（（英文参考文献及译文）二〇一六年六月本科毕业论文 题 目：STATISTICAL SAMPLING METHOD, USED INTHE AUDIT学生姓名：王雪琴学 院：管理学院系 别：会计系专 业：财务管理班 级：财管12-2班 学校代码： 10128 学 号： 201210707016Statistics and AuditRomanian Statistical Review nr. 5 / 2010STATISTICAL SAMPLING METHOD, USED IN THE AUDIT - views, recommendations, fi ndingsPhD Candidate Gabriela-Felicia UNGUREANUAbstractThe rapid increase in the size of U.S. companies from the earlytwentieth century created the need for audit procedures based on the selectionof a part of the total population audited to obtain reliable audit evidence, tocharacterize the entire population consists of account balances or classes oftransactions. Sampling is not used only in audit – is used in sampling surveys,market analysis and medical research in which someone wants to reach aconclusion about a large number of data by examining only a part of thesedata. The difference is the “population” from which the sample is selected, iethat set of data which is intended to draw a conclusion. Audit sampling appliesonly to certain types of audit procedures.Key words: sampling, sample risk, population, sampling unit, tests ofcontrols, substantive procedures.Statistical samplingCommittee statistical sampling of American Institute of CertifiedPublic Accountants of (AICPA) issued in 1962 a special report, titled“Statistical sampling and independent auditors’ which allowed the use ofstatistical sampling method, in accordance with Generally Accepted AuditingStandards (GAAS). During 1962-1974, the AICPA published a series of paperson statistical sampling, “Auditor’s Approach to Statistical Sampling”, foruse in continuing professional education of accountants. During 1962-1974,the AICPA published a series of papers on statistical sampling, “Auditor’sApproach to Statistical Sampling”, for use in continuing professional educationof accountants. In 1981, AICPA issued the professional standard, “AuditSampling”, which provides general guidelines for both sampling methods,statistical and non-statistical.Earlier audits included checks of all transactions in the period coveredby the audited financial statements. At that time, the literature has not givenparticular attention to this subject. Only in 1971, an audit procedures programprinted in the “Federal Reserve Bulletin (Federal Bulletin Stocks)” includedseveral references to sampling such as selecting the “few items” of inventory.Statistics and Audit The program was developed by a special committee, which later became the AICPA, that of Certified Public Accountants American Institute.In the first decades of last century, the auditors often applied sampling, but sample size was not in related to the efficiency of internal control of the entity. In 1955, American Institute of Accountants has published a study case of extending the audit sampling, summarizing audit program developed by certified public accountants, to show why sampling is necessary to extend the audit. The study was important because is one of the leading journal on sampling which recognize a relationship of dependency between detail and reliability testing of internal control.In 1964, the AICPA’s Auditing Standards Board has issued a report entitled “The relationship between statistical sampling and Generally Accepted Auditing Standards (GAAS)” which illustrated the relationship between the accuracy and reliability in sampling and provisions of GAAS.In 1978, the AICPA published the work of Donald M. Roberts,“Statistical Auditing”which explains the underlying theory of statistical sampling in auditing.In 1981, AICPA issued the professional standard, named “Audit Sampling”, which provides guidelines for both sampling methods, statistical and non-statistical.An auditor does not rely solely on the results of a single procedure to reach a conclusion on an account balance, class of transactions or operational effectiveness of the controls. Rather, the audit findings are based on combined evidence from several sources, as a consequence of a number of different audit procedures. When an auditor selects a sample of a population, his objective is to obtain a representative sample, ie sample whose characteristics are identical with the population’s characteristics. This means that selected items are identical with those remaining outside the sample.In practice, auditors do not know for sure if a sample is representative, even after completion the test, but they “may increase the probability that a sample is representative by accuracy of activities made related to design, sample selection and evaluation” [1]. Lack of specificity of the sample results may be given by observation errors and sampling errors. Risks to produce these errors can be controlled.Observation error (risk of observation) appears when the audit test did not identify existing deviations in the sample or using an inadequate audit technique or by negligence of the auditor.Sampling error (sampling risk) is an inherent characteristic of the survey, which results from the fact that they tested only a fraction of the total population. Sampling error occurs due to the fact that it is possible for Revista Română de Statistică nr. 5 / 2010Statistics and Auditthe auditor to reach a conclusion, based on a sample that is different from the conclusion which would be reached if the entire population would have been subject to audit procedures identical. Sampling risk can be reduced by adjusting the sample size, depending on the size and population characteristics and using an appropriate method of selection. Increasing sample size will reduce the risk of sampling; a sample of the all population will present a null risk of sampling.Audit Sampling is a method of testing for gather sufficient and appropriate audit evidence, for the purposes of audit. The auditor may decide to apply audit sampling on an account balance or class of transactions. Sampling audit includes audit procedures to less than 100% of the items within an account balance or class of transactions, so all the sample able to be selected. Auditor is required to determine appropriate ways of selecting items for testing. Audit sampling can be used as a statistical approach and a non- statistical.Statistical sampling is a method by which the sample is made so that each unit consists of the total population has an equal probability of being included in the sample, method of sample selection is random, allowed to assess the results based on probability theory and risk quantification of sampling. Choosing the appropriate population make that auditor’ findings can be extended to the entire population.Non-statistical sampling is a method of sampling, when the auditor uses professional judgment to select elements of a sample. Since the purpose of sampling is to draw conclusions about the entire population, the auditor should select a representative sample by choosing sample units which have characteristics typical of that population. Results will not extrapolate the entire population as the sample selected is representative.Audit tests can be applied on the all elements of the population, where is a small population or on an unrepresentative sample, where the auditor knows the particularities of the population to be tested and is able to identify a small number of items of interest to audit. If the sample has not similar characteristics for the elements of the entire population, the errors found in the tested sample can not extrapolate.Decision of statistical or non-statistical approach depends on the auditor’s professional judgment which seeking sufficient appropriate audits evidence on which to completion its findings about the audit opinion.As a statistical sampling method refer to the random selection that any possible combination of elements of the community is equally likely to enter the sample. Simple random sampling is used when stratification was not to audit. Using random selection involves using random numbers generated byRomanian Statistical Review nr. 5 / 2010Statistics and Audit a computer. After selecting a random starting point, the auditor found the first random number that falls within the test document numbers. Only when the approach has the characteristics of statistical sampling, statistical assessments of risk are valid sampling.In another variant of the sampling probability, namely the systematic selection (also called random mechanical) elements naturally succeed in office space or time; the auditor has a preliminary listing of the population and made the decision on sample size. “The auditor calculated a counting step, and selects the sample element method based on step size. Step counting is determined by dividing the volume of the community to sample the number of units desired. Advantages of systematic screening are its usability. In most cases, a systematic sample can be extracted quickly and method automatically arranges numbers in successive series.”[2].Selection by probability proportional to size - is a method which emphasizes those population units’recorded higher values. The sample is constituted so that the probability of selecting any given element of the population is equal to the recorded value of the item;Stratifi ed selection - is a method of emphasis of units with higher values and is registered in the stratification of the population in subpopulations. Stratification provides a complete picture of the auditor, when population (data table to be analyzed) is not homogeneous. In this case, the auditor stratifies a population by dividing them into distinct subpopulations, which have common characteristics, pre-defined. “The objective of stratification is to reduce the variability of elements in each layer and therefore allow a reduction in sample size without a proportionate increase in the risk of sampling.” [3] If population stratification is done properly, the amount of sample size to come layers will be less than the sample size that would be obtained at the same level of risk given sample with a sample extracted from the entire population. Audit results applied to a layer can be designed only on items that are part of that layer.I appreciated as useful some views on non-statistical sampling methods, which implies that guided the selection of the sample selecting each element according to certain criteria determined by the auditor. The method is subjective; because the auditor selects intentionally items containing set features him.The selection of the series is done by selecting multiple elements series (successive). Using sampling the series is recommended only if a reasonable number of sets used. Using just a few series there is a risk that the sample is not representative. This type of sampling can be used in addition to other samples, where there is a high probability of occurrence of errors. At the arbitrary selection, no items are selected preferably from the auditor, Revista Română de Statistică nr. 5 / 2010Statistics and Auditthat regardless of size or source or characteristics. Is not the recommended method, because is not objective.That sampling is based on the auditor’s professional judgment, which may decide which items can be part or not sampled. Because is not a statistical method, it can not calculate the standard error. Although the sample structure can be constructed to reproduce the population, there is no guarantee that the sample is representative. If omitted a feature that would be relevant in a particular situation, the sample is not representative.Sampling applies when the auditor plans to make conclusions about population, based on a selection. The auditor considers the audit program and determines audit procedures which may apply random research. Sampling is used by auditors an internal control systems testing, and substantive testing of operations. The general objectives of tests of control system and operations substantive tests are to verify the application of pre-defined control procedures, and to determine whether operations contain material errors.Control tests are intended to provide evidence of operational efficiency and controls design or operation of a control system to prevent or detect material misstatements in financial statements. Control tests are necessary if the auditor plans to assess control risk for assertions of management.Controls are generally expected to be similarly applied to all transactions covered by the records, regardless of transaction value. Therefore, if the auditor uses sampling, it is not advisable to select only high value transactions. Samples must be chosen so as to be representative population sample.An auditor must be aware that an entity may change a special control during the course of the audit. If the control is replaced by another, which is designed to achieve the same specific objective, the auditor must decide whether to design a sample of all transactions made during or just a sample of transactions controlled again. Appropriate decision depends on the overall objective of the audit test.Verification of internal control system of an entity is intended to provide guidance on the identification of relevant controls and design evaluation tests of controls.Other tests:In testing internal control system and testing operations, audit sample is used to estimate the proportion of elements of a population containing a characteristic or attribute analysis. This proportion is called the frequency of occurrence or percentage of deviation and is equal to the ratio of elements containing attribute specific and total number of population elements. WeightRomanian Statistical Review nr. 5 / 2010Statistics and Audit deviations in a sample are determined to calculate an estimate of the proportion of the total population deviations.Risk associated with sampling - refers to a sample selection which can not be representative of the population tested. In other words, the sample itself may contain material errors or deviations from the line. However, issuing a conclusion based on a sample may be different from the conclusion which would be reached if the entire population would be subject to audit.Types of risk associated with sampling:Controls are more effective than they actually are or that there are not significant errors when they exist - which means an inappropriate audit opinion. Controls are less effective than they actually are that there are significant errors when in fact they are not - this calls for additional activities to establish that initial conclusions were incorrect.Attributes testing - the auditor should be defining the characteristics to test and conditions for misconduct. Attributes testing will make when required objective statistical projections on various characteristics of the population. The auditor may decide to select items from a population based on its knowledge about the entity and its environment control based on risk analysis and the specific characteristics of the population to be tested.Population is the mass of data on which the auditor wishes to generalize the findings obtained on a sample. Population will be defined compliance audit objectives and will be complete and consistent, because results of the sample can be designed only for the population from which the sample was selected.Sampling unit - a unit of sampling may be, for example, an invoice, an entry or a line item. Each sample unit is an element of the population. The auditor will define the sampling unit based on its compliance with the objectives of audit tests.Sample size - to determine the sample size should be considered whether sampling risk is reduced to an acceptable minimum level. Sample size is affected by the risk associated with sampling that the auditor is willing to accept it. The risk that the auditor is willing to accept lower, the sample will be higher.Error - for detailed testing, the auditor should project monetary errors found in the sample population and should take into account the projected error on the specific objective of the audit and other audit areas. The auditor projects the total error on the population to get a broad perspective on the size of the error and comparing it with tolerable error.For detailed testing, tolerable error is tolerable and misrepresentations Revista Română de Statistică nr. 5 / 2010Statistics and Auditwill be a value less than or equal to materiality used by the auditor for the individual classes of transactions or balances audited. If a class of transactions or account balances has been divided into layers error is designed separately for each layer. Design errors and inconsistent errors for each stratum are then combined when considering the possible effect on the total classes of transactions and account balances.Evaluation of sample results - the auditor should evaluate the sample results to determine whether assessing relevant characteristics of the population is confirmed or needs to be revised.When testing controls, an unexpectedly high rate of sample error may lead to an increase in the risk assessment of significant misrepresentation unless it obtained additional audit evidence to support the initial assessment. For control tests, an error is a deviation from the performance of control procedures prescribed. The auditor should obtain evidence about the nature and extent of any significant changes in internal control system, including the staff establishment.If significant changes occur, the auditor should review the understanding of internal control environment and consider testing the controls changed. Alternatively, the auditor may consider performing substantive analytical procedures or tests of details covering the audit period.In some cases, the auditor might not need to wait until the end audit to form a conclusion about the effectiveness of operational control, to support the control risk assessment. In this case, the auditor might decide to modify the planned substantive tests accordingly.If testing details, an unexpectedly large amount of error in a sample may cause the auditor to believe that a class of transactions or account balances is given significantly wrong in the absence of additional audit evidence to show that there are not material misrepresentations.When the best estimate of error is very close to the tolerable error, the auditor recognizes the risk that another sample have different best estimate that could exceed the tolerable error.ConclusionsFollowing analysis of sampling methods conclude that all methods have advantages and disadvantages. But the auditor is important in choosing the sampling method is based on professional judgment and take into account the cost / benefit ratio. Thus, if a sampling method proves to be costly auditor should seek the most efficient method in view of the main and specific objectives of the audit.Romanian Statistical Review nr. 5 / 2010Statistics and Audit The auditor should evaluate the sample results to determine whether the preliminary assessment of relevant characteristics of the population must be confirmed or revised. If the evaluation sample results indicate that the relevant characteristics of the population needs assessment review, the auditor may: require management to investigate identified errors and likelihood of future errors and make necessary adjustments to change the nature, timing and extent of further procedures to take into account the effect on the audit report.Selective bibliography:[1] Law no. 672/2002 updated, on public internal audit[2] Arens, A şi Loebbecke J - Controve …Audit– An integrate approach”, 8th edition, Arc Publishing House[3] ISA 530 - Financial Audit 2008 - International Standards on Auditing, IRECSON Publishing House, 2009- Dictionary of macroeconomics, Ed C.H. Beck, Bucharest, 2008Revista Română de Statistică nr. 5 / 2010Statistics and Audit摘要美国公司的规模迅速增加，从第二十世纪初创造了必要的审计程序，根据选定的部分总人口的审计，以获得可靠的审计证据，以描述整个人口组成的帐户余额或类别的交易。
