Statistical Sampling In Auditing Research Articles

Statistical audit sampling for portfolio‐at‐risk in microfinance

PurposeThe purpose of this paper is to provide a rigorous, statistically correct, and low‐cost way to audit sample a lender's loan portfolio, be they a microlender or other type of lender. No other paper applies this method to loan portfolios, even though it is a high demand application.Design/methodology/approachStandard techniques of audit sampling and dollar unit sampling with stratification are applied to the particular case of a microlender's portfolio. Unlike the audit sampling that almost all auditors use, no arbitrary rules of thumb are applied.FindingsThe paper finds that statistical audit sampling for a lender's loan portfolio is simple, rigorous, and inexpensive.Practical implicationsIn audit sampling, most auditors use arbitrary rules of thumb and have no idea whether they are sampling enough items to actually be sure, with some desired level of confidence, that they have found no defects. This simple, inexpensive, and statistically rigorous technique will allow auditors who actually want to do a good job to quantify the precision of their statements in a very common application.Originality/valueThis paper combines several disparate threads from the statistical literature on audit sampling in a way that auditors (who are usually not statisticians) can apply them for auditing the quality of a lender's portfolio – microfinance or otherwise – which is a very common need.

The Problems Resulting from Using the Statistical Sampling in Auditing and the Contribution Fields of the External Auditor to Decrease its Effects on the Financial Statements: Analytical Study of External Auditor’s Viewpoints in Gaza Province

The Problems Resulting from Using the Statistical Sampling in Auditing and the Contribution Fields of the External Auditor to Decrease its Effects on the Financial Statements: Analytical Study of External Auditor’s Viewpoints in Gaza Province

An Alternative Approach for Controlling Statistical Audit Sampling Risks

Traditional approaches to risk control used for planning, executing, and evaluating substantive audit tests focus primarily on the risk of accepting a materially misstated amount (β risk) and only consider passively the risk of rejecting a correctly stated amount (α risk). This article discusses an alternative – the trade‐off approach – that formally considers both risks. Although the traditional and the trade‐off approach frequently lead to the same statistical conclusion, there are some applications in which only the trade‐off approach, can provide a statistical conclusion in support of the auditor′s assertion that a client′s balance is correctly stated. The article identifies these applications and suggests that the trade‐off approach merits further consideration.

Probability and Statistics: Essays in Honor of Franklin A. Graybill.

Admissibility in Linear Models with Polyhedral Covariance Structure (A.-M. Azzam, D. Birkes, J. Seely). Simulated Power Comparisons of the Asymptotic and Nonasymptotic Goodman and Kruskal Tau Tests for Sparse R and C Tables (K.J. Berry, P.W. Mielke, Jr.). Schemes Exhibiting Hurst Behavior (D.C. Boes). The Extension of Grubb's Estimators for Classes of Incomplete Block Designs (R.A. Bradley, D.A. Rollier). Applications of Innovation Representations in Time Series Analysis (P.J. Brockwell, R.A. Davis). Karl Pearson at Gresham College (J.L. Folks). On an Intermittent Stochastic Process (J. Gani, P. Todorovic). On the Unification of Bias Reduction and Numerical Approximation (H.L. Gray). Invariant Inference for Variance Components (D.A. Harville). An Argument for Adaptive Robust Estimation (R.V. Hogg et al.). Distribution Free Procedures for Some Ratio Problems (H.K. Iyer, L. Kaiser). Prediction Intervals in Balanced One-Factor Random Model (S. Jeyaratnam, S. Panchapakesan). Goodness-of-Fit and g-Sample Omnibus Tests Based on Coverages (P.W. Mielke, Jr.). Statistical Sampling in Auditing: A Review (J. Neter, J. Godfrey). Sums of Independent Random Variables with the Extreme Terms Excluded (W.E. Pruitt). Uniform Rates of Convergence to Extreme Value Distributions (S.I. Resnick). Best Linear Unbiased Estimation in Mixed Models of the Analysis of Variance (S.R. Searle). High Resolution Frequency Analysis of Almost Periodic Processes (M.M. Siddiqui, C.C. Wang). On a General Theory of Sampling Using Experimental Design Concepts II: Relation with Arrays (J.N. Srivastava). beta-Expectation Tolerance Limits for Balanced One-Way Random-Effects Model (C.M. Wang). Linear Calibration when the Coefficient of Variation is Constant (Y.-C. Yao, D.F. Vecchia, H.K. Iyer). Generalizations for Second-Order and Multivariate Normal Linear Models (J.S. Williams, M.K. Zaatar).

The lack of uniformity in statistical audit sampling terminology

There is currently no standard terminology in statistical audit sampling that is commonly accepted and used in all auditing textbooks. As a result, students and professionals are faced with the frustrating and arduous task of learning new symbols and terms when attending advanced auditing classes and continuing professional education courses and the public accounting profession has difficulty in testing adequately CPA candidates' proficiency in the statistical sampling area. This article examines the extent of the problem of lack of uniformity and suggests a possible solution.

An Introduction to Statistical Sampling in Auditing.

An Introduction to Statistical Sampling in Auditing.

Statistical Sampling in Auditing: A Statistician's Viewpoint

The auditor's final judgement is based on enquiries, tests and previous knowledge. Some of these enquiries and tests are simple checks that the accounting system works according to its specification, others are subjective assessments. An auditor knows a priori that a good accounting system will not be liable to serious errors in the final accounts. But no system is perfect and some items are likely to be in error due to carelessness or some other random occurrence. The auditor's final check is to carry out substantive tests of the details of the actual transactions carried out during the period under examination. It is this final check which appears straightforward.

Statistical Sampling in Auditing: An Auditor's Viewpoint

The use of statistical sampling techniques to assist the auditor in arriving at his audit opinion poses a number of statistical problems. Accounting populations are frequently very highly skewed and the error rates which the auditor is seeking to detect are often extremely low. This paper seeks to review the various techniques currently being used by auditors and to consider the practical problems involved in relating statistical sampling to the auditor's objectives. Over the years many articles and books on applying statistical techniques to auditing procedures have been published. Initially, there was little interest within the auditing profession as statistical techniques were generally difficult to apply manually and were often insufficiently related to audit objectives. The former objection began to dissipate in the early 1960s with the introduction of computerized audit software for the processing of accounting information. A major step forward came in 1963 with the publication of Arkin's Handbook of Sampling for Auditinzg and Accounting, a book giving comprehensive and not too technical details of how to apply statistical techniques in auditing situations. The techniques discussed included various methods of attribute and variables The auditor would use an attribute sampling tecnhique when his objective was to determine the occurrence rate of some population characteristic or he would use a variables method when his objective was to estimate the value of the particular population. At about the same time as Arkin's book was published, a major United States' accounting firm introduced an audit sampling plan which was fundamentally different to the sampling plans discussed by Arkin. The great claim of this audit sampling plan was that it used the simple statistical theory of attribute sampling to give a result in terms of value rather than as an error rate. The plan is based on the deceptively simple concept of defining the sampling unit as each individual pound (or dollar) rather than defining the sampling unit as the more usual item or balance. Hence, the term monetary unit sampling. However, the mathematical principles underlying unit sampling were not immediately published and it was some years before the principles were published by Anderson and Teitlebaum (1973).

Ratio Estimation in Accounting Populations with Probabilities of Sample Selection Proportional to Size of Book Values

It is generally recognized that accounting populations possess statistical characteristics which render inappropriate the routine application of sample survey techniques to auditing problems. Kaplan [1973] points out that inferences about accounting populations are probably best made using auxiliary information, such as recorded book values. However, since typical accounting populations are highly skewed and contain relatively few accounts in error, the standard distributional assumptions1 underlying auxiliary information estimators (e.g., ratio or regression estimators) are likely to be violated. This leads Kaplan to conclude that entirely new approaches may be required for statistical sampling in auditing. In this paper we study a modification of a standard unbiased ratio estimator2 based on a population sample selected with probability pro-

Discussion of Considerations in Choosing Statistical Sampling Procedures in Auditing

The basic theme of the Loebbecke-Neter paper is that the choice of an appropriate statistical audit sampling procedure depends upon audit objectives, the audit environment, and audit procedures. Under certain conditions of each of these three factors, various statistical estimators perform poorly. Instances of this poor performance were studied in an extensive empirical study by the same two authors.' While the NeterLoebbecke empirical study is as yet unpublished, many of its conclusions are referred to in the paper under discussion, and the authors were good enough to make a draft copy of the study available to us for purposes of this discussion. Based on the study conclusions, Loebbecke and Neter have presented in the current paper a suggested decision flowchart to aid the auditor in selecting various sampling procedures which they feel are appropriate in various specified circumstances. In discussing this paper, it is impossible to avoid reference to the empirical study on which its principal conclusions are based. At the same time, it would not be proper in this forum, prior to the study's publication, to begin an exhaustive analysis of the study's numerical findings. We will confine ourselves, therefore, to such general comments about the study and its findings as are necessary to a meaningful consideration of the present paper. In our view, the most important contribution made by this paper, and by the study on which it is based, is the dramatic demonstration that many classical sampling plans are subject to significant unstated risks in certain

Statistical Sampling in Auditing with Auxiliary Information Estimators

The traditional literature applying statistical sampling to auditing has recognized neither the special structure of auditing populations nor the unique environment in which this sampling occurs. Much of the literature is based on techniques developed for sample surveys. But the auditor typically has a great deal more information about his population than is available to the social scientist in sample surveys. Counterbalancing this, the auditor operates under much tighter precision requirements than the sample survey investigator. In this paper, we explore these issues in greater detail and show how the auditor must use statistical estimators which explicitly use all the auxiliary information available to him. We investigate a class of such estimators and show that, for typical auditing populations, the standard distribution theory is not always appropriate for statistical inference. Therefore, we conclude that entirely new approaches may be required for statistical sampling in auditing.

A Bayesian Approach to Asset Valuation and Audit Size

There now exists a relatively large body of literature dealing with statistical sampling in auditing. This literature is mainly classical, in the sense that the auditor subjectively specifies desired confidence intervals1 and confidence levels as the basis for designing his audit sample.2 In specifying a confidence level, the auditor should take his evaluation of the adequacy of the firm's internal control into account, i.e., better internal control allows a lower audit size and enables the auditor to accept the resulting lower level of confidence in his estimates. However, no formal mechanism exists for linking the auditor's prior assessment of internal control and his sample design. Rather, this is left to the auditor's judgment.3 The lack of such a mechanism is a major defect of the classical approach to statistical sampling in auditing.