**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

*Statistical Models and Analysis in Auditing: A Study of Statistical Models and Methods for Analyzing Nonstandard Mixtures of Distributions in Auditing*. Washington, DC: The National Academies Press. doi: 10.17226/1363.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

*Statistical Models and Analysis in Auditing: A Study of Statistical Models and Methods for Analyzing Nonstandard Mixtures of Distributions in Auditing*. Washington, DC: The National Academies Press. doi: 10.17226/1363.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

*Statistical Models and Analysis in Auditing: A Study of Statistical Models and Methods for Analyzing Nonstandard Mixtures of Distributions in Auditing*. Washington, DC: The National Academies Press. doi: 10.17226/1363.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

**Suggested Citation:**"BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING." National Research Council. 1988.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

IV. BIBLIOGRAPHY OF STATISTICAL PRACTICE IN AUDITING 1. Alphabetical Annotated Bibliography Aitchison, I. (1955~. On He Distribution of a Positive Random V an able Having a Discrete Probability Mass at He Origin. Journal of the American Statistical Association, 50: 901-908. This paper is the first to address He problem of the estimation of parameters from data containing many zeros. The best unbiased estimators of the population mean and the variance are derived. However, the paper does not consider me sampling distnbution of these estimators and Gus results are not of immediate use to auditors. American Institute of Certified Public Accountants (ATCPA). (1981~. Statement on Auditing Starboards (SAS No. 391. New York: AICPA. American Institute of Certified Public Accountants (ATCPA). (1983~. Audit Sampling. New York: AICPA. Auditing practices are regulated by a number of national organizations. Among them, the most influential organization is the American Institute of Certified Public Accountants, a national organization of practicing certified public accountants. The current auditing standards are stated in: Statement on Auditing Standards (SAS No. 391. Audit Sampling is a detailed interpretation of SAS No. 39 and descnbes procedures and practicing guides that auditors should adhere to when me auditing is performed based on examination of less than 100% of the items of an accounting balance. Anderson, R. J. and Teitlebaum, A. D. (1973~. DolUar-unit Sampling. Canadian Chartered Accountant (after 1973, this publication became CA Magazine ), April: 30-39. This expository article introduces dolHar unit sampling in a way understandable to a broader group of researchers and practitioners. Anderson, R. I. and Leslie, D. A. (1975~. Discussion of Consideration in Choosing Statistical Sampling Procedures in Auditing. Journal of Accounting Research, Supplement: 53-64. 60

The discussion focuses partly on the paper by Loebbecke and Neter and partly on tile ~en-for~coming AT CPA Monograph No. 2, Behavior of Major Statistical Estimators in Sampling Accounting Populations. With respect to He former, Anderson and Leslie question He distinction between whether an audit should have "attributes" or"vanables" objectives, arguing that an audit objectives should be expressed in monetary teens. Wig respect to the latter study, Anderson and Leslie argue Hat He ATCPA study should have included doBar-un~t sampling with He Stnnger bound, rather than the combined attributes-vanables bound because He Stnnger bound is less conservative and more widely used. The discussants believe mat doBar-unit sampling wid1 He Stnnger boulKl is appropnae in almost all circumstances so that He auditor need not consider altemative sampling approaches and fall-back procedures if the anticipated environmental conditions are not met, as proposed by Loebbecke and Neter. Baker, R. L. and Copeland, R. M. (1979). Evaluation of the Stratified Regression Estimator for Auditing Accounting Populations Journal of Accounting Research, 17: 606- ~ 7. This study supplements the Neter and Loebbecke AICPA Monograph No. 2 by studying the behavior of the stratified regression estimation for the same four accounting populations used in the AICPA study. The precision of me regression estimator in general tends to be almost the same as the precision of the stratified difference, ratio, and regression estimators. As for these other estimators, the reliability of the nominal confidence coefficient for the stratified regression estimator is poor at low error rates, win the regression estimator performing even more poorly than the other estimators. Barkman, A. (19771. Within-Item Vanation: A Stochastic Approach to Audit Uncertainty. The Accounting Review, 52: 450464. The author proposes that the audit amount to be established by the auditor for a line item be treated as a random variable, such as when the line item is the amount of bad debt for an account receivable. The author assumes that the distribution reflecting the uncertainty of the line item audit amount is given by the beta distnbution and that the distnbution of the total amount is normal. A simulation study was camed out to study the behavior of sample estimates under different population conditions for 61

mean-per-un~t and difference estimators. Beck, P. I. (1980~. A Cntical Analysis of the Regression Estimator in Audit Sampling. Journal of Accounting Research, IS: 16-37. This study supplements the Neter and T-oebbecke study In ATCPA Research Monograph No. 2 by examining We behavior of the stratified and unstratified regression estimators for the accounting populations considered in me ATCPA monograph. ~ addition, one of these populations was filcher manipulated in order to vary the extent of heteroscedasticity in the population. The results obtained were similar to those previously reported for me difference and ratio estimators in the Never and Loebbecke sly. The author concludes mat heteroscedasticity appear to be a significant factor in the behavior of He regression estimator in two of the four accounting populations and mat stratification cannot always be relied upon to provide a confidence level close lo the nominal one. The author also made a limited study of me power of statistical tests based on the regression estimator. Burdick, R. K. and Reneau, I. H. (1978~. The Impact of Different Error Distributions on the Performance of Selected Sampling Estimators in Accounting Populations. Proceedings of Business and Economic Statistics Section: 779-781, Washington, D.C.: Arnencan Statistical Association This paper reports on a simulation study based on one of me accounting populations employed In the Neter and Loebbecke (1975) study. Errors were injected into the population at different error rates, win equal probability for each line item, with probability proportional to book amount, and with probability inversely proportional to book amount. A number of estimators were studied as to their precision and me closeness of the actual confidence level to the nominal one based on large-sample theory. The authors conclude that an estimator developed by Hartley is to be preferred over me other estimators studied. Sampan, Lewis A. (1933~. The Efficacy of Tests. The American Accountant, December: 360-366. This paper proposes application of a simple probability model for computing He sampling risk in auditing and is the first publication of such an attempt in accounting. 62

Cox, D. R. and SneD, E. I. (1979~. On Sampling and Me Estimation of Rare Errors. Biometrika, 66: 124-132. After describing a theoretical mode} of monetary unit sampling, me paper presents a Bayesian analysis of We problem. Spec~ficaDy, me authors consider me case where the number of errors has a Poisson distribution and the proportional error density is exponential. Using a simple conjugate pnor, they denve the posterior distribution and discuss some possibilities for the parameters of me prior distribution. Cox, D. R. and SneH, E. I. (19X2~. Correction Note on Sampling and the Estimation of the Rare Enors. Biometrika, 69: 491. Co~necdons to their 1979 paper are announced in this note. Cyert, R. M. and Davidson, H. Justin. (1962~. Statistical Samplingfor Accounting Information. Englewood Cliffs, New Jersey: Prentice- Hall, hnc. This basic text In statistical sampling for auditing introduces among other standard topics the application of sequential sampling for compliance test. Deakin, E. B. (1977~. Discussant's Response to Computing Upper Error Limits in Dollar Unit Sampling. Frontiers of Auditing Research, edited by B. E. Cushing and ]. L. Krogstad. Austin: Bureau of Business Research, The University of Texas at Austin: 19S-201. This critique of Garstka(1977b) mentions that the conservatism of upper error bounds should be reduced by research on the handling of unobserved errors, that me models proposed by Gars~ca lack empirical support, that the proposed use of altemative models provides no rationale for selecting an appropriate model in a given situation, and that He research does not provide sufficient evidence to support the assumption Cat generalized or compound Poisson models would be any more useful in auditing than the present dollar-unit sampling models. Duke, Gordon L., Neter, I. and Leitch, R.A. (19821. Power Characteristics of Test Statistics in He Auditing Environment: An Empincal Study. Journal of Accounting Research, 20 :42-67. The power characteristics of eight test statistics, used with both 63

the positive and negative testing approaches, are studied for four different accounting populations. Two error characteristics linkage models were developed for systematically creating different total error amounts In an accounting population. It was found Mat no one test statistic and either of the two testing approaches is uniformly superior, and that audit decisions based on a sample of 100 observations tend to involve high sampling risks for me auditor. Dworin, L. and Gnmiund, R. A. (1984~. Dollar Unit Sampling for Accounts Receivable and Inventor. The Accounting Review, 59 :218-241. The development of the moment bound is discussed in detail in this article. The authors state Mat Weir methods are based on Me assumption that Me doBar unit tainting follows a mixture of two y2 distributions. A helpful chart is provided in Weir Table 1 for computing the bound. Its performance is compared with that of the mulunomial bound. Dwonn, L. and GnmIund, R. A. (1986~. Dollar Unit Sampling: A Comparison of me Quasi-Bayesian and Moments Bounds. The Accounting Review, 61 :36-57. This article reports the results of comparing the performance of the moments bound with that of McCray's quasi-Bayesian bound using the unifonn pnor. A slight modification is proposed in the original moment bound to make me bound more efficient without any noticeable Toss of the reliability of the bound. For me pop~anons considered, the true level of confidence tends to be higher than the nominal level of 95% used in the study for bow bounds. Silk, both bounds are considerably tighter than He Stanger bound. However, between He two, the perfonnance is relatively comparable. Felix, W. L., Jr., Leslie, D.A. and Neter, I. (19821. University of Georgia Center for Audit Research Monetary Unit Sampling Conference, March 24, 1981. Auditing: A Journal of Practice & Theory, I: 92-103. This paper reports He results of the conference on Dollar Unit Sampling held at the University of Georgia in March, 1981. A short summary of existing methods for computing bounds is given. Also, the advantages and disadvantages of DUS compared 64

to line item sampling are discussed. Several DUS mess are presented and compared. Research issues are also su~nmanzed. Felix, W. Lo. Jr. and Gnmlund, R. A. (1977~. Sampling Model for Audit Tests of Composite Accounts. Journal of Accounnng Research, 15:2342. This article discusses an altemative statistical sampling model which avoids some of the assumptions of conventional mesons. It is a Bayesian approach where the book value and audit value are analy~caDy combined win the auditor's prior judgments. A single combined "bem-nomlal" probability distribution for Me total enor in an account balance is denved. Several properties of this distribution are presented, followed by a discussion of how the auditor may use it to make probabilistic statements about Me total enor amount in a population. The computational procedure for using Me beta-no~mal distribution is cumbersome, Bus several altemative computational procedures are suggested, followed by a brief discussion of how the analysis may be used to preselect a sample size. Festige, M. O. (1979~. Discussion of An Empirical Study of Error Charactenstics in Audit Populations. Journal of Accounting Research, 17 Supplement: 103-107. This is a discussion of the study by Ramage et al. (1979) by a practicing auditor. One of his comments is that the study may be biased because the audit data base used In the study is supplied by one of the major accounting firms and thus may reflect their audit objectives which may also vary from one case to another. Fienberg, S. E., Neter, I. and Leitch, R.A. (1977~. Estimating Be Tom Overstatement Error in Accounting Populations. Journal of the American Statistical Association, 72 :295-302. This paper presents a statistical sampling approach based on the multinomial distribution for obtaining a bound for either the total population overstatement or understatement, or both. The bound is denved by using an optimization routine that finds Be maximum monetary error subject to constraints representing the joint confidence region for the multinomial parameters. The key element is the definition of the S set which denotes me set of ad outcomes as extreme or less extreme Man the observed outcomes. The multinomial bound is numencaBy compared to Be Stringer 65

bound and the results indicate that the multinomial bound is less conservative Man We Stringer bound. Financial Accounting Standards Board (FASB). (1980~. Statement of Financial Accounting Concepts No. 2 (SFAC2 - Qualitative Characteristics of Accounting Information). Stamford, Conn: FASB. The Securities Exchange Act of 1934 gave the SEC me authority to promulgate financial reporting standards (Generally Accepted Accounting Principles or GAAP) for Nose companies subject to the jurisdiction of the SEC. The SEC, in rum, has delegated this authority to the FASB. The definition of a material error is from paragraph 132 of SFAC2 issued in May, 1980. Frost, P. A. and Tamura, H. (1982~. Jackknifed Ratio Estimation in Statistical Auditing. Journal of Accounting Research, 20: 103-120. One recent development in statistics is the use of computer intensive methods for data analysis. In this article, Me performance of the ratio estimation is studied when the starboard enor is computed using the conventional method and using the jackknife. The accounting data used in the Neter and Loebbecke study are employed as the populations for simulation. Their conclusion is that when error rates are not too small, so that the problem of the mixture as discussed in the main text is not severe, the jackknife clearly gives a better performance and should be used. Frost, P. A. and Tamura, H. (1986~. Accuracy of Auxiliary InfoImation Interval Estimation in Statistical Auditing. Journal of Accounting Research, 24: 57-75. This work extends Kaplan's 1973 investigation of the performance of the auxiliary information interval estimators and traces the cause of the poor performance of these estimators to the skewness of the accounting population induced by the mass of probability at the ongin. Analysis is done based on the difference estimator but indicates that the result can be applicable to the ratio estimator. Frost' P. A. and Tamura, H. (1987~. Accuracy of Auxiliary Infonnation Interval Estimation In Statistical Auditing. Working Paper Series #2-87, Department of Management Science, School & 66

Graduate Schools of Business A~nin~stration, University of Washington, Seance, WA 98195. This working paper contains additional results to those that are reported in Frost and Tamura (1986~. Garstka, S. I. (1977a). Models for Computing Upper Error Limits in DoDar-Urut Sampling. Journal of Accounang Research, 15 :179-92. This paper investigates alternative mesons of computing upper error limits for the monetary error in an accounting population. The compound Poisson process is used to model We error rate and We distnbunon of error sizes in the population. Simulations are used to demonstrate mat tighter upper error limits can be achieved using Bayesian procedures compared to the Stringer bound. Garstka, S. J. (1977b). Computing Upper Error Limits in DoBar-Un~t Sampling. Fronners of Auditing Research, edited by Cushing, B.E. and Krogstad, J.~. Austin: Bureau of Business Research, The University of Texas at Austin: 163-82. This paper poses a number of models to be used in conjunction win doBar-un~t sampling. In particular, six compound Poisson models and three generalized Poisson models are considered and upper error bounds developed for each. A simulation study is then used to examine the properties of the venous bounds. Use of prior information in selecting the appropriate Poisson model can lead to tighter upper error limits. Garstka, S. I. (19791. Discussion of An Empirical Study of Error Charactenstics in Audit Populations. Journal of Accounting Research,-17 Supplement: 103-113. Based on the argument that me characteristics of an accounting population should assist the auditor in selecting a proper estimator, the author comments that the measures reported in Me study by Ramage et al. (1979) may not be useful for the auditors. For example, he points out Cat the fractional errors are computed in teens of the audited amount as He base. However, the audited amount is not available for most of me items. Garstka, S. J. and Ohlson, P.A. (1979~. Ratio Estimation in Accounting Populations with Probabilities of Sample Selection 67

Proportional to Size of Book Values, Journal of Accounting Research, 17: 23-59. The authors propose a modification of the standard PPS estimator of the population total monetary error. The modification involves denying a factor to use as a multiple of the standa~ ever in constructing an upper confidence limit for Me total monetary error. The basis for the factor is largely heuristic. Lunited simulation is used to test We performance of the procedure. Godfiey, I. T. and Neter, I. (1984~. Bayesian Bounds for Monetary Unit Sampling in Accounthng and Auditing. Journal of Accounting Research, 22: 497-525. In 1979 Cox and Sne]1 published a Bayesian mode} for analysis of Dollar Unit Sample data. This work investigates Me sensitivity of the Cox and Snell bound if me auditor's knowledge is incorporated by using different prior distnbutions, e.g., by using a Beta distribution instead of the Gamma distnbution as proposed by Cox arid SneD for the error rate. The authors observe that the effects are moderate. The authors, however, report that the Cox and SneB bound is sensitive to me choice of the prior parameter values. Using simulation, they conclude, it iS possible to find the prior parameter values for which the bound demonstrates a desirable relative frequency property. GooUfellow, I. L., Loebbecke, I. K. and Neter, I. (1974~. Some Perspectives on CAV Sampling Plans. Part I, CA Magazine, October: 93-30; Part II, CA Magazine, November: 46-53. Combined attr~buees-vanables (CAY) sampling plans were developed to overcome inadequacies In both attributes and variables sampling plans. CAV plans seek to combine the two approaches to obtain effective and efficient estimates of dollar errors in audit populations with low error rates. Part ~ of Me article discusses the basic concepts of CAV sampling. It explains how an attributes sampling plan of unstratified audit units can lead to upper dollar precision limits for Me population total overstatement, and how stratification of the mats improves the efficiency of the estimate. Finally, it considers units selected with probabilities proportional to the book amounts and the essentially equivalent procedures of unstratified random selection of dollar units. Pan I! explains how Me combined attributes 68

vanables approach provides lighter precision limits. The strengths of CAV sampling plans are Hat Key provide dolBar precision estimates even when Me sample contains no error, incorporate the efficiency advantages of stratification without revering stratified selection, and rely on simple conceptual foundations. The weaknesses of the CAV approach include; Be unbalanced treatment of overstatement and understatement errors, inapplicability to sampling non-dollar audit units, ineffective design for disclosing errors, inadequacy of one-sided precision Innits for detenn~ng the amount of adjusunent Squired, assumption of a zero error rate for planning sample size, and emphasis on conservation of precision limits. - Gnmiund, R. A. and Felix. W. L. (1987~. Simulation Evidence and Analysis of Altemative Methods of Evaluating Dollar-Un~t Samples. The Accounting Review, 62 :455479. The long run performances of thme Bayesian bounds and the moment bolmd by Dwonn and Gnmiund are compared. Thme Bayesian models are: the Nonnal error model as developed by Gnmiund and Felix, the Cox and SnelB bound and Be multinomial bound with the Dinchlet nnor hv T~l.i P. "' The populations used for simulation utilize the mode] descnbed in Dwonn and Grimiund (1984~. The non-zero tastings are specified by a mixture of x2 distnbutions and include negative values. The performance of a Bayesian bound depends on the prior parameter values. However, for the prior settings used in this study the Bayesian nonnal error mode] and He multinomial bound indicate more consistent performance than the Cox and SneP bound. The multinomial bound with the Dinchiet prior is reported to be too conservative. rat ~ -- ~. ma. ^ ,. Ham, J., hostel, D. and Smieliauskas, W. (19851. An Empirical Study of Error CharactensUcs in Accounting Populations. The Acenun~inP Review, 60: 387406 . ,0 The empirical study of audit populations is scarce and this work is one of four such studies published. While the previous We studies used the data base supplied by one major accounting finn, this work is based on the data from another major accounting firm. Three factors are considered as possibly affecting me error distnbution: (1) account category, (2) company size and (3) industry . 69

Hylas, R. E. arid Ashton, R. H. (1982). Audit Detection of Financial Statement Erwrs. The Accounting Review, 57: 751-765. Based on 152 audit cases of one of major public accounting finns the causes of errors are traced. In these 152 audits 281 errors requinng financial statement adjustments were fourth. The error causes are classified into seven categories and their frequencies are reported. Intemal Revenue Service. (1972~. Audit Assessments Based on Statistical Samples (Memorandum to Assistant Commissioner from Chief Counsel). Washington, D.C.: IRS Intema1 Revenue Service. (1975~. Audit Assessments Based on Statistical Samples - Supplemental Memorandum (March 6 Memorandum to Chief Counsel from Director, Refund Litigation Division & Acting Director, Tax Court Litigation Division). Washington, D. C.: IRS. The legal ramifications of statistical sampling for tax audit are studied in these documents and the opinion of the Chief Counsel is stated. It is concluded that "although the propriety of the use of such techniques is not free from doubt, there is sufficient merit in the proposal to warrant judicial testing". Johnson, J. R., Leitch, R. A and Neter' I. (1981~. Characteristics of Errors in Accounts Receivable and Inventory Audits. The Accounting Review, 56 :270-293. Auditors and accountants require empinca1 information about He characteristics of audit populations and error distnbutions to plan the audit strategy. There is a need for information about He relative frequency, magnitude, distribution, and possible causes of errors. In this article, the enor characteristics and the relationship between errors and book values in 55 accounts receivable and 26 inventory audits are examined. The distnbutions of the error amounts and error tintings were studied, as well as the relation between ever amounts and book amounts. A summary of the findings is; (i) Here is great vanability in error rates, wide those of inventory audits tending to be much higher, (ii) evidence suggests Blat the error rates may be higher for larger accounts and for accounts with larger line items; (iii) most errors in receivable audits are overstatements, while in inventory audits, overstatements and understatements are more balanced in number, (iv) the distribution of error amounts are far 70

from normals with peak near Me mean and fanher tails ~ e upper diction, win receivable errors tending to be larger and less variable Wan inventory enors; (v) me distributions of error tangs are characterized by pronounced discontinu~ties at 100 percent, especially for receivables audits where 100 percent overstatement errors are frequent; (vi) Me mean faintings for receivables are Sue singly large, while those for inventories are smaller, but inventories show large negative faintings which occur frequency; (vii) the distributions of faintings are variable and depart substantially from a normal distribution, with some negatively skewed tainting distributions for inventones; and (viii) a study of 20 audits failed to disclose any strong linear relation between ever amount and book value, but errors for larger book amounts tend to be more variable. Since the study was based on data from only one CPA Inn, the authors emphasize the need for replication studies of the issues raised in me article. Kaplan, R. S. (1973~. Stochastic Model for Auditing. Journal of Accounting Research, Il :3846. A stochastic model is proposed for variable estimation in auditing. The model is based on the use of ratio and regression estimators. These estimators are valuable in audit applications because they utilize the recorded or book value of sample items in the estimation procedure. A disadvantage of ratio or regression estimates is that they are biased, but the bias becomes small as Me sample size increases. The model can be used in conjunction with classical techniques to estimate sample size and obtain standard errors of estimates. The sample size would be a function of the auditor's estimates of the error rate and the first two moments of the error distribution as weld as the distnbudon of book values which is known at tile time of audit. The model focuses on the need to estimate two different parameters in an audited population - the error rate and the distribution of errors. Kaplan contends Mat techniques (such as mean-per-un~t estimation using sample values only) which fad] to recognize this underlying structure will probably be of little value to auditors. Kaplan, R. S. (19731. Statistical Sampling in Auditing with Auxiliary Information Estimators. Journal of Accounting Research, I} :238-SX. Much of the literature applying statistical sampling to auditing is usually based on techniques developed for sample surveys, such as the simple mean-per-uriit estimator. But the auditor typically 71

has more information about the population than is available to those conducting sample surveys. The article indicates how He auditor should use statishcal estimators which explicidy use an the available auxiliary information. A class of auxiliary information estimators (difference, ratio, unbiased rabo-~e, mean rang, regression and audit models) and their variance estimates are investigated. Kaplan concludes Cat to use relatively small sample sizes, while working win stringent materiality factors, auditors must use auxiliary information estimators. Classical techniques am designed for homogeneous populations, whereas audit populations consist of two parts: one of an correct items, and the over of items in ear. Therefore, techniques which do not explicitly recognize this seem inadequate for auditing applications, and thus, there is a challenge to develop statistically valid techniques which utilize this information. Kaplan, R. S. (1975~. Sample Size Computations for DoBar-Unit Sampling. Journal of Accounting Research, Supplement: 126-133. This paper discusses a procedure which computes doBar-urut sample size as a function of materiality and the risks of making alpha and beta ethos. In order to control for alpha risk and also allow for some errors In He sample, a low rawer than zero error rate is specified. This low error rate is chosen such Cat one would not expect to reject a population with an error rate this low more than alpha percent of me the. Given a materiality percentage, a specified low error rate and the alpha and beta risks levels, the procedure derives the sample size required and He cntica1 number of total errors before rejecting the population. The sample sizes generated by this procedure are much larger than Hose which are based on an assumption of a zero enor rate. Keying, Nathan (19841. Heterogeneity and Selection In Population Analysis. Statistics Canada Research Paper, No. 10, September 1984. The concept and effect of heterogeneity in populations are discussed with examples. Heterogeneity and mixtures are closely related. Here the emphasis is upon its effect on error stucco and bias in data as well as upon the analysis of data that arises from statistically following groups over time. 72

Knight, P. (1979). Statistical Sampling in Auditing: an Auditor's View Point. The Statistician, 28 :253-266. Statistical sampling for auditing is reviewed In the auditorts context. Vanous Cons commonly used among practicing auditors are explained. Leitch, R. A., Neter, ]. Plante, P. and Sinha, P. (1981~. Implementation of Upper Muliinomial Bound Using Clustering. Journal of the American Statistical Association, 76: 530-533. The multinomial bound proposed by Fienberg et al. is difficult to compute when He number of enors In He sample increases. The authors suggest grouping error observations to reduce He number of enors to be used for computation of tile bound. This, of course, leads to losing some efficiency. However, the loss is shown to be not too large for He number of errors between five and eight. Beyond eight errors, me comparison win uncIustered bound is not available because of He difficulty in computing the latter. Leitch, R. A., Neter,]. Plante, R. and Sinha, P. (1982) Modified Multinomial Bounds for Larger Numbers of Errors in Audits. The Accounting Review, 57 :384400. A modification of the multinomial bound is presented which enables He auditor to obtain bounds for substantially larger numbers of errors in audit samples than was possible with the basic methodology for the multinomial bound. The modification consists of clustering taint~ngs found in the sample and obta~rung a conservative bound by assuming aU faintings in a cluster are as large as the largest tainting in the cluster. It is found that the modified muldnomial bound is usually considerably tighter than the Stringer bound. A simulation study indicated that doe confidence level for He modified multinomial bound exceeds or is close to the nominal level for Al populations studied. Leslie, D. A. (1977~. Discussants Response to Computing Upper Error Limits in Dollar Unit Sampling. Frontiers of Auditing Research, edited by Cushing, B. E. and K=gstad, I. L. Austin: Bureau of Business Research, The University of Texas at Austin: 183-91. Some criticisms of the Garstka paper include He fact Hat many of the populations used In He simulation stably did not contain material total error amounts and that the Poisson models are 73

unrealistic In not taking into account bunchings of 100% tailings found in actual accounting populations. Leslie, D. A., Teitlebaum, A. D. and Anderson, R. I. (1980~. Doliar- Unit Sampling - A Practical Guide for Auditors. London: Pinnan Publishing, Ltd. This is the first book on doBar-un~t sampling, a procedure in which the sampling mat is defined as an individual doBar. Aside from He appendices, which account for more than one-~ird of the publication, it is divided into four parts: auditing foundations for sampling, dollar-unit sampling, planning and evaluation, and applications and practical guidance. Much of the book is devoted to extolling the superiority of doBar-un~t sampling over audit unit sampling procedures. The primary advantages of dollar-unit sampling are that it requires no assumption regarding He distnbution of erwrs, and it provides an upper monetary error limit when there are no non-zero differences between He reported value and the audited value. L~llestol, I. (1981~. A Note on Computing Upper E'Tor Limits in Dollar Unit Sampling. JournalofAccounting Research, 19: 263-267. This paper comments on the work of Marsha (1977) and demonstrates that if the logar~nic series distribution is used to model the tainting, instead of He geometric series, as proposed by Garstlca, the upper bound could change noticeably. Yet' it is difficult to determine which mode] to use when the auditor expects only several ever observations in the sample. Loebbecke, I. K. and Neter, I. (1975~. Considerations in Choosing Statistical Sampling Procedures in Auditing, Journal of Accounting Research, 13 Supplement: 38-52. It is suggested that the sampling procedure to be used in a particular auditing application be determined after consideration of audit objectives and environment factors expected to be encountered in the application. Some of the charactenshcs of the audit procedure to be considered in choosing an appropn ate one include the ability to enlarge the sample, the nature of the sampling frame, and the bias of He audit procedure. The authors suggest that the auditorts plan include a provision for a fall-back procedure in case the anticipated environmental factors differ from the actual ones. 74

McKay, I. H. (19841. A Quasi-Bayesian Audit Risk Model for Dollar Unit Sampling. The Accounnng Review, 59: 35-51. Muldnomial modeling of He audit data by F~er~erg et al. appears to provide venous extensions. In this work He author Heats He mean tainting as a discrete vanable and develops a heuristic Bayesian approach to the problem. The wow is reviewed in Section Il.7 above. McRae, T. W. (1974~. Stanst~cal Sampling for Audit and Control. London: John Wiley. This text covers the major topics In statistical sampling for auditing, including He basics of statistics sampling, mesons of sample selection, estimating population means and proportions, acceptance and discovery sampling, and monetary-unit sampling. In addidon, the text considers more specialized topics such as cluster, multistage, and replicated sampling and He Bayesian approach to malting inferences. The text contains a bibliography and a number of tables, including tables for discovery sampling, estimation of population proportion, and acceptance sampling. The text is written at a non-technical level and does not contain significant elements of theory. Meikle, G. R. (1972~. Statistical Sampling in an Audit Context, Toronto: Canadian Institute of Chartered Accountants. This monograph discusses an early version of monetary unit sampling where a stratified design is employed. Menzefncke, U. (1983). On Sampling Plan Selection with Doliar-Unit Sampling. Journal of Accounting Research, 21 :96-105. An approach for deterrnin~ng the sample size In dollar unit sampling is developed. All enors are assumed to be 100 percent overstatements. Menzefricke, U. (1984~. Using Decision Theory for Planning Audit Sample Size Dollar Unit Sampling. Journal of Accounting Research, 22 :570-587. Using Bayesian models for the error distribution, an approach for sample size determination in dollar unit sampling is developed. 75

Mer~fr~cke, U. and Smieliauskas. W. (1984~. A Sunulabon Study of me Perfo'~ance of Pa~ametnc DolBar Unit Sampling Statistical P~c~ures, Journal of Accounang Research, 22 :588-603. The perfon~ances of certain Bayesian parametric models are investigated In the presence of both over and understatements. Their performances am Compaq with those of the Stringer bound and the Load and Spread bound, which is another nonparame~ic bound used by practitioners. One Bayesian bound is an application of me Felix and Gnmlund's nomlal error model; the second bound also uses the same structure but develops the bound using a different approach then Felix and Grimiund. (The two bounds show different results. ~ Another Bayesian mode} is Cox and Sneers exponential ever model. Only one parameter value configuration was used for each Bayesian modele The study concludes that in me presence of understatement error, Me nonnal model, using Weir own denvabon of me bourns, appears to show the best performance. Moors, I. I. A. (1983~. B ayes ' Estimation In Sampling for Auditing. The Statistician, 32: 281-288. This paper reports an error in Me Cox and SneU model and presents an altemative derivation of the parametric bound. Neter, I., Leitch, R. A. and Fienberg, S. E. (1978~. Dollar Unit Sampling: Multinominal Bounds for Total Overstatement and Understatement Errors. The Accounting Review, 53: 77-93. The results cited in Fienberg, Neter, and Leitch (1977) are presented here in language more suited to auditors. Additionally, the paper contains a good survey of previous research In the area of upper bounds on monetary unit sampling. Meter, J., Johnson, J.R. and Leitch' R. A. (19851. Charactenstics of Dollar Unit Taints and Error Rates In Accounts Receivables and Inventory. The Accounting Review, 60: 4X8-499. The distribution of doDar unit taints is studied using Me same data used in We authors' previous study (Johnson, L~eitch and Neter (l981~. Neter, I. and Godfrey, I. (1985~. Robust Bayesian Bounds for Monetary Unit Sampling in Auditing. Applied Statistics, 34: 157- 76

168. The main problem in using a Bayesian bound is to identify proper prior parameter values. Using extensive simulation studies, Me authors find certain al~mative prior configurations for the Cox and Sned bound that produce desirable relative frequency performance hem the bound. Neter, I. (1986~. Boundanes of Statistics - Sharp or Fuzzy? Journal of the American Statistical Assoc~ai~on, XI: Ike. this 1985 American Statistical Association Presidential Address me auditor reviews He problems of statistical auditing. He comments Hat He existing solutions often contain heunshc elements, and cans for more active participation of professional statisticians to solve He problem. Neter, I., and Loebbecke, I. (1975~. Behavior of Major Statistical Estimators in Sampling Accounting Populations--An Empirical Study, New York: American Institute of Certified Public Accountants. This monograph is an empincal study of die behavior of statistical estimators commonly used In auditing, based on simulated audit populations with varying error rate patterns constructed by extrapolating error characteristics found in audits of four actual populations. These four populations represent a variety of skewness, error rates, and mixture of overstannent and understatements for two types of accounts. The authors report on bow the shapes of the book value distributions and error characteristics including rate, magnitude, and Heir relation to book value. The major conclusion of He study is that many widely used statistical procedures may not be reliable when applied to audit populations, especially when He error rate is low. Some other conclusions from the study are that the standard errors for many estimators tend to increase with increases ~ He error rates, contradicting me assumption that the standard error of the estimator is constant; no one sta~cishcal procedure is optimal under Al audit circumstances; and furler research is needed involving larger samples, different numbers of strata, over estimators, 100 percent examined strain truncation, effective hypothesis testing procedures, and new statistical procedures especially useful for auditing. 77

Neter, I. and Loebbecke, I. K. (1977~. On the Behavior of Statishcal Estimators when Sampling Accounting Populations, Journal of He American Statistical Association, 72: 501-507. This article is a condensed version - win emphasis on Me statistical aspects - of the Neter and Loebbecke (1975) AICPA empirical study on the precision and reliability of several statistical estimators in sampling four accounting populations with various error rates. Problems in using difference and ratio estimators, as wed as over estimators, for constructing large- s~nple nonnal confidence intervals when We population error rate is low are explored empir~caBy. The findings indicate me need for great care in using large-sample normal confidence intervals for sample sizes of 100 or 200, which are frequency used In auditing practice. The authors conclude Nat me conditions governing Me appropriateness of large-sample nonnal theory results for ratio and difference estimators need more research, including investigations of the sources of unreliability of the standard large-sample procedures. Plante, R., Neter, I. and Leitch, R. A. (1985~. Comparative Performance of Multinomial, Cell, and Stringer Bounds. Auditing: A Journal of Practice & Theory, S: 40-56. In this simulation study, superiority of me multinomial bound is demonstrated as compared to popularly used non-parametnc bounds. The effect of altemative Dollar Unit Sampling is also investigated when the population line items are randomly ordered. For companson, stratified difference estimator using line item sampling is also included. Plante,R.~1987~. Personalcommuriication. Plante developed a personal computer software to compute Me multinomial bound for up to 25 errors. For the number of errors exceeding 10, the program uses clustenng of errors. The program is available from Plante, Krannert School of Management, Purdue University, West Lafayette, Indiana 47909. Ramage, I. G., Krieger, A. M. and Spero, L-. L. (1979~. An Empincal Study of Enor Characteristics in Audit Populations. Journal of Accounting Research 17, Supplement: 72-102. The authors contend that audit population eIror charactenstics, 78

aside from distributional shape, can be described by duee rates and a ratio. The rates are: i) overall enor rate, F. ii) the fraction of errors which are overstatements, FOV, and iii) contaminator - the fraction of errors with reladve magnitudes greater than one, CON. The ratio is He error magnitude relative to audit value, denoted by RM. The results of an empirical study of these characteristics indicate that estimates of the Wee rates van widely among populations; mere is lithe evidence Cat either FOV or CON vanes systematically with He error rate; for a specific population, none of Free rates appears to vary systematically as book value increases; error-absolute magnitude increases roughly in proportion to bow book and audit values, but the error magnitude relative to audit value is nearly constant as He audit value increases in magnitude; and inventory populations have widely ranging error rates, typically higher than accounts receivable. However, the usefulness of CON and RM as systematic measures of error magnitude would seem to be limited, since audit sample planning and selection are related to book value, not audit value. Reneau, J. H. (1978~. CAV Bounds in Dollar Unit Sampling: Some Simulation Results. The Accounting Review, 53: 669-80. This article presents the results of a simulation designed to examine the behavior of five procedures for computing an upper bound on monetary error. The simulation involves Wee population error direction-conditions, seven ever rate conditions, and five sample size conditions. The study population was generated to resemble a population previously studied by Neter and Loebbecke. Summary results of He simulation are included in the paper. Robbins, Herbert and Pinnan, E. ]. G. (19491. Application of the Method of Mixtures to Quadratic Forms in Nominal Vanates. Annals of Mathematical Statistics, 20: 552-560. The distributions of linear combinations of independent chi- square random v enables with possibly different degrees-of- freedom are obtained as mixtures of chi-square distributions. This use of mixtures is furler applied to the ratio of independent quadratic forTns of normal random variables. 79

Roberts, D. M. (1978~. StatisnicalAuditing. New York: American Institute of Certified Public Accountants. This reference book describes He standard statistical techniques used by auditors. Attention is given to the special problems faced by the auditor, namely, that monetary errors may be confined to a relatively small proportion of the population. Some rules of Numb are suggested to guide the auditor in selecting an appropriate technique. A simple stochastic mode! is presented to describe Me error generating process. Based upon this model, Me author suggests some modifications of He standard techniques to adapt to the case of rare monetary errors. Robens, D.M. and Shedd, M.D. and MacGuidwin, M. I. (1982~. The Behavior of Selected Upper Bounds of Monetary Error Using PPS Sampling. Symposium in Auditing Research [V, The Center for International Education and Research in Accounting, University of Illinois, Urbana-Champaign, Illinois. (Reviewed in Auditing: A Journal of Practice ~ Theory, 2, 1983 :112) This paper describes the results of a simulation study of six PPS estimators used to compute the upper limit of monetary error. One bound represents a variation of the Stringer bound, two of the bounds represent v anations of the Garstka-Ohlson bound, and two represent v anations of the used estimators based upon normal theory. The paper presents detailed analysis of He performance of the bounds as a function of the number of errors observed, thus permitting the reader to observe the behavior of using a combination of bounds. A limitation of me study was the fact that no randomization of He population order was made between simulation trials, Bus raising the possibility that population order might be a factor in affecting the observed result. Robens, D. M. (19861. Stratified Sampling Using a Stochastic Model. Journal of Accounting Research, 24 :111-126. Using a model similar to Kaplan (1973), dais work develops a procedure to test materiality of the total overstatement. Stratification is used to improve the normality of He test statistic. Smieliauskas, W. (1986) A Note on a Comparison of Bayesian with Non- Bayesian Dollar-Unit Sampling Bounds for Overstatement Errors of Accounting Populations. The Accounting Review, 61 :118- 80

128. This work compams We long run performance of venous Bayesian and non-Bayesian bounds. Smith, T. M. F. (1976~. Statistical Sampling for Accountants London: Accountancy Age Books This text covers the major topics In statistical sampling for accountants and auditors. Additionally, Me last chapter in Me book (Chapter 14), describes the problem of sampling for rare events. Monetary units sampling is described as a technique for coping with the auditor's problem of determining me monetary error when those errors are rare. Criticism of monetary unit sampling is also presented, particularly as related to Me effect of the selected doBar being a part of an account balance or transaction that represents Me audit unit. Smith, T. M. F. (1979~. Statistical Sampling in Auditing: a Stai~stician's Viewpoint. The Statistician, 28 :267-280. The statistical problems mat arise in auditing are summanzed and the validity of Dollar Unit Sampling is discussed. The Cox and SneB infinite population mode] is presented as me only available theoretical justification for DUS. Stringer, K. W. (19631. Practical Aspects of Staiishcal Sampling in Auditing. Proceedings of the Business and Economic Statistics Section :405411, Washington, D. C.: American Statistical · . . Assoclanon This paper describes some difficulties of using statistical procedures based on normal theory in many auditing situations where monetary errors are rare. While few details are given there is a brief description of me methodology now known as monetary unit sampling. Stnnger, K. W. (1979~. Statistical Sampling In Audinng-The State of He Art Annual Accounting Review, 1:~ ~ 3-127. It is fair to say that the author is most instnunental In introducing statistical sampling in auditing. This article reviews its histoncal development. He also predicts that use of statistical sampling, particularly of Dollar Unit Sampling, win expand in auditing 81

practice and calls for msearch to develop more efficient bounds. Tamura, H. (1985). Analysis of He Garstka-Ohison Bounds. Auditing: A Journal of Practice & Theory, 4: 133-142. This article comments on a property of He Gars~a-Ohison bound. It is demonstrated Hat He bound may not work because it does not take into account the skewness of the sampling distribution of the estimator. Tamura, H. and Frost, P.A. (1986~. Tightening CAV (DUS) Bounds by Using a Pararnewc Model. Journal of Accounting Research, 24: 364-371. A potentially profitable application of computer intensive data analysis is in approximating He small sample sampling distnbution. In this article the authors apply the par~etnc bootstrap to determine the sampling distribution of He estimator of He mean tainting. A power function is proposed for modeling the faintings. Their model is described in Section II.6 above. Tarnura, H. (1988~. Estimation of Rare Errors Using Expert Judgement. Biometrika, 7S To appear. A nonparametac Bayesian model is proposed using Ferguson's DinchIet process to specify the prediction of the conditional distnbution of the error. The distnbudon of the conditional mean of the error is obtained by numerically inverting the characteristic function. The error rate is modeled by a beta distnbution. The distribution of the mean error is derived by taking the expectation of the mean of He conditional en or over the error rate. Numencal examples are given and comparisons with parametric models are discussed. The model is discussed in Section II.7 above. Teitlebaum, A. D., Leslie, D. A. and Anderson, R. I. (1975~. An Analysis of Recent Commentary on Doldar-Unit Sampling in Auditing, McGill University working paper, March. This paper is a response to tile two-part article in the October and November 1974 issues of CA Magazine by GooUfeBow, Loebbecke, and Neter. Issues under contention to which responses are made In this paper include He planning of sample size win dollar-unit sampling, the handling of over- and understatement errors, the method of sample selection, He 82

evaluation of an upper bound, and a compan son of monetary t sampling with the Stringer bound and line-item sampling with variables estimation. Tittenngton, D. M., Smith, A. F. M. and Makov, U. E. (1985). Stadst~cal Analysis of Finite Mixture Distributions. New Yoric: John Wiley. An extensive list of references on mixture is provided In this wed organized exposition of Me subject Tsui, K. W., Matsumura, E. M and Tsui, K. L. (19X5~. Muldnomial- Dinchiet Bounds for Dollar Unit Sampling in Auditing. The Accounting Review, 60 :76-96. The multinomial bound developed by Fienberg et al. (1977) is difficult to compute. It is also subject to the definidon of We S set. ~ this article, the authors develop a Bayesian approach to ache problem. The model is described In Section Il.7 above. van Heerden, A. (1961~. Steekproeven als Midde] van Accountantscontrolex (Statistical Sampling as a Means of Auditing). Maar~blad voor Accountancy en Bedrijishuishou~kur~e, I} :453. This is He earliest known publication proposing the use of monetary unit sampling in auditing. The suggested evaluation technique involved regarding the monetary uruts within any audit as being either correct or in en on For example, if an audit unit win a recorded amount of 100 doBars had an audited amount of 80 doDars, the 80 doBars of the 100 doBars were regarded as correct and the last 20 dollars were regarded as incorrect. 83

2. Chronological Bibliography 1933 Carman, L. A. The Efficacy of Tests. The American Accountant. December: 360-366. 1949 Robbers, Herbert and PiDnan, E. I. G. Application of the method of mixtures to quadratic forms in normal vanates. Annals of Mathematical Statistics, 20: 552-560. 195S Aitchison, I. On the Distribution of a Positive Random Vanable Having a Discrete Probability Mass at He Origin. Journal of the American Statistical Association, 50: 901-908. 1961 van Heerden, A. Steekproeven als Middel van Accountantscontrolex (Statistical Sampling as a Means of Auditing). Maandblad voor Accountancy en Bedri~shuishou~kunde, I-1 :453. 1962 Cyert, R. M. and Davidson, H. fusion. Statistical Sampl~ngfor Accounting Ir,formation. Englewood Cliffs, NI: Prentice-HaU, hnc. 1963 Stnnger, K. W. Practical Aspects of Statistical Sampling in Auditing. Proceedings of the Business and Economic Stans~cs Section, 405411, Washington, D.C.: American Statistical Association. 1972 Intemal Revenue Service. Audit Assessments Based on Statistical Samples (Memorandum to Assistant Commissioner from Chief Counsel). Washington, D.C.: IRS. Meikle, G. R. Statistical Sampling in an Audit Context. Toronto: Canadian Institute of Chartered Accountants. 84

1973 Anderson, R. J. and Teitlebaum, A. D. Dollars t Sarnpl~ng. Canadian Chartered Accountant ( after 1973 this joumal became CA Magazine ), Apnl: 3~39. Kaplan, R. S. Stochastic Model for Auditing. Journal of Accounting Research, 11: 3846. Kaplan, R. S. Statistical Sampling in Auditing with Auxiliary [nfonnabon Estimators. Journal of Accounting Research, 11 :238-258. 1974 GooUfellow, I. L., Loebbecke, I.K. and Neter, J. Some Perspectives on CAV Sampling Plans. Part I, CA Magazine, October: 23-30; Part II, CA Magazine, November: 46-53. McRae, T. W. Statistical Sampling for Audit and Control. London: John Wiley. 197S Anderson, R. I. and Leslie, D. A. Discussion of Consideration in Choosing Statistical Sampling Procedures In Auditing. Journal of Accounting Research, 13 Supplement: 53-64. Internal Revenue Service. Audit Assessments Based on Statistical Samples - Supplemental Memorandum (March 6 Memorandum to Chief Counsel from Director, Refund Litigation Division & Acing Director, Tax Court Litigation Division). Washington, D. C.: IRS. Kaplan, R. Sample Size Computations for Dollar-Unit Sampling. Journal of Accounting Research, 13 Supplement: 126-133. Loebbecke, I. K. and Neter,]. Considerations in Choosing Statistical Sampling Procedures in Auditing, Journal of Accounting Research, 13 Supplement: 38-52. Neter, J., and L~oebbecke, I. Behavior of Major Statistical Estimators in Sampling Accounting Populations--An Empirical Study, New York: American Institute of Certified Public Accountants. 85

Teitlebaum, A. D., Leslie, D. A. and Anderson, R. I. An Analysis of Recent Commentary on DoBar-Un~t Sampling In Auditing, McGill L7niversity Working Paper, March. 1976 Smith, T. M. F. Statistical Sampling for Accountants. London: Accountancy Age Books. 1977 Barman, A. Wi~in-Item Vanation: A Stochastic Approach to Audit Uncenamty. The Accounting Review, 52 :4S0~64. Deakin, E.B. Discussants Response to Computing Upper Error Limits in DolBar Unit Sampling. Frontiers of Auditing Research, edited by B.E. Cushing and J.~. K~gstad. Austin: Bureau of Business Research, The University of Texas at Austin: 195-201. Felix, W. L. Ir. and Gr~mlund, R. A. Sampling Model for Audit Tests of Composite Accounts. Journal of Accounting Research, 15: 2342. Fienberg, S. E., Neter, I. and Leitch, R. A. Estimating the Total Overstatement Error in Accounting Populations. Journal of the American Statistical Association, 72: 295-302. Garstka, S. J. Computing Upper Error Limits In DoBar-Un~t Sampling. Frontiers of Auditing Research, edited by B. E. Cushing and I. L. Krogstad. Austin: Bureau of Business Research, The University of Texas at Austin, 163-82. Garstka. S. I. Models for Computing Upper Error Limits in Dollar-Unit Sampling. Journal ofAccouniingResearch, 15:179-192. Leslie, D. A. Discussant's Response to Computing Upper Error Limits in Dollar Unit Sampling. Frontiers calf Auditing Research, edited by B. E. Cushing and I. L. Krogstad. Austin: Bureau of Business Research, The University of Texas at Austin: ~X3-91. Neter, I. and Loebbecke, I.K. On the Behavior of Statistical Estimators when Sampling Accounting Populations, Journal of the American Statistical Association, 72: 501-507. 86

lg78 Burdick, R. K. and Reneau, J.H. The Impact of Different Ever Distributions on He Performance of Selected Sampling Estimators in Accounting Populations. Proceedings of Business and Economic Statistics Section, 779-78 1, Washington, D. C.: American Statistical Association Neter, J., Leitch, R. A. and Fienberg, S. E. Dollar Unit Sampling: Multinomial Bounds for Total Overstatement and Understatement Errors. The Accounting Review, 53: 77-93. Reneau, I. H. CAV Bounds In Dollar Unit Sampling: Some Simulation Results. The Accounting Review, 53: 669-80. Roberts, D. M. Statistical Auditing. New York: American Institute of Certified Public Accountants. 1979 Baker, R. L. and Copeland, R. M. Evaluation of the Stratified Regression Estimator for Auditing Accounting Populations. Journal of Accounting Research, 17: 606-17. Cox, D. R. and Snell, E. J. On Sampling and the Estimation of Rare Errors. Biometrika, 66 :124-132. Festige, M. O. Discussion of An Empirical Study of Error Characteristics In Audit Populations. Journal of Accounting Research, 17 Supplement: 103-la7. Garstka, S. I. Discussion of An Empirical Study of Error Characteristics in Audit Populations. Journal of Accounting Research, 17 Supplement: 103-113. Garstka, S. J. and Ohison, P.A. Ratio Estimation in Accounting Populations with Probabilities of Sample Selection Proportional to Size of Book Values, Journal of Accounang Research, -17: 23-59. Knight, P. Statistical Sampling in Auditing: an Auditor's View Point. The Statistician, 28 :253-266. 87 'I

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Duke, G. L., Never, I. and Leitch, R. A. Power Charactenstics of Test Statistics In He Auditing Environment: An Empirical Sway. Journal of Accounting Research, 20 :42-67. Felix, W. L., Ir., Leslie, D. A. and Neter, I. University of Georgia Center for Audit Research Monetary Unit Sampling Conference, March 24, 1981. Auditing: A Journal of Practice & Theory, -1: 92-103. Frost, P. A. and Tamura, H. Jackknifed Ratio Esi~mabon in Statistical Auditing. Journal of Accounting Research, 20: 103-120. Hylas, R. E. and Ashton, R. H. Audit Detection of Financial Statement Errors. The Accounting Review, 57: 751-765. Leitch, R. A., Neter,]., Plante, R. and Sinha, P. Modified Multinomial Bounds for Larger Numbers of Enors in Audits. The Accounting Review, S7 :384-400. 1983 American Institute of Certified Public Accountants (AICPA). Audit Sampling. New York: AICPA. Menzefncke, U. On Sampling Plan Selection with DoBar-Un~t Sampling. journal of Accounting Research, 2~1 :96-I OS. Moors, I. I. A. B ayes ' Estimation In Sampling for Auditing. The Statistician, 32: 281-288. Roberts, D. M., Shedd, M. D. and MacGuidwin, M. I. The Behavior of Selected Upper Bounds of Monetary Error Using PPS Sampling. Symposium in Auditing Research IV, The Center for Intemational Education and Research in Accounting, University of Illinois, Urbana- Champa~gn, Illinois. (Reviewed in Auditing: A Journal of Practice & Theory, 2 :112) 1984 Dwonn, L. and GnmIund, R. A. Dollar Unit Sampling for Accounts Receivable and Inventory. The Accounting Review, 59: 2 ~ 8-24 I . 89

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