaviour of Major Statistical Estimators in Sampling Accounting Population - An Empirical Study. AICP, New York (1975)

    Google Scholar 

  • Neter, J., Loebbecke, J.K.: On the behavior of statistical estimators when sampling accounting populations. J. Am. Stat. Assoc. 72(359), 501–507 (1977)

    Article  Google Scholar 

  • Neter, J., Johnson, J.R., Leitch, R.A.: Characteristics of dollar-unit taints and error rates in accounts receivables and inventory. Account. Rev. 60, 488–499 (1985)

    Google Scholar 

  • Pap, G., van Zuijlen, M.C.A.: On the asymptotic behaviour of the stringer bound. Stat. Neerl. 50(3), 367–389 (1996)

    Article  MATH  Google Scholar 

  • Plante, R., Neter, J., Leitch, R.A.: Comparative performance of the multinomial, cell and stringer bound. Auditing J. Pract. Theory 5, 40–56 (1985)

    Google Scholar 

  • Ramage, J.G., Kreieger, A.M., Spero, L.L.: An empirical study of error characteristics in audit populations. J. Account. Res. 17(Suppl.), 72–102 (1979)

    Google Scholar 

  • Reneau, J.H.: CAV bounds in dollar unit sampling: some simulation results. Account. Rev. 53(3), 669–680 (1978)

    Google Scholar 

  • Rohrbach, K.J.: Variance augmentation to achieve nominal coverage probability in sampling from audit populations. Auditing J. Pract. Theory 12(2), 79–97 (1993)

    Google Scholar 

  • Smieliauskas, W.: Control of sampling risks in auditing. Contemp. Account. Res. 3(1), 102–124 (1986)

    Article  Google Scholar 

  • Smith, T.M.F.: Statistical sampling in: Auditing: A Statistician’s viewpoint. Statistician 28(4), 267–280 (1979)

    Article  Google Scholar 

  • Stringer, K.W.: Practical aspects of statistical sampling in auditing. In: Proceedings of the Business and Economics Statistics Section, pp. 405–411. ASA (1963)

    Google Scholar 

  • Swinamer, K., Lesperance, M.L., Will, H.: Optimal bounds used in dollar unit sampling: A comparison of reliability and efficiency. Communications in Statistics - Simulation and Computation, 33 (1), pp. 109–143 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Tsui, K.W., Matsumura, E.M., Tsui, K.L.: Multinomial-Dirichlet bounds for dollar-unit sampling in auditing. Account. Rev. 60(1), 76–97 (1985)

    Google Scholar 

  • Wurst, J., Neter, J., Godfrey, J.: Comparison of sieve sampling with random and cell sampling of monetary units. Statistician 11(2), 235–249 (1989)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milano, Italy

    Paola M. Chiodini & Mariangela Zenga

Authors
  1. Paola M. Chiodini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mariangela Zenga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mariangela Zenga .

Editor information

Editors and Affiliations

  1. Dept. of Sociology and Social Research, University of Milano-Bicocca, Milano, Milano, Italy

    Fulvia Mecatti

  2. Dept. of Statistical Sciences, Sapienza - University of Rome, Roma, Roma, Italy

    Pier Luigi Conti

  3. Dept. Economics, Finance and Statistics, University of Perugia, Perugia, Perugia, Italy

    Maria Giovanna Ranalli

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Chiodini, P.M., Zenga, M. (2014). Comparing the Efficiency of Sample Plans for Symmetric and Non-symmetric Distributions in Auditing. In: Mecatti, F., Conti, P., Ranalli, M. (eds) Contributions to Sampling Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-05320-2_7

Download citation

Publish with us

Policies and ethics

Search

Navigation