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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Audit Sampling: An Overview and Application to Tests of Controls Chapter Eight

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Introduction Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling. Two technological advances have reduced the number of times auditors need to apply sampling techniques to gather audit evidence: 1 Development of well-controlled, automated accounting systems. 1 Development of well-controlled, automated accounting systems. 2 Advent of powerful PC audit software to download and examine client data 2 Advent of powerful PC audit software to download and examine client data

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Introduction However, technology will never eliminate the need for auditors to rely on sampling to some degree because: 1.Many control processes require human involvement. 2.Many testing procedures require the auditor to physically examine an asset. 3.In many cases auditors are required to obtain and examine evidence from third parties.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Definitions and Key Concepts On the following slides we will define: 1. Audit Sampling 2. Sampling Risk 3. Confidence Level 4. Tolerable and Expected Error On the following slides we will define: 1. Audit Sampling 2. Sampling Risk 3. Confidence Level 4. Tolerable and Expected Error

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Audit Sampling The application of audit procedures to less than 100 per cent of items within a population of audit relevance such that all sampling units have a chance of selection in order to provide the auditor with a reasonable basis on which to draw conclusions about the entire population.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Sampling Risk Sampling risk is the element of uncertainty that enters into the auditors conclusions anytime sampling is used. There are two types of sampling risk. Risk of incorrect rejection (Type I) – in a test of internal controls, it is the risk that the sample supports a conclusion that the control is not operating effectively when, in fact, it is operating effectively. In substantive testing, it is the risk that the sample indicates that the recorded balance is materially misstated when, in fact, it is not. Risk of incorrect acceptance (Type II) – in a test of internal controls, it is the risk that the sample supports a conclusion that the control is operating effectively when, in fact, it is not operating effectively. In substantive testing, it is the risk that the sample supports the recorded balance when it is, in fact, materially misstated.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Sampling Risk Three Important Factors in Determining Sample Size The desired level of assurance in the results (or confidence level), 2. Acceptable defect rate (or tolerable error), and 3. The historical defect rate (or expected error) The desired level of assurance in the results (or confidence level), 2. Acceptable defect rate (or tolerable error), and 3. The historical defect rate (or expected error).

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Confidence Level Confidence level is the complement of sampling risk. The auditor may set sampling risk for a particular sampling application at 5 per cent, which results in a confidence level of 95 per cent.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Tolerable and Expected Error Once the desired confidence level is established, the sample size is determine largely by how much the tolerable error exceeds expected error. Precision, at the planning stage of audit sampling, is the difference between the expected and tolerable deviation rates. The term allowance for sampling risk is used to reflect the concept of precision in a sampling application.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Audit Evidence – To Sample or Not?

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Audit Evidence – To Sample or Not? Inspection of tangible assets. Auditors typically attend the clients year-end inventory count. When there are a large number of items in inventory, the auditor will select a sample to physically inspect and count. Inspection of records or documents. Certain controls may require the matching of documents. The activity may take place many times a day. The auditor may gather evidence on the effectiveness of the control by testing a sample of the document packages. Inspection of tangible assets. Auditors typically attend the clients year-end inventory count. When there are a large number of items in inventory, the auditor will select a sample to physically inspect and count. Inspection of records or documents. Certain controls may require the matching of documents. The activity may take place many times a day. The auditor may gather evidence on the effectiveness of the control by testing a sample of the document packages.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Audit Evidence – To Sample or Not? Reperformance. The auditor may reperform a sample of the tests performed by the client. Confirmation. Rather than confirm all customer account receivable balances, the auditor may select a sample of customers. Reperformance. The auditor may reperform a sample of the tests performed by the client. Confirmation. Rather than confirm all customer account receivable balances, the auditor may select a sample of customers.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Testing All Items with a Particular Characteristic When an account or class of transactions is made up of a few large items, the auditor may examine all the items in the account or class of transaction. When a small number of large transactions make up a relatively large per cent of an account or class of transactions, auditors will typically test all the transactions greater than a particular monetary amount.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Testing Only One or a Few Items Highly automated information systems process transactions consistently unless the system or programs are changed. The auditor may test the general controls over the system and any program changes, but test only a few transactions processed by the IT system.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Types of Audit Sampling Auditing standards recognize and permit both statistical and non-statistical methods of audit sampling. In non-statistical sampling, the auditor does not use statistical techniques to determine sample size, select the sample items, or measure sampling risk. Statistical sampling, uses the laws of probability to compute sample size and evaluate the sample results. The auditor is able to use the most efficient sample size and quantify sampling risk.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Types of Audit Sampling Advantages of statistical sampling 1.Design an efficient sample. 2.Measure the sufficiency of evidence obtained. 3.Quantify sampling risk. Advantages of statistical sampling 1.Design an efficient sample. 2.Measure the sufficiency of evidence obtained. 3.Quantify sampling risk. Disadvantages of statistical sampling 1.Training auditors in proper use. 2.Time to design and conduct sampling application. 3.Lack of consistent application across audit engagement teams. Disadvantages of statistical sampling 1.Training auditors in proper use. 2.Time to design and conduct sampling application. 3.Lack of consistent application across audit engagement teams.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Statistical Sampling Techniques 1. Attribute Sampling. 2. Monetary-Unit Sampling. 3. Classical Variables Sampling.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Used to estimate the proportion of a population that possess a specified characteristic. The most common use of attribute sampling is for tests of controls. Our clients controls require that sales are authorized for credit approval. Yes, I know. We are planning a test of that control using attribute sampling.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Monetary-Unit Sampling Monetary-unit sampling uses attribute sampling theory to estimate the monetary (e.g. in ) amount of misstatement for a class of transactions or an account balance. This technique is used extensively because it has a number of advantages over classical variables sampling

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Classical Variables Sampling Auditors sometimes use variables sampling to estimate the monetary value of a class of transactions or account balance. It is more frequently used to determine whether an account is materially misstated.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Applied to Tests of Controls In conducting a statistical sample for a test of controls, auditing standards require the auditor to properly plan, perform, and evaluate the sampling application and to adequately document each phase of the sampling application. PlanPerformEvaluateDocument

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning The objective of attribute sampling when used for tests of controls is to evaluate the operating effectiveness of the internal control.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning All of the items that constitute the class of transactions make up the sampling population.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning Each sampling unit makes up one item in the population. The sampling unit should be defined in relation to the specific control being tested.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning A deviation is a departure from adequate performance of the internal control.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning The confidence level is the desired level of assurance that the sample results will support a conclusion that the control is functioning effectively. Generally, when the auditor has decided to rely on controls, the confidence level is set at 90% or 95%. This means the auditor is willing to accept a 10% or 5% risk of accepting the control as effective when it is not.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning The tolerable deviation rate is the maximum deviation rate from a prescribed control that the auditor is willing to accept and still consider the control effective. Example Suggested Tolerable Deviation Rates:

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Planning The expected population deviation rate is the rate the auditor expects to exist in the population. The larger the expected population deviation rate, the larger the sample size must be, all else equal. EXAMPLE: Assume a desired confidence level of 95%, and a large population, the effect of the expected population deviation rate on sample size is shown right:

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Population Size: Attributes Sampling Population size is not an important factor in determining sample size for attributes sampling. The population size has little or no effect on the sample size, unless the population is relatively small, say less than 500 items.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance Every item in the population has the same probability of being selected as every other sampling unit in the population.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance The auditor determines the sampling interval by dividing the population by the sample size. A starting number is selected in the first interval and every n th item is selected.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance For example, assume a sales invoice should not be prepared unless there is a related shipping document. If the shipping document is present, there is evidence the control is working properly. If the shipping document is not present a control deviation exists.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance Unless the auditor finds something unusual about either of these items, they should be replaced with a new sample item.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance If the auditor is unable to examine a document or to use an alternative procedure to test the control, the sample item is a deviation for purposes of evaluating the sample results.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Performance If a large number of deviations are detected early in the tests of controls, the auditor should consider stopping the test, as soon as it is clear that the results of the test will not support the planned assessed level of control risk.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Evaluation After completing the audit procedures, the auditor summarizes the deviations for each control tested and evaluates the results. For example, if the auditor discovered two deviations in a sample of 50, the deviation rate in the sample would be 4% (2 ÷ 50). The upper deviation rate is the sum of the sample deviation rate and an appropriate allowance for sampling risk.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Evaluation The auditor compares the tolerable deviation rate to the computed upper deviation rate.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Example The auditor has decided to test a control at Calabro Wireless Services. The test is to determine the sales and service contracts are properly authorized for credit approval. A deviation in this test is defined as the failure of the credit department personnel to follow proper credit approval procedures for new and existing customers. Here is information relating to the test:

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Example Part of the table used to determine sample size when the auditor specifies a 95% desired confidence level. If there are 125,000 items in the population numbered from 1 to 125,000, the auditor can use Excel to generate random selections from the population for testing.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Example The auditor examines each selected contract for credit approval and determines the following: Lets see how we get the computed upper deviation rate.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Example Part of the table used to determine the computed upper deviation rate at 95% desired confidence level:

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Attribute Sampling Example Tolerable Deviation Rate (6%) Computed Upper Deviation Rate (8.2%) < Auditors Decision: Does not support reliance on the control. Auditors Decision: Does not support reliance on the control.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Non-Statistical Sampling for Tests of Control Determining the Sample Size An auditing firm may establish a non-statistical sampling policy like the one below: Such a policy will promote consistency in sampling applications.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Non-Statistical Sampling for Tests of Control Selecting the Sample Items Non-statistical sampling allows the use of random or systematic selection, but also permits the use of other methods such as haphazard sampling.. When haphazard sample selection is used, sampling units are selected without any bias, that is to say, without a special reason for including or omitting the item in the sample.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Non-Statistical Sampling for Tests of Control Calculating the Upper Deviation Rate With a non-statistical sample, the auditor can calculate the sample deviation rate, but cannot mathematically quantify the computed upper deviation rate and sampling risk associated with the test.

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 Considering the Effect of Population Size The sample size tables in the chapter assume a large population. Sample size can be adjusted using the finite correction factor in the Advanced Module or by using the table below for very small populations: Control Frequency and Population SizeSample Size Quarterly (4) 2 Monthly (12) 2-4 Semimonthly (24) 3-8 Weekly (52) 5-9

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McGraw-Hill/Irwin © The McGraw-Hill Companies 2010 End of Chapter 8

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