Chapter 15
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Audit Sampling for Tests of Controls and
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Substantive Tests of Transactions
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15-1
Sampling risk is the risk
... [Show More] that the auditor reaches the wrong conclusion because a sample is not representative of the population. Sampling risk is an inherent part of sampling because the auditor is not testing the entire population. To reduce sampling risk, the auditor could increase sample size or use a sampling method that increases the likelihood of having a representative sample. Nonsampling risk is the risk that an auditor reaches the wrong conclusion for any reason other than sampling risk. For example, the auditor may perform procedures incorrectly or fail to correctly interpret the audit evidence. To reduce nonsampling risk, the auditor can follow auditing standards related to careful design of audit procedures, and proper supervision and review of audit work performed.
15-2
For both statistical and nonstatistical methods, the three main phases of audit sampling are:
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1. Plan the sample
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2. Select the sample and perform the tests
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3. Evaluate the results
15-3
In probabilistic sample selection, the auditor randomly selects items from a population such that each item has a known probability of being included in the sample. Three examples of probabilistic sample methods include simple random sample selection, systematic sample selection, and probability proportional to size sample selection. In nonprobabilistic sample selection methods, such as haphazard sample selection and block sample selection, the auditor uses nonprobabilistic methods that approximate a random sampling approach.
15-4
A block sample is the selection of several items in sequence. Once the first item in the block is selected, the remainder of the block is chosen automatically. Thus, to select 5 blocks of 20 sales invoices, one would select one invoice and the block would be that invoice plus the next 19 entries. This procedure would be repeated 4 other times.
15-5
In replacement sampling, an element in the population can be included in the sample more than once if the random number corresponding to that element is selected more than once. In nonreplacement sampling, an element can be included only once. If the random number corresponding to an element is selected more than once, it is simply treated as a discard the second time. Although both selection approaches are consistent with sound statistical theory, auditors rarely use replacement sampling; it seems more intuitively satisfying to auditors to include an item only once.
15-6
A simple random sample is one in which every possible combination of elements in the population has an equal chance of selection. Two methods of simple random selection are use of a random number table and use of the computer to generate random numbers. Auditors most often use the computer to generate random numbers because it saves time, reduces the likelihood of error, and provides automatic documentation of the sample selected.
15-7
In systematic sampling, the auditor calculates an interval and then methodically selects the items for the sample based on the size of the interval. The interval is set by dividing the population size by the number of sample items desired.
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To select 40 numbers from a population of 2,800, the auditor divides 40 into 2,800 and gets an interval of 70. He or she then selects a random number between 0 and 69. Assume the auditor chooses 17. The first item is the number 17. The next is 87, then 157, 227, and so on.
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The advantage of systematic sampling is its ease of use. In most populations a systematic sample can be drawn quickly, the approach automatically puts the numbers in sequential order, and documentation is easy.
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A major problem with the use of systematic sampling is the possibility of bias. Because of the way systematic samples are selected, once the first item in the sample is selected, other items are chosen automatically. This causes no problems if the characteristics of interest, such as control deviations, are distributed randomly throughout the population; however, in many cases they are not. If all items of a certain type are processed at certain times of the month or with the use of certain document numbers, a systematically drawn sample has a higher likelihood of failing to obtain a representative sample. This shortcoming is sufficiently serious that some CPA firms prohibit the use of systematic sampling.
15-8
Random (probabilistic) selection is a part of statistical sampling, but it is not, by itself, statistical measurement. To have statistical measurement, it is necessary to mathematically generalize from the sample to the population.
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Probabilistic selection must be used if the sample is to be evaluated statistically, although it is also acceptable to use probabilistic selection with a nonstatistical evaluation. If nonprobabilistic selection is used, nonstatistical evaluation must be used.
15-9
The purpose of using nonstatistical sampling for tests of controls and substantive tests of transactions is to estimate the proportion of items in a population containing a characteristic or attribute of interest. The auditor is ordinarily interested in determining internal control deviations or monetary misstatements for tests of controls and substantive tests of transactions.
15-10
An attribute is the definition of the characteristic being tested and the exception conditions whenever audit sampling is used. The attributes of interest are determined directly from the audit program. In a test of control, that attribute is evidence of the operation of the control consistent with the design. In a substantive test, the attribute is the absence of monetary misstatement.
15-11
An attribute is the characteristic being tested for in a population. An exception occurs when the attribute being tested for is absent. The exception for the audit procedure, the duplicate sales invoice has been initialed indicating the performance of internal verification, is the lack of initials on duplicate sales invoices.
15-12
The terms below are defined as follows:
15-13
The sampling unit is the population item from which the auditor selects sample items. The major consideration in defining the sampling unit is making it consistent with the objectives of the audit tests. Thus, the definition of the population and the planned audit procedures usually dictate the appropriate sampling unit.
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The sampling unit for verifying the occurrence of recorded sales would be the entries in the sales journal since this is the record the auditor wishes to validate. The sampling unit for testing the possibility of omitted sales is the shipping document from which sales are recorded, because the failure to bill a shipment is the exception condition of interest to the auditor.
15-14
The tolerable exception rate (TER) represents the exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and/or the amount of monetary misstatements in the transactions established during planning. TER is determined by choice of the auditor on the basis of his or her professional judgment.
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The computed upper exception rate (CUER) is the highest estimated exception rate in the population, at a given ARO. For nonstatistical sampling, CUER is determined by adding an estimate of sampling risk to the SER (sample exception rate). For statistical sampling, CUER is determined by using a statistical sampling table after the auditor has completed the audit testing and therefore knows the number of exceptions in the sample.
15-15
Tolerable exception rate (TER) is the result of an auditor's judgment. The suitable TER is a question of materiality and is therefore affected by both the definition and the importance of the attribute in the audit plan. It represents the exception rate that the auditor will permit in the population and still be willing to conclude that the control is operating effectively and/or the amount of monetary misstatements in the transactions established during planning is acceptable.
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The sample size for a TER of 7% would be smaller than that for a TER of 4%, all other factors being equal.
15-16
The appropriate ARO is a decision the auditor must make using professional judgment. The degree to which the auditor wishes to reduce assessed control risk below the maximum is the major factor determining the auditor's ARO.
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The auditor will choose a smaller sample size for an ARO of 10% than would be used if the risk were 5%, all other factors being equal.
15-17
The relationship between sample size and the four factors determining sample size are as follows:
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a. As the ARO increases, the required sample size decreases.
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b. As the population size increases, the required sample size is normally unchanged, or may increase slightly.
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c. As the TER increases, the sample size decreases.
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d. As the EPER increases, the required sample size increases.
15-18
When the CUER exceeds the TER, the auditor may do one or more of the following:
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1. Revise the TER or the ARO. This alternative should be followed only when the auditor has concluded that the original specifications were too conservative, and when he or she is willing to accept the risk associated with the higher specifications.
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2. Expand the sample size. This alternative should be followed when the auditor expects the additional benefits to exceed the additional costs. That is, the auditor believes that the sample tested was not representative of the population and that exceptions are not expected in the expanded sample.
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3. Revise assessed control risk upward. This is likely to increase substantive procedures. Revising assessed control risk may be done if 1 or 2 is not practical and additional substantive procedures are possible.
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4. Write a letter to management. This action should be done in conjunction with each of the three alternatives above. Management should always be informed when its internal controls are not operating effectively. If a deficiency in internal control is considered to be a significant deficiency in the design or operation of internal control, professional standards require the auditor to communicate the significant deficiency to the audit committee or its equivalent in writing. If the client is an accelerated filer publicly traded company, the auditor must evaluate the deficiency to determine the impact on the auditor's report on internal control over financial reporting. If the deficiency is deemed to be a material weakness, the auditor's report on internal control would contain an adverse opinion.
15-19
Attributes sampling is a statistical, probabilistic sampling method that results in an estimate of the proportion of items in a population containing a characteristic or attribute of interest. Attributes sampling is commonly used for tests of controls and substantive tests of transactions.
15-20
In this situation, the sample exception rate (SER) is 4%, the sample size is 100 and the ARO is 10%. From the 10% ARO table (Table 15-9) then, the CUER is 7.9%. This means that the auditor can state with a 10% risk of being wrong that the true population exception rate does not exceed 7.9%.
15-21
The decisions the auditor must make in using attributes sampling are:
What are the objectives of the audit test?
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Does audit sampling apply?
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What attributes are to be tested and what exception conditions are identified?
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What is the population?
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What is the sampling unit?
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15-21 (continued)
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What should the TER be?
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What should the ARO be?
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What is the EPER?
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What generalizations can be made from the sample to the population?
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What are the causes of the individual exceptions?
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Is the population acceptable?
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In making the above decisions, the following should be considered:
The individual situation.
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Time and budget constraints.
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The availability of additional substantive procedures.
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The professional judgment of the auditor.
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15-28
(see text Web site for Excel solution for part c.- Filename P1528.xls)
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a. To test whether shipments have been billed, a sample of warehouse removal slips should be selected and examined to see if they have the proper sales invoice attached. The sampling unit will therefore be the warehouse removal slip.
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b. Attributes sampling method: Assuming the auditor is willing to accept a TER of 4% at a 5% ARO, expecting no exceptions in the sample, the appropriate sample size would be 74, determined from Table 15-8.
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Nonstatistical sampling method: There is no one right answer to this question because the sample size is determined using professional judgment. Due to the relatively small TER (4%), the sample size should not be small. It will most likely be similar in size to the sample chosen by the statistical method.
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c. Systematic sample selection:
22946
= Population size of warehouse removal slips (34687-11741).
74
= Sample size using statistical sampling (students' answers will vary if nonstatistical sampling was used in part b.)
310
= Interval (22946/74) if statistical sampling is used (students' answers will vary if nonstatistical sampling was used in part b.).
11878
= Random starting point.
Select warehouse removal slip 11878 and every 310th warehouse removal slip after (12188, 12498, etc.)
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Computer generation of random numbers using Excel (P1528.xls):
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=RANDBETWEEN(11741,34687)
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The command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the formula (math & trig) tab. It may be necessary to add the analysis tool pack to access the RANDBETWEEN function. Once the formula is entered, it can be copied down to select additional random numbers.
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d. Other audit procedures that could be performed are:
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1. Test extensions on attached sales invoices for clerical accuracy. (Accuracy)
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2. Test time delay between warehouse removal slip date and billing date for timeliness of billing. (Timing)
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3. Trace entries into perpetual inventory records to determine that inventory is properly relieved for shipments. (Posting and summarization)
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e. The test performed in part c. cannot be used to test for occurrence of sales because the auditor already knows that inventory was shipped for these sales. To test for occurrence of sales, the sales invoice entry in the sales journal is the sampling unit. Since the sales invoice numbers are not identical to the warehouse removal slips it would be improper to use the same sample.
15-31
a.
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Students' answers as to whether the calculated allowance for sampling risk is sufficient will vary, depending on their judgment. However, they should recognize the effect that lower sample sizes have on the allowance for sampling risk in situations 2, 5, and 8.
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b. Using the attributes sampling table in Table 15-9, the CUERs for columns 1-8 are:
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4.6%
2.
6.2% [Show Less]