Bartłomiej Janusz

(English) PDF


Auditors need information on the performance of different statistical methods when applied to audit populations. The aim of the study was to examine the reliability and efficiency of a strategy combining systematic Monetary Unit Sampling and confidence intervals for the total error based on the Horvitz-Thompson estimator with normality assumption. This strategy is a possible alternative for testing audit populations with high error rates. Using real and simulated data sets, for the majority of populations, the interval coverage rate was lower than the assumed confidence level. In most cases confidence intervals were too wide to be of practical use to auditors. Confidence intervals tended to become wider as the observed error rate increased. Tests disclosed the distribution of the Horvitz-Thompson estimator was not normal. A detailed analysis of the distributions of the error amount in the examined real audit populations is also given.


audit sampling, Monetary Unit Sampling, Horvitz-Thompson estimator, error distribution


ALLEN, R. D., ELDER, R. J., (2005). A Longitudinal Investigation of Auditor Error Projection Decisions, Auditing: A Journal of Practice & Theory, 24 (2), pp. 69–84.

ARENS, A. A., LOEBBECKE, J. K., (1981). Applications of Statistical Sampling to Auditing, Englewood Cliffs: Prentice – Hall, Inc.

BERGER, Y. G., (1998). Rate of convergence to normal distribution for the Horvitz-Thompson estimator. Journal of Statistical Planning and Inference, 67 (2), pp. 209–226.

CHRISTENSEN, ELDER, GLOVER, (2015). Behind the Numbers: Insights into Large Audit Firm Sampling Policies, Accounting Horizons, 29 (1), pp. 61–81.

DURNEY, M., ELDER, R. J., GLOVER, S. M., (2014). Field Data on Accounting Error Rates and Audit Sampling, Auditing: A Journal of Practice & Theory, 33 (2), pp. 79–110.

DWORIN, L., GRIMLUND, R. A., (1984). Dollar Unit Sampling for Accounts Receivable and Inventory, The Accounting Review, LIX(2), pp. 218–241.

HAM, J., LOSELL, D., SMIELIAUSKAS, W., (1985). An Empirical Study of Error Characteristics in Accounting Populations, The Accounting Review, LX (3), pp. 387–406.

HARTLEY, H. O., RAO, J. N. K., (1962). Sampling with Unequal Probabilities and without Replacement, The Annals of Mathematical Statistics, 33 (2), pp. 350–374.

HÁJEK, J., (1964). Asymptotic theory of rejective sampling with varying probabilities from a finite population, The Annals of Mathematical Statistics, 35 (4), pp. 1491–1523.

HOOGDUIN, L. A., HALL, T. W., TSAY, J. J., PIERCE, B. J., (2015). Does Systematic Selection Lead to Unreliable Risk Assessments in Monetary – Unit Sampling Applications? Auditing: A Journal of Practice & Theory, 34 (4), pp. 85–107.

HORVITZ, D. G., THOMPSON, D. J., (1952). A Generalization of Sampling Without Replacement From a Finite Universe, Journal of the American Statistical Association, 47 (260), pp. 663–685.

JOHNSON, J. R., LEITCH, R. A., NETER J., (1981). Characteristics of Errors in Accounts Receivable and Inventory Audits, The Accounting Review, LVI (2), pp. 270–293.

KIM, H. S., NETER, J., GODFREY, J. T., (1987). Behavior of Statistical Estimators in Multilocation Audit Sampling, Auditing: A Journal of Practice & Theory, 6 (2), pp. 40–58.

MARAZZI, A., TILLÉ, Y., (2017). Using past experience to optimize audit sampling design, Review of Quantitative Finance and Accounting, 49 (2), pp. 435–462.

NETER, J.,. JOHNSON, J. R, LEITCH, R. A., (1985). Characteristics of Dollar – Unit Taints and Error Rates in Accounts Receivable and Inventory, The Accounting Review, LX (3), pp. 488–499.

ROYSTON, P., (1992). Approximating the Shapiro – Wilk W-test for non-normality, Statistics and Computing, 2, pp. 117–119.

SARNDAL, C. E., SWENSSON, B., WRETMAN, J., (1992). Model Assisted Survey Sampling, Springer – Verlag New York, Inc.

STATISTICAL MODELS AND ANALYSIS IN AUDITING, (1989). Panel on Nonstandard Mixtures of Distributions, Statistical Science, 4 (1), pp. 2–33.

TILLÉ, Y., (2006). Sampling Algorithms, Springer Science+Business Media, Inc.

WOLTER, K. M., (1985). Introduction to Variance Estimation, Springer – Verlag New York, Inc.

WYWIAŁ, J. L., (2016). Contributions to Testing Statistical Hypotheses in Auditing, Warszawa: Wydawnictwo Naukowe PWN SA.

YATES, F., GRUNDY, P. M., (1953). Selection without Replacement from Within Strata with Probability Proportional to Size, Journal of the Royal Statistical Society. Series B (Methodological), 15 (2), pp. 253–261.

Back to top
© 2019–2023 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0